Preliminary Design Considerations for Access and Operations in Earth-Moon L1/L2 Orbits

NASA Technical Reports Server (NTRS)

Folta, David C.; Pavlak, Thomas A.; Haapala, Amanda F.; Howell, Kathleen C.

2013-01-01

Within the context of manned spaceflight activities, Earth-Moon libration point orbits could support lunar surface operations and serve as staging areas for future missions to near-Earth asteroids and Mars. This investigation examines preliminary design considerations including Earth-Moon L1/L2 libration point orbit selection, transfers, and stationkeeping costs associated with maintaining a spacecraft in the vicinity of L1 or L2 for a specified duration. Existing tools in multi-body trajectory design, dynamical systems theory, and orbit maintenance are leveraged in this analysis to explore end-to-end concepts for manned missions to Earth-Moon libration points.

Use of libration-point orbits for space observatories

NASA Technical Reports Server (NTRS)

Farquhar, Robert W.; Dunham, David W.

1990-01-01

The sun-earth libration points, L1 and L2, are located 1.5 million kilometers from the earth toward and away from the sun. Halo orbits about these points have significant advantages for space observatories in terms of viewing geometry, thermal and radiation environment, and delta-V expediture.

The research of the coupled orbital-attitude controlled motion of celestial body in the neighborhood of the collinear libration point L1

NASA Astrophysics Data System (ADS)

Shmyrov, A.; Shmyrov, V.; Shymanchuk, D.

2017-10-01

This article considers the motion of a celestial body within the restricted three-body problem of the Sun-Earth system. The equations of controlled coupled attitude-orbit motion in the neighborhood of collinear libration point L1 are investigated. The translational orbital motion of a celestial body is described using Hill's equations of circular restricted three-body problem of the Sun-Earth system. Rotational orbital motion is described using Euler's dynamic equations and quaternion kinematic equation. We investigate the problem of stability of celestial body rotational orbital motion in relative equilibrium positions and stabilization of celestial body rotational orbital motion with proposed control laws in the neighborhood of collinear libration point L1. To study stabilization problem, Lyapunov function is constructed in the form of the sum of the kinetic energy and special "kinematic function" of the Rodriguez-Hamiltonian parameters. Numerical modeling of the controlled rotational motion of a celestial body at libration point L1 is carried out. The numerical characteristics of the control parameters and rotational motion are given.

Access to Mars from Earth-Moon Libration Point Orbits:. [Manifold and Direct Options

NASA Technical Reports Server (NTRS)

Kakoi, Masaki; Howell, Kathleen C.; Folta, David

2014-01-01

This investigation is focused specifically on transfers from Earth-Moon L(sub 1)/L(sub 2) libration point orbits to Mars. Initially, the analysis is based in the circular restricted three-body problem to utilize the framework of the invariant manifolds. Various departure scenarios are compared, including arcs that leverage manifolds associated with the Sun-Earth L(sub 2) orbits as well as non-manifold trajectories. For the manifold options, ballistic transfers from Earth-Moon L(sub 2) libration point orbits to Sun-Earth L(sub 1)/L(sub 2) halo orbits are first computed. This autonomous procedure applies to both departure and arrival between the Earth-Moon and Sun-Earth systems. Departure times in the lunar cycle, amplitudes and types of libration point orbits, manifold selection, and the orientation/location of the surface of section all contribute to produce a variety of options. As the destination planet, the ephemeris position for Mars is employed throughout the analysis. The complete transfer is transitioned to the ephemeris model after the initial design phase. Results for multiple departure/arrival scenarios are compared.

Earth-Moon Libration Point Orbit Stationkeeping: Theory, Modeling and Operations

NASA Technical Reports Server (NTRS)

Folta, David C.; Pavlak, Thomas A.; Haapala, Amanda F.; Howell, Kathleen C.; Woodard, Mark A.

2013-01-01

Collinear Earth-Moon libration points have emerged as locations with immediate applications. These libration point orbits are inherently unstable and must be maintained regularly which constrains operations and maneuver locations. Stationkeeping is challenging due to relatively short time scales for divergence effects of large orbital eccentricity of the secondary body, and third-body perturbations. Using the Acceleration Reconnection and Turbulence and Electrodynamics of the Moon's Interaction with the Sun (ARTEMIS) mission orbit as a platform, the fundamental behavior of the trajectories is explored using Poincare maps in the circular restricted three-body problem. Operational stationkeeping results obtained using the Optimal Continuation Strategy are presented and compared to orbit stability information generated from mode analysis based in dynamical systems theory.

Applying Dynamical Systems Theory to Optimize Libration Point Orbit Stationkeeping Maneuvers for WIND

NASA Technical Reports Server (NTRS)

Brown, Jonathan M.; Petersen, Jeremy D.

2014-01-01

NASA's WIND mission has been operating in a large amplitude Lissajous orbit in the vicinity of the interior libration point of the Sun-Earth/Moon system since 2004. Regular stationkeeping maneuvers are required to maintain the orbit due to the instability around the collinear libration points. Historically these stationkeeping maneuvers have been performed by applying an incremental change in velocity, or (delta)v along the spacecraft-Sun vector as projected into the ecliptic plane. Previous studies have shown that the magnitude of libration point stationkeeping maneuvers can be minimized by applying the (delta)v in the direction of the local stable manifold found using dynamical systems theory. This paper presents the analysis of this new maneuver strategy which shows that the magnitude of stationkeeping maneuvers can be decreased by 5 to 25 percent, depending on the location in the orbit where the maneuver is performed. The implementation of the optimized maneuver method into operations is discussed and results are presented for the first two optimized stationkeeping maneuvers executed by WIND.

Orbit Determination Issues for Libration Point Orbits

NASA Technical Reports Server (NTRS)

Beckman, Mark; Bauer, Frank (Technical Monitor)

2002-01-01

Libration point mission designers require knowledge of orbital accuracy for a variety of analyses including station keeping control strategies, transfer trajectory design, and formation and constellation control. Past publications have detailed orbit determination (OD) results from individual libration point missions. This paper collects both published and unpublished results from four previous libration point missions (ISEE (International Sun-Earth Explorer) -3, SOHO (Solar and Heliospheric Observatory), ACE (Advanced Composition Explorer) and MAP (Microwave Anisotropy Probe)) supported by Goddard Space Flight Center's Guidance, Navigation & Control Center. The results of those missions are presented along with OD issues specific to each mission. All past missions have been limited to ground based tracking through NASA ground sites using standard range and Doppler measurement types. Advanced technology is enabling other OD options including onboard navigation using seaboard attitude sensors and the use of the Very Long Baseline Interferometry (VLBI) measurement Delta Differenced One-Way Range (DDOR). Both options potentially enable missions to reduce coherent dedicated tracking passes while maintaining orbital accuracy. With the increased projected loading of the DSN (Deep Space Network), missions must find alternatives to the standard OD scenario.

Long Term Missions at the Sun-Earth Libration Point L1: ACE, SOHO, and WIND

NASA Technical Reports Server (NTRS)

Roberts, Craig E.

2011-01-01

Three heliophysics missions - the Solar Heliospheric Observatory (SOHO), the Advanced Composition Explorer (ACE), and the Global Geoscience WIND - have been orbiting the Sun-Earth interior libration point L1 continuously since 1996, 1997, and 2004, respectively. ACE and WIND (both NASA missions) and SOHO (an ESA-NASA joint mission) are all operated from the NASA Goddard Space Flight Center Flight Dynamics Facility. While ACE and SOHO have been dedicated libration point orbiters since their launches, WIND prior to 2004 flew a remarkable 10-year deep-space trajectory that featured 38 targeted lunar flybys. The L1 orbits and the mission histories of the three spacecraft are briefly reviewed, and the station-keeping techniques and orbit maneuver experience are discussed.

Formation Flying With Decentralized Control in Libration Point Orbits

NASA Technical Reports Server (NTRS)

Folta, David; Carpenter, J. Russell; Wagner, Christoph

2000-01-01

A decentralized control framework is investigated for applicability of formation flying control in libration orbits. The decentralized approach, being non-hierarchical, processes only direct measurement data, in parallel with the other spacecraft. Control is accomplished via linearization about a reference libration orbit with standard control using a Linear Quadratic Regulator (LQR) or the GSFC control algorithm. Both are linearized about the current state estimate as with the extended Kalman filter. Based on this preliminary work, the decentralized approach appears to be feasible for upcoming libration missions using distributed spacecraft.

Human Exploration of Earth's Neighborhood and Mars

NASA Technical Reports Server (NTRS)

Condon, Gerald

2003-01-01

The presentation examines Mars landing scenarios, Earth to Moon transfers comparing direct vs. via libration points. Lunar transfer/orbit diagrams, comparison of opposition class and conjunction class missions, and artificial gravity for human exploration missions. Slides related to Mars landing scenarios include: mission scenario; direct entry landing locations; 2005 opportunity - Type 1; Earth-mars superior conjunction; Lander latitude accessibility; Low thrust - Earth return phase; SEP Earth return sequence; Missions - 200, 2007, 2009; and Mission map. Slides related to Earth to Moon transfers (direct vs. via libration points (L1, L2) include libration point missions, expeditionary vs. evolutionary, Earth-Moon L1 - gateway for lunar surface operations, and Lunar mission libration point vs. lunar orbit rendezvous (LOR). Slides related to lunar transfer/orbit diagrams include: trans-lunar trajectory from ISS parking orbit, trans-Earth trajectories, parking orbit considerations, and landing latitude restrictions. Slides related to comparison of opposition class (short-stay) and conjunction class (long-stay) missions for human exploration of Mars include: Mars mission planning, Earth-Mars orbital characteristics, delta-V variations, and Mars mission duration comparison. Slides related to artificial gravity for human exploration missions include: current configuration, NEP thruster location trades, minor axis rotation, and example load paths.

Libration Point Navigation Concepts Supporting the Vision for Space Exploration

NASA Technical Reports Server (NTRS)

Carpenter, J. Russell; Folta, David C.; Moreau, Michael C.; Quinn, David A.

2004-01-01

This work examines the autonomous navigation accuracy achievable for a lunar exploration trajectory from a translunar libration point lunar navigation relay satellite, augmented by signals from the Global Positioning System (GPS). We also provide a brief analysis comparing the libration point relay to lunar orbit relay architectures, and discuss some issues of GPS usage for cis-lunar trajectories.

Resonance and Capture of Jupiter Comets

NASA Astrophysics Data System (ADS)

Koon, W. S.; Lo, M. W.; Marsden, J. E.; Ross, S. D.

A number of Jupiter family comets such as Oterma and Gehrels 3 make a rapid transition from heliocentric orbits outside the orbit of Jupiter to heliocentric orbits inside the orbit of Jupiter and vice versa. During this transition, the comet can be captured temporarily by Jupiter for one to several orbits around Jupiter. The interior heliocentric orbit is typically close to the 3:2 resonance while the exterior heliocentric orbit is near the 2:3 resonance. An important feature of the dynamics of these comets is that during the transition, the orbit passes close to the libration points L_1 and L_2, two of the equilibrium points for the restricted three-body problem for the Sun-Jupiter system. Studying the libration point invariant manifold structures for L_1 and L_2 is a starting point for understanding the capture and resonance transition of these comets. For example, the recently discovered heteroclinic connection between pairs of unstable periodic orbits (one around the L_1 and the other around L_2) implies a complicated dynamics for comets in a certain energy range. Furthermore, the stable and unstable invariant manifold `tubes' associated to libration point periodic orbits, of which the heteroclinic connections are a part, are phase space conduits transporting material to and from Jupiter and between the interior and exterior of Jupiter's orbit.

Stationkeeping of Lissajous Trajectories in the Earth-Moon System with Applications to ARTEMIS

NASA Technical Reports Server (NTRS)

Folta, D. C.; Pavlak, T. A.; Howell, K. C.; Woodard, M. A.; Woodfork, D. W.

2010-01-01

In the last few decades, several missions have successfully exploited trajectories near the.Sun-Earth L1 and L2 libration points. Recently, the collinear libration points in the Earth-Moon system have emerged as locations with immediate application. Most libration point orbits, in any system, are inherently unstable. and must be controlled. To this end, several stationkeeping strategies are considered for application to ARTEMIS. Two approaches are examined to investigate the stationkeeping problem in this regime and the specific options. available for ARTEMIS given the mission and vehicle constraints. (I) A baseline orbit-targeting approach controls the vehicle to remain near a nominal trajectory; a related global optimum search method searches all possible maneuver angles to determine an optimal angle and magnitude; and (2) an orbit continuation method, with various formulations determines maneuver locations and minimizes costs. Initial results indicate that consistent stationkeeping costs can be achieved with both approaches and the costs are reasonable. These methods are then applied to Lissajous trajectories representing a baseline ARTEMIS libration orbit trajectory.

Transfers between libration-point orbits in the elliptic restricted problem

NASA Astrophysics Data System (ADS)

Hiday, L. A.; Howell, K. C.

The present time-fixed impulsive transfers between 3D libration point orbits in the vicinity of the interior L(1) libration point of the sun-earth-moon barycenter system are 'optimal' in that the total characteristic velocity required for implementation of the transfer exhibits a local minimum. The conditions necessary for a time-fixed, two-impulse transfer trajectory to be optimal are stated in terms of the primer vector, and the conditions necessary for satisfying the local optimality of a transfer trajectory containing additional impulses are addressed by requiring continuity of the Hamiltonian and the derivative of the primer vector at all interior impulses.

User and technical documentation

NASA Astrophysics Data System (ADS)

1988-09-01

The program LIBRATE calculates velocities for trajectories from low earth orbit (LEO) to four of the five libration points (L2, L3, L4, and L5), and from low lunar orbit (LLO) to libration points L1 and L2. The flight to be analyzed departs from a circular orbit of any altitude and inclination about the Earth or Moon and finishes in a circular orbit about the Earth at the desired libration point within a specified flight time. This program produces a matrix of the delta V's needed to complete the desired flight. The user specifies the departure orbit, and the maximum flight time. A matrix is then developed with 10 inclinations, ranging from 0 to 90 degrees, forming the columns, and 19 possible flight times, ranging from the flight time (input) to 36 hours less than the input value, in decrements of 2 hours, forming the rows. This matrix is presented in three different reports including the total delta V's, and both of the delta V components discussed. The input required from the user to define the flight is discussed. The contents of the three reports that are produced as outputs are also described. The instructions are also included which are needed to execute the program.

Design of optimal impulse transfers from the Sun-Earth libration point to asteroid

NASA Astrophysics Data System (ADS)

Wang, Yamin; Qiao, Dong; Cui, Pingyuan

2015-07-01

The lunar probe, Chang'E-2, is the first one to successfully achieve both the transfer to Sun-Earth libration point orbit and the flyby of near-Earth asteroid Toutatis. This paper, taking the Chang'E-2's asteroid flyby mission as an example, provides a method to design low-energy transfers from the libration point orbit to an asteroid. The method includes the analysis of transfer families and the design of optimal impulse transfers. Firstly, the one-impulse transfers are constructed by correcting the initial guesses, which are obtained by perturbing in the direction of unstable eigenvector. Secondly, the optimality of one-impulse transfers is analyzed and the optimal impulse transfers are built by using the primer vector theory. After optimization, the transfer families, including the slow and the fast transfers, are refined to be continuous and lower-cost transfers. The method proposed in this paper can be also used for designing transfers from an arbitrary Sun-Earth libration point orbit to a near-Earth asteroid in the Sun-Earth-Moon system.

Effect of electromagnetic field on Kordylewski clouds formation

NASA Astrophysics Data System (ADS)

Salnikova, Tatiana; Stepanov, Sergey

2018-05-01

In previous papers the authors suggest a clarification of the phenomenon of appearance-disappearance of Kordylewski clouds - accumulation of cosmic dust mass in the vicinity of the triangle libration points of the Earth-Moon system. Under gravi-tational and light perturbation of the Sun the triangle libration points aren't the points of relative equilibrium. However, there exist the stable periodic motion of the particles, surrounding every of the triangle libration points. Due to this fact we can consider a probabilistic model of the dust clouds formation. These clouds move along the periodical orbits in small vicinity of the point of periodical orbit. To continue this research we suggest a mathematical model to investigate also the electromagnetic influences, arising under consideration of the charged dust particles in the vicinity of the triangle libration points of the Earth-Moon system. In this model we take under consideration the self-unduced force field within the set of charged particles, the probability distribution density evolves according to the Vlasov equation.

Early Mission Maneuver Operations for the Deep Space Climate Observatory Sun-Earth L1 Libration Point Mission

NASA Technical Reports Server (NTRS)

Roberts, Craig; Case, Sara; Reagoso, John; Webster, Cassandra

2015-01-01

The Deep Space Climate Observatory mission launched on February 11, 2015, and inserted onto a transfer trajectory toward a Lissajous orbit around the Sun-Earth L1 libration point. This paper presents an overview of the baseline transfer orbit and early mission maneuver operations leading up to the start of nominal science orbit operations. In particular, the analysis and performance of the spacecraft insertion, mid-course correction maneuvers, and the deep-space Lissajous orbit insertion maneuvers are discussed, com-paring the baseline orbit with actual mission results and highlighting mission and operations constraints..

Transfers between libration-point orbits in the elliptic restricted problem

NASA Astrophysics Data System (ADS)

Hiday-Johnston, L. A.; Howell, K. C.

1994-04-01

A strategy is formulated to design optimal time-fixed impulsive transfers between three-dimensional libration-point orbits in the vicinity of the interior L1 libration point of the Sun-Earth/Moon barycenter system. The adjoint equation in terms of rotating coordinates in the elliptic restricted three-body problem is shown to be of a distinctly different form from that obtained in the analysis of trajectories in the two-body problem. Also, the necessary conditions for a time-fixed two-impulse transfer to be optimal are stated in terms of the primer vector. Primer vector theory is then extended to nonoptimal impulsive trajectories in order to establish a criterion whereby the addition of an interior impulse reduces total fuel expenditure. The necessary conditions for the local optimality of a transfer containing additional impulses are satisfied by requiring continuity of the Hamiltonian and the derivative of the primer vector at all interior impulses. Determination of location, orientation, and magnitude of each additional impulse is accomplished by the unconstrained minimization of the cost function using a multivariable search method. Results indicate that substantial savings in fuel can be achieved by the addition of interior impulsive maneuvers on transfers between libration-point orbits.

Servicing and Deployment of National Resources in Sun-Earth Libration Point Orbits

NASA Technical Reports Server (NTRS)

Folta, David C.; Beckman, Mark; Mar, Greg C.; Mesarch, Michael; Cooley, Steven; Leete, Steven J.

2002-01-01

Spacecraft travel between the Sun-Earth system, the Earth-Moon system, and beyond has received extensive attention recently. The existence of a connection between unstable regions enables mission designers to envision scenarios of multiple spacecraft traveling cheaply from system to system, rendezvousing, servicing, and refueling along the way. This paper presents examples of transfers between the Sun-Earth and Earth-Moon systems using a true ephemeris and perturbation model. It shows the (Delta)V costs associated with these transfers, including the costs to reach the staging region from the Earth. It explores both impulsive and low thrust transfer trajectories. Additionally, analysis that looks specifically at the use of nuclear power in libration point orbits and the issues associated with them such as inadvertent Earth return is addressed. Statistical analysis of Earth returns and the design of biased orbits to prevent any possible return are discussed. Lastly, the idea of rendezvous between spacecraft in libration point orbits using impulsive maneuvers is addressed.

Orbit Determination Error Analysis Results for the Triana Sun-Earth L2 Libration Point Mission

NASA Technical Reports Server (NTRS)

Marr, G.

2003-01-01

Using the NASA Goddard Space Flight Center's Orbit Determination Error Analysis System (ODEAS), orbit determination error analysis results are presented for all phases of the Triana Sun-Earth L1 libration point mission and for the science data collection phase of a future Sun-Earth L2 libration point mission. The Triana spacecraft was nominally to be released by the Space Shuttle in a low Earth orbit, and this analysis focuses on that scenario. From the release orbit a transfer trajectory insertion (TTI) maneuver performed using a solid stage would increase the velocity be approximately 3.1 km/sec sending Triana on a direct trajectory to its mission orbit. The Triana mission orbit is a Sun-Earth L1 Lissajous orbit with a Sun-Earth-vehicle (SEV) angle between 4.0 and 15.0 degrees, which would be achieved after a Lissajous orbit insertion (LOI) maneuver at approximately launch plus 6 months. Because Triana was to be launched by the Space Shuttle, TTI could potentially occur over a 16 orbit range from low Earth orbit. This analysis was performed assuming TTI was performed from a low Earth orbit with an inclination of 28.5 degrees and assuming support from a combination of three Deep Space Network (DSN) stations, Goldstone, Canberra, and Madrid and four commercial Universal Space Network (USN) stations, Alaska, Hawaii, Perth, and Santiago. These ground stations would provide coherent two-way range and range rate tracking data usable for orbit determination. Larger range and range rate errors were assumed for the USN stations. Nominally, DSN support would end at TTI+144 hours assuming there were no USN problems. Post-TTI coverage for a range of TTI longitudes for a given nominal trajectory case were analyzed. The orbit determination error analysis after the first correction maneuver would be generally applicable to any libration point mission utilizing a direct trajectory.

The Inherent Limitations of Spacepower: Fact or Fiction?

DTIC Science & Technology

1995-01-01

advantageously to affect near-earth space, as well as the Earth, itself. These are termed the libration points . Collins writes: The five so-called libration ... Libration points allow for little or no energy expense for station keeping, while operating from atop the "gravity well" allows for high potential energy...navigation, communica- tions, earth resources, lift orbit transfer , and tracking and control systems. Integrating many aspects of these systems to serve both

Libration Point Navigation Concepts Supporting Exploration Vision

NASA Technical Reports Server (NTRS)

Carpenter, J. Russell; Folta, David C.; Moreau, Michael C.; Gramling, Cheryl J.

2004-01-01

Farquhar described several libration point navigation concepts that would appear to support NASA s current exploration vision. One concept is a Lunar Relay Satellite operating in the vicinity of Earth-Moon L2, providing Earth-to-lunar far-side and long- range surface-to-surface navigation and communications capability. Reference [ 1] lists several advantages of such a system in comparison to a lunar orbiting relay satellite constellation. Among these are one or two vs. many satellites for coverage, simplified acquisition and tracking due to very low relative motion, much longer contact times, and simpler antenna pointing. An obvious additional advantage of such a system is that uninterrupted links to Earth avoid performing critical maneuvers "in the blind." Another concept described is the use of Earth-Moon L1 for lunar orbit rendezvous, rather than low lunar orbit as was done for Apollo. This rendezvous technique would avoid large plane change and high fuel cost associated with high latitude landing sites and long stay times. Earth-Moon L1 also offers unconstrained launch windows from the lunar surface. Farquhar claims this technique requires only slightly higher fuel cost than low lunar orbit rendezvous for short-stay equatorial landings. Farquhar also describes an Interplanetary Transportation System that would use libration points as terminals for an interplanetary shuttle. This approach would offer increased operational flexibility in terms of launch windows, rendezvous, aborts, etc. in comparison to elliptical orbit transfers. More recently, other works including Folta[3] and Howell[4] have shown that patching together unstable trajectories departing Earth-Moon libration points with stable trajectories approaching planetary libration points may also offer lower overall fuel costs than elliptical orbit transfers. Another concept Farquhar described was a Deep Space Relay at Earth-Moon IA and/or L5 that would serve as a high data rate optical navigation and communications relay satellite. The advantages in comparison to a geosynchronous relay are minimal Earth occultation, distance from large noise sources on Earth, easier pointing due to smaller relative velocity, and a large baseline for interferometry if both L4 and L5 are used.

The Propeller and the Frog

NASA Astrophysics Data System (ADS)

Pan, Margaret; Chiang, Eugene

2010-10-01

"Propellers" in planetary rings are disturbances in ring material excited by moonlets that open only partial gaps. We describe a new type of co-orbital resonance that can explain the observed non-Keplerian motions of propellers. The resonance is between the moonlet underlying the propeller and co-orbiting ring particles downstream of the moonlet where the gap closes. The moonlet librates within the gap about an equilibrium point established by co-orbiting material and stabilized by the Coriolis force. In the limit of small libration amplitude, the libration period scales linearly with the gap azimuthal width and inversely as the square root of the co-orbital mass. The new resonance recalls but is distinct from conventional horseshoe and tadpole orbits; we call it the "frog" resonance, after the relevant term in equine hoof anatomy. For a ring surface density and gap geometry appropriate for the propeller Blériot in Saturn's A ring, our theory predicts a libration period of ~4 years, similar to the ~3.7 year period over which Blériot's orbital longitude is observed to vary. These librations should be subtracted from the longitude data before any inferences about moonlet migration are made.

THE PROPELLER AND THE FROG

DOE Office of Scientific and Technical Information (OSTI.GOV)

Pan, Margaret; Chiang, Eugene, E-mail: mpan@astro.berkeley.ed

2010-10-20

'Propellers' in planetary rings are disturbances in ring material excited by moonlets that open only partial gaps. We describe a new type of co-orbital resonance that can explain the observed non-Keplerian motions of propellers. The resonance is between the moonlet underlying the propeller and co-orbiting ring particles downstream of the moonlet where the gap closes. The moonlet librates within the gap about an equilibrium point established by co-orbiting material and stabilized by the Coriolis force. In the limit of small libration amplitude, the libration period scales linearly with the gap azimuthal width and inversely as the square root of themore » co-orbital mass. The new resonance recalls but is distinct from conventional horseshoe and tadpole orbits; we call it the 'frog' resonance, after the relevant term in equine hoof anatomy. For a ring surface density and gap geometry appropriate for the propeller Bleriot in Saturn's A ring, our theory predicts a libration period of {approx}4 years, similar to the {approx}3.7 year period over which Bleriot's orbital longitude is observed to vary. These librations should be subtracted from the longitude data before any inferences about moonlet migration are made.« less

Lunar flyby transfers between libration point orbits

NASA Astrophysics Data System (ADS)

Qi, Yi; Xu, Shijie; Qi, Rui

2017-06-01

Lunar flyby or lunar gravity assist is a classical technique to change the energy and trajectory of space vehicle in space mission. In this paper, lunar flyby transfers between Sun-Earth/Moon libration point orbits with different energies are investigated in the Sun-Earth-Moon restricted four-body problem. Distinguished by behaviours before and after lunar flyby, classification of lunar flyby orbits is defined and studied. Research indicates that junction point of special regions of four types of lunar flyby orbits denotes the perilune of lunar flyby transfer between libration point orbits. Based on those special perilunes, retrograde and prograde lunar flyby transfers are discussed in detail, respectively. The mean energy level transition distribution is proposed and applied to analyse the influence of phase angle and eccentricity on lunar flyby transfers. The phase space is divided into normal and chaotic intervals based on the topology pattern of transfers. A continuation strategy of lunar flyby transfer in the bicircular model is presented. Numerical examples show that compared with the single-impulse transfers based on patched invariant manifolds, lunar flyby transfers are more energy efficient. Finally, lunar flyby transfers are further extended to the realistic models.

Spacecraft Maneuvering at the Sun/Earth-Moon L2 Libration Point

NASA Astrophysics Data System (ADS)

Shahid, Kamran

Spacecraft formation flying in the vicinity of the Sun/Earth-Moon libration points offers many promising possibilities for space exploration. The concept of formation flying involves the distribution of the functionality of a single spacecraft among several smaller, cooperative spacecraft. The libration points are locations relative to two large orbiting bodies where a third body with relatively small mass can remain stationary relative to the two larger bodies. The most significant perturbation experienced by a spacecraft at the libration point is effect of solar radiation pressure. This thesis presents the development of nonlinear control techniques for maneuvering control at the Sun-Earth/Moon L2 libration point. A new thruster based formation control technique is presented. We also consider a leader/follower formation architecture, and examine the station keeping control of the leader spacecraft and the formation control of the follower spacecraft using solar radiation pressure. Reference trajectories of the leader spacecraft, halo and Lissajous orbits, are determined using a numerical technique in order to take into account all major gravitational perturbations. The nonlinear controllers are developed based on Lyapunov analysis, including non-adaptive and adaptive designs. Thruster based and solar radiation pressure based control laws for spacecraft maneuvering at the Sun-Earth/Moon libration point are developed. Higher order sliding mode control is utilized to address the non-affine structure of the solar sail control inputs. The reduced input solar radiation pressure problem is properly addressed as an underactuated control problem. The development of adaptive control for solar sail equipped spacecraft is an innovation and represents and advancement in solar sailing control technology. Controller performance is evaluated in a high fidelity ephemeris model to reflect a realistic simulated space environment. The numerical results demonstrate the effectiveness of the proposed control techniques for spacecraft maneuvering using solar radiation pressure at the L2 libration point. Stationkeeping accuracies of 50m and formation maintenance accuracies of less than 1m are possible using solar radiation pressure at a sub-L2 libration point. The benefits of these control techniques include increasing libration point mission lifetimes and doubling payload mass fractions as compared to conventional propulsion methods.

Human Exploration Missions Study: Space Surveillance Telescope Transfer to and Station at a Halo Orbit at the Earth-Sun Libration Point L2

NASA Technical Reports Server (NTRS)

Dauro, Vincent A., Sr.

2001-01-01

This study was undertaken to determine mission profile and delta velocity requirements to place a telescope at the Earth-Sun libration point L2. The program, Integrated Mission Program (IMP), was selected to be used in the investigation. A description of IMP and its capabilities may be found in the Addenda. The Addenda also contains the libration halo equations, constants and other parameters. Comments regarding the chaotic nature of numerical integration near the libration points are also attached in the Addenda. A basic two stage S/C with a simple mission profile was selected. This profile is shown.

Frozen Orbits-Near Constant or Beneficially Varying Orbital Parameters.

DTIC Science & Technology

1986-05-15

89 6.3 Equatorial Near-Circular Orbits ............................... 92 6.4 Stable and Unstable Equilibrium Points ...Angle Libration Period......................................... 78 5-2 Lunar Gravitational Effect on Near-Circular Orbits .................... 80 5-3...6-1 Period of Oscillation about the Stable Equilibrium Point ............... 102 FIGURES Figure 2.1 Orbital Parameters

A note on libration point orbits, temporary capture and low-energy transfers

NASA Astrophysics Data System (ADS)

Fantino, E.; Gómez, G.; Masdemont, J. J.; Ren, Y.

2010-11-01

In the circular restricted three-body problem (CR3BP) the weak stability boundary (WSB) is defined as a boundary set in the phase space between stable and unstable motion relative to the second primary. At a given energy level, the boundaries of such region are provided by the stable manifolds of the central objects of the L1 and L2 libration points, i.e., the two planar Lyapunov orbits. Besides, the unstable manifolds of libration point orbits (LPOs) around L1 and L2 have been identified as responsible for the weak or temporary capture around the second primary of the system. These two issues suggest the existence of natural dynamical channels between the Earth's vicinity and the Sun-Earth libration points L1 and L2. Furthermore, it has been shown that the Sun-Earth L2 central unstable manifolds can be linked, through an heteroclinic connection, to the central stable manifolds of the L2 point in the Earth-Moon three-body problem. This concept has been applied to the design of low energy transfers (LETs) from the Earth to the Moon. In this contribution we consider all the above three issues, i.e., weak stability boundaries, temporary capture and low energy transfers, and we discuss the role played by the invariant manifolds of LPOs in each of them. The study is made in the planar approximation.

On the use of a sunward-libration-point orbiting spacecraft as an IMF monitor for magnetospheric studies

NASA Technical Reports Server (NTRS)

Kelly, T. J.; Crooker, N. U.; Siscoe, G. L.; Russell, C. T.; Smith, E. J.

1984-01-01

Magnetospheric studies often require knowledge of the orientation of the IMF. In order to test the accuracy of using magnetometer data from a spacecraft orbiting the sunward libration point for this purpose, the angle between the IMF at ISEE 3, when it was positioned around the libration point, and at ISEE 1, orbiting Earth, has been calculated for a data set of two-hour periods covering four months. For each period, a ten-minute average of ISEE 1 data is compared with ten-minute averages of ISEE 3 data at successively lagged intervals. At the lag time equal to the time required for the solar wind to convect from ISEE 3 to ISEE 1, the median angle between the IMF orientation at the two spacecraft is 20 deg, and 80% of the cases have angles less than 38 deg. The results for the angles projected on the y-z plane are essentially the same.

Analytical and numerical construction of vertical periodic orbits about triangular libration points based on polynomial expansion relations among directions

NASA Astrophysics Data System (ADS)

Qian, Ying-Jing; Yang, Xiao-Dong; Zhai, Guan-Qiao; Zhang, Wei

2017-08-01

Innovated by the nonlinear modes concept in the vibrational dynamics, the vertical periodic orbits around the triangular libration points are revisited for the Circular Restricted Three-body Problem. The ζ -component motion is treated as the dominant motion and the ξ and η -component motions are treated as the slave motions. The slave motions are in nature related to the dominant motion through the approximate nonlinear polynomial expansions with respect to the ζ -position and ζ -velocity during the one of the periodic orbital motions. By employing the relations among the three directions, the three-dimensional system can be transferred into one-dimensional problem. Then the approximate three-dimensional vertical periodic solution can be analytically obtained by solving the dominant motion only on ζ -direction. To demonstrate the effectiveness of the proposed method, an accuracy study was carried out to validate the polynomial expansion (PE) method. As one of the applications, the invariant nonlinear relations in polynomial expansion form are used as constraints to obtain numerical solutions by differential correction. The nonlinear relations among the directions provide an alternative point of view to explore the overall dynamics of periodic orbits around libration points with general rules.

Halo-orbit and lunar-swingby missions of the 1990's

NASA Technical Reports Server (NTRS)

Farquhar, Robert W.

1990-01-01

A significant number of spacecraft are planning to use halo orbits and lunar-swingby trajectories in the next decade. Four spacecraft will be placed into halo orbits around the earth's sunward libration point, while two others will be stationed near the sun-earth L2 libration point in the distant geomagnetic tail. Six spacecraft, including two of the aforementioned halo orbiters, will make use of lunar-swingby maneuvers to fulfill their mission objectives. Thus, a total of ten spacecraft, five from the Soviet Union, two from Japan, two from the United States, and one from the European Space Agency, will employ halo orbits and/or lunar-swingby trajectories in the 1990's. Pertinent facts are presented for each of these missions.

Librations and Interior Structure of the Galilean Satellites

NASA Astrophysics Data System (ADS)

van Hoolst, T.; Baland, R.; Karatekin, O.; Rambaux, N.

2009-12-01

We investigate the influence of the interior structure of the Galilean satellites on their rotation variations (or librations). Since the Galilean satellites are significantly aspherical due to rotation and static tides, Jupiter exerts a gravitational torque on them. In a circular orbit, the long axis of a satellite would always point towards Jupiter and the gravitational torque would be zero. However, the eccentric orbits of the Galilean satellites lead to misalignment of the long axis with the direction to Jupiter and result in non-zero gravitational torques that tend to modify the rotation of the satellites. Since the torque varies with the orbital phase, the main libration period is equal to the orbital period. In a first-order approximation, the libration amplitude is usually calculated by assuming that the satellite reacts rigidly to the gravitational torque. The corresponding amplitudes, expressed as a shift at the surface of the orientation of the long axis with respect to that for the mean rotation rate, decrease with increasing distance from Jupiter from a few hundred meters for Io to about ten meter for Callisto. Internal liquid layers, such as a subsurface ocean, can lead to differential rotation of the solid and liquid layers and to differences of the libration of surface with respect to that for a rigid libration. Here, we present a method to determine the influence of gravitational and pressure interactions between internal layers on the libration of the Galilean satellites. For Io, we show that the liquid core has only a small effect on the surface librations. For Europa, Ganymede and Callisto, the presence of a subsurface ocean can significantly increase the libration amplitude. We also study the effect of the possible existence of two liquid layers in Ganymede and Europa: a subsurface ocean and a liquid core. We quantify the sensitivity of the libration amplitude to the internal structure and assess expected improvements in the interior structure of the Galilean satellites from future libration observations with the joint NASA/ESA Europa Jupiter System Mission.

Invariant Manifolds, the Spatial Three-Body Problem and Space Mission Design

NASA Technical Reports Server (NTRS)

Gomez, G.; Koon, W. S.; Lo, Martin W.; Marsden, J. E.; Masdemont, J.; Ross, S. D.

2001-01-01

The invariant manifold structures of the collinear libration points for the spatial restricted three-body problem provide the framework for understanding complex dynamical phenomena from a geometric point of view. In particular, the stable and unstable invariant manifold 'tubes' associated to libration point orbits are the phase space structures that provide a conduit for orbits between primary bodies for separate three-body systems. These invariant manifold tubes can be used to construct new spacecraft trajectories, such as 'Petit Grand Tour' of the moons of Jupiter. Previous work focused on the planar circular restricted three-body problem. The current work extends the results to the spatial case.

Continuation of periodic orbits in the Sun-Mercury elliptic restricted three-body problem

NASA Astrophysics Data System (ADS)

Peng, Hao; Bai, Xiaoli; Xu, Shijie

2017-06-01

Starting from resonant Halo orbits in the Circular Restricted Three-Body Problem (CRTBP), Multi-revolution Elliptic Halo (ME-Halo) orbits around L1 and L2 points in the Sun-Mercury Elliptic Restricted Three-Body Problem (ERTBP) are generated systematically. Three pairs of resonant parameters M5N2, M7N3 and M9N4 are tested. The first pair shows special features and is investigated in detail. Three separated characteristic curves of periodic orbit around each libration point are obtained, showing the eccentricity varies non-monotonically along these curves. The eccentricity of the Sun-Mercury system can be achieved by continuation method in just a few cases. The stability analysis shows that these orbits are all unstable and the complex instability occurs with certain parameters. This paper shows new periodic orbits in both the CRTBP and the ERTBP. Totally four periodic orbits with parameters M5N2 around each libration points are extracted in the Sun-Mercury ERTBP.

Stationkeeping of the First Earth-Moon Libration Orbiters: The ARTEMIS Mission

NASA Technical Reports Server (NTRS)

Folta, David; Woodard, Mark; Cosgrove, D.

2011-01-01

Libration point orbits near collinear locations are inherently unstable and must be controlled. For Acceleration Reconnection and Turbulence and Electrodynamics of the Moon's Interaction with the Sun (ARTEMIS) Earth-Moon Lissajous orbit operations, stationkeeping is challenging because of short time scales, large orbital eccentricity of the secondary, and solar gravitational and radiation pressure perturbations. ARTEMIS is the first NASA mission continuously controlled at both Earth-Moon L1 and L2 locations and uses a balance of optimization, spacecraft implementation and constraints, and multi-body dynamics. Stationkeeping results are compared to pre-mission research including mode directions.

L1 libration point manned space habitat

NASA Technical Reports Server (NTRS)

Luttges, Marvin; Johnson, Steve; Banks, Gary; Johnson, Richard; Meyer, Christian; Pepin, Scott; Macelroy, Robert

1989-01-01

Second generation stations or Manned Space Habitats (MSHs) are discussed for an Earth-Moon libration point and in lunar orbit. The conceptual design of such a station is outlined. Systems and subsystems described reflect anticipation of moderate technology growth. The evolution of the L1 environments is discussed, several selected subsystems are outlined, and how the L1 MSH will complete some of its activities is described.

Stationkeeping Approach for the Microwave Anisotropy Probe (MAP)

NASA Technical Reports Server (NTRS)

Rohrbaugh, Dave; Schiff, Conrad

2002-01-01

The Microwave Anisotropy Probe was successfully launched on June 30, 2001 and placed into a Lissajous orbit about the L2 Sun-Earth-Moon libration point. However, the L2 libration point is unstable which necessitates occasional stationkeeping maneuvers in order to maintain the spacecraft s Lissajous orbit. Analyses were performed in order to develop a feasible L2 stationkeeping strategy for the MAP mission. The resulting strategy meets the allotted fuel budget, allowing for enough fuel to handle additional he1 taxes, while meeting the attitude requirements for the maneuvers. Results from the first two stationkeeping maneuvers are included.

Low-energy transfers to cislunar periodic orbits visiting triangular libration points

NASA Astrophysics Data System (ADS)

Lei, Hanlun; Xu, Bo

2018-01-01

This paper investigates the cislunar periodic orbits that pass through triangular libration points of the Earth-Moon system and studies the techniques on design low-energy transfer trajectories. In order to compute periodic orbits, families of impulsive transfers between triangular libration points are taken to generate the initial guesses of periodic orbits, and multiple shooting techniques are applied to solving the problem. Then, varieties of periodic orbits in cislunar space are obtained, and stability analysis shows that the majority of them are unstable. Among these periodic orbits, an unstable periodic orbit in near 3:2 resonance with the Moon is taken as the nominal orbit of an assumed mission. As the stable manifolds of the target orbit could approach the Moon, low-energy transfer trajectories can be designed by combining lunar gravity assist with the invariant manifold structure of the target orbit. In practice, both the natural and perturbed invariant manifolds are considered to obtain the low-energy transfers, which are further refined to the Sun-perturbed Earth-Moon system. Results indicate that (a) compared to the case of natural invariant manifolds, the optimal transfers using perturbed invariant manifolds could reduce flight time at least 50 days, (b) compared to the cheapest direct transfer, the optimal low-energy transfer obtained by combining lunar gravity assist and invariant manifolds could save on-board fuel consumption more than 200 m/s, and (c) by taking advantage of the gravitational perturbation of the Sun, the low-energy transfers could save more fuel consumption than the corresponding ones obtained in the Earth-Moon system.

Lunar Navigation with Libration Point Orbiters and GPS

NASA Technical Reports Server (NTRS)

Carpenter, J. Russell

2004-01-01

NASA is currently studying a Vision for Space Exploration based on spiral development of robotic and piloted missions to the moon and Mars, but research into how to perform such missions has continued ever since the first era of lunar exploration. One area of study that a number of researchers have pursued is libration point navigation and communication relay concepts. These concepts would appear to support many of NASA's current requirements for navigation and communications coverage for human and robotic spacecraft operating in lunar space and beyond. In trading libration point concepts against other options, designers must consider issues such as the number of spacecraft, required to provide coverage, insertion and stationkeeping costs, power and data rate requirements, frequency allocations, and many others. The libration points, along with a typical cis-lunar trajectory, are equilibrium locations for an infinitesimal mass in the rotating coordinate system that follows the motion of two massive bodies in circular orbits with respect to their common barycenter. There are three co-linear points along the line connecting the massive bodies: between the bodies, beyond the secondary body, and beyond the primary body. The relative distances of these points along the line connecting the bodies depend on the mass ratios. There are also two points that form equilateral triangles with the massive bodies. Ideally, motion in the neighborhood of the co-linear points is unstable, while motion near the equilibrium points is stable. However, in the real world, the motions are highly perturbed so that a satellite will require stationkeeping maneuvers.

Solar radiation pressure application for orbital motion stabilization near the Sun-Earth collinear libration point

NASA Astrophysics Data System (ADS)

Polyakhova, Elena; Shmyrov, Alexander; Shmyrov, Vasily

2018-05-01

Orbital maneuvering in a neighborhood of the collinear libration point L1 of Sun-Earth system has specific properties, primarily associated with the instability L1. For a long stay in this area of space the stabilization problem of orbital motion requires a solution. Numerical experiments have shown that for stabilization of motion it is requires very small control influence in comparison with the gravitational forces. On the other hand, the stabilization time is quite long - months, and possibly years. This makes it highly desirable to use solar pressure forces. In this paper we illustrate the solar sail possibilities for solving of stabilization problem in a neighborhood L1 with use of the model example.

ADRC for spacecraft attitude and position synchronization in libration point orbits

NASA Astrophysics Data System (ADS)

Gao, Chen; Yuan, Jianping; Zhao, Yakun

2018-04-01

This paper addresses the problem of spacecraft attitude and position synchronization in libration point orbits between a leader and a follower. Using dual quaternion, the dimensionless relative coupled dynamical model is derived considering computation efficiency and accuracy. Then a model-independent dimensionless cascade pose-feedback active disturbance rejection controller is designed to spacecraft attitude and position tracking control problems considering parameter uncertainties and external disturbances. Numerical simulations for the final approach phase in spacecraft rendezvous and docking and formation flying are done, and the results show high-precision tracking errors and satisfactory convergent rates under bounded control torque and force which validate the proposed approach.

Solar Warning Architecture for Manned Missions to Mars

DTIC Science & Technology

2011-06-01

public discussions of manned missions to return to the Moon, explore near-earth asteroids , and even visit Mars, a deep-space solar weather warning...mission planning, and libration points. In addition, the limited previous analysis on this problem was mined for information. 2.2 Radiation Effects...behind the Earth, on its orbital path. These two libration points are stable along all 3 axes, leading some to theorize there may be asteroids or

Lunar Gravity-Assist Maneuver As a Way of Reducing the Orbit Amplitude in the Spectrum-Röntgen-Gamma Project

NASA Astrophysics Data System (ADS)

Kovalenko, I. D.; Eismont, N. A.

2018-04-01

Spectrum-Röntgen-Gamma (SRG) is a space observatory designed to observe astrophysical objects in the X-ray range of the electromagnetic spectrum. SRG is planned to be launched in 2019 by a Proton-M launch vehicle with a DM3 upper stage. The spacecraft will be delivered to an orbit around the Sun-Earth collinear libration point L2 located at a distance of 1.5 million km from the Earth. Although the SRG launch scheme has already been determined at present, in this paper we consider an alternative spacecraft transfer scenario using a lunar gravity-assist maneuver. The proposed scenario allows a oneimpulse transfer from a low Earth orbit to a small-amplitude orbit around the libration point to be performed while fulfilling the technical constraints and the scientific requirements of the mission.

Steady Motions of Rigid Body Satellites in a Central Gravitational Field

DTIC Science & Technology

1993-12-01

been explored for several centuries. Orbiting bodies investigated include point masses, spheres, cylinders, rods, ball-and-socket connected objects...of the satellite model relative to its orbit radius could lead to 5 its treatment as a point mass, doing so would prevent analysis of satellite...8217 librational ’ motion ... and internal elastic forces in the structure balance the orbital dynamic accelerations tending to separate masses orbiting at

Time and Energy, Exploring Trajectory Options Between Nodes in Earth-Moon Space

NASA Technical Reports Server (NTRS)

Martinez, Roland; Condon, Gerald; Williams, Jacob

2012-01-01

The Global Exploration Roadmap (GER) was released by the International Space Exploration Coordination Group (ISECG) in September of 2011. It describes mission scenarios that begin with the International Space Station and utilize it to demonstrate necessary technologies and capabilities prior to deployment of systems into Earth-Moon space. Deployment of these systems is an intermediate step in preparation for more complex deep space missions to near-Earth asteroids and eventually Mars. In one of the scenarios described in the GER, "Asteroid Next", there are activities that occur in Earth-Moon space at one of the Earth-Moon Lagrange (libration) points. In this regard, the authors examine the possible role of an intermediate staging point in an effort to illuminate potential trajectory options for conducting missions in Earth-Moon space of increasing duration, ultimately leading to deep space missions. This paper will describe several options for transits between Low Earth Orbit (LEO) and the libration points, transits between libration points, and transits between the libration points and interplanetary trajectories. The solution space provided will be constrained by selected orbital mechanics design techniques and physical characteristics of hardware to be used in both crewed missions and uncrewed missions. The relationships between time and energy required to transfer hardware between these locations will provide a better understanding of the potential trade-offs mission planners could consider in the development of capabilities, individual missions, and mission series in the context of the ISECG GER.

A Solar System Survey of Forced Librations in Longitude

NASA Technical Reports Server (NTRS)

Cornstock, Robert L.; Bills, Bruce G.

2003-01-01

Forced librations are periodic rotational rate variations due to gravitational interactions with an orbital partner. We have developed an analytic theory capable of calculating expected amplitudes of forced librations for nonresonant rotators as well as for bodies existing in a spin-orbit resonance. The theory has been applied to 34 solar system bodies, including terrestrial planets, planetary satellites, and the asteroid Eros. Parameters governing libration amplitude are the body s orbital eccentricity, moment difference, and the ratio of its spin rate to its orbital rate. In each case the largest libration amplitude is associated with the forcing frequency 2 (p - 1) n, where n is the orbital mean motion and p is the spin/orbit rate ratio. This dominant frequency is simply semidiurnal as seen from the position of the torquing body. The maximum libration angular amplitude is 1.3 x 10(exp -2) radians for Thebe, and the maximum mean equatorial displacement is 1.4 km for Mimas.

On Space Warfare: A Space Power Doctrine

DTIC Science & Technology

1998-06-01

called Panama Theory: that there are strategic places (geostationary orbits , libration points ) in space that have military value similar to the...initial training courses for the orbital analyst career field. In 1969, Lupton was transferred to the Headquarters Strategic Air Command, Directorate...over a point on the equator even though the satellite is moving in a circular orbit through space. This altitude (19,360 nautical miles) is the only

On the restricted four-body problem with the effect of small perturbations in the Coriolis and centrifugal forces

NASA Astrophysics Data System (ADS)

Suraj, Md Sanam; Aggarwal, Rajiv; Arora, Monika

2017-09-01

We have studied the restricted four-body problem (R4BP) with the effect of the small perturbation in the Coriolis and centrifugal forces on the libration points and zero velocity curves (ZVCs). Further, we have supposed that all the primaries are set in an equilateral triangle configuration, moving in the circular orbits around their common centre of mass. We have observed that the effect of the small perturbation in centrifugal force has a substantial effect on the location of libration points but a small perturbation in the Coriolis force has no impact on the location of libration points. But the stability of the libration points is highly influenced by the effect of the small perturbation in the Coriolis force. It is observed that as the Coriolis parameter increases, the libration points become stable. Further, it is found that the effect of the small perturbation in the centrifugal force has a substantial influence on the regions of possible motion. Also, when the effect of small perturbation in the centrifugal force increases the forbidden region decreases; here the motion is not possible for the infinitesimal mass. It is observed when the value of the Jacobian constant decreases, the regions of possible motion increase. In addition, we have also discussed how small perturbations in the Coriolis and centrifugal forces influence the Newton-Raphson basins of convergence.

A Librational Model for the Propeller Blériot in the Saturnian Ring System

NASA Astrophysics Data System (ADS)

Seiler, M.; Sremčević, M.; Seiß, M.; Hoffmann, H.; Spahn, F.

2017-05-01

The reconstruction of the orbital evolution of the propeller structure Blériot orbiting in Saturn’s A ring from recurrent observations in Cassini ISS images yielded a considerable offset motion from the expected Keplerian orbit. This offset motion can be composed by three sinusoidal harmonics with amplitudes and periods of 1845, 152, 58 km and 11.1, 3.7, and 2.2 years, respectively. In this paper we present results from N-body simulations, where we integrated the orbital evolution of a moonlet, which is placed at the radial position of Blériot under the gravitational action of the Saturnian satellites. Our simulations yield that, especially the gravitational interactions with Prometheus, Pandora, and Mimas are forcing the moonlet to librate with the right frequencies, but the libration amplitudes are too small to explain the observations. Thus, further mechanisms are needed to explain the amplitudes of the forced librations—e.g., moonlet-ring interactions. Here, we develop a model, where the moonlet is allowed to be slightly displaced with respect to its created gaps breaking the point symmetry and causing a repulsive force in this way. As a result, the evolution of the moonlet’s longitude can be described by a harmonic oscillator. In the presence of external forcing by the outer moons, the libration amplitudes get the more amplified the closer the forcing frequency is to the eigenfrequency of the disturbed propeller oscillator. Applying our model to Blériot, it is possible to reproduce a libration period of 13 years with an amplitude of about 2000 km.

A possible space VLBI constellation utilizing the stable orbits around the TLPs in the Earth-Moon system.

NASA Astrophysics Data System (ADS)

Liu, Bin; Tang, Jingshi; Hou, Xiyun

2016-07-01

Current studies indicate that there are stable orbits around but far away from the triangular libration points .Two special quasi-periodic orbits around each triangular libration points L4 , L5 in the Earth-Moon sys-tem perturbed by Sun are gain , and the stable orbits discussed in this work are ideal places for space colonies because no orbit control is needed. These stable orbits can also be used as nominal orbits for space VLBI (Very Long Baseline Interferometry) stations. The two stations can also form baselines with stations on the Earth and the Moon, or with stations located around another TLP. Due to the long distance between the stations, the observation precision can be greatly enhanced compared with the VLBI stations on the Earth. Such a VLBI constellation not only can advance the radio astronomy, but also can be used as a navigation system for human activities in the Earth-Moon system and even in the solar system. This paper will focus on the navigation constellation coverage issues, and the orbit determination accuracy problems within the Earth-Moon sys-tem and interplanetary space.

Suitable configurations for triangular formation flying about collinear libration points under the circular and elliptic restricted three-body problems

NASA Astrophysics Data System (ADS)

Ferrari, Fabio; Lavagna, Michèle

2018-06-01

The design of formations of spacecraft in a three-body environment represents one of the most promising challenges for future space missions. Two or more cooperating spacecraft can greatly answer some very complex mission goals, not achievable by a single spacecraft. The dynamical properties of a low acceleration environment such as the vicinity of libration points associated to a three-body system, can be effectively exploited to design spacecraft configurations able of satisfying tight relative position and velocity requirements. This work studies the evolution of an uncontrolled formation orbiting in the proximity of periodic orbits about collinear libration points under the Circular and Elliptic Restricted Three-Body Problems. A three spacecraft triangularly-shaped formation is assumed as a representative geometry to be investigated. The study identifies initial configurations that provide good performance in terms of formation keeping, and investigates key parameters that control the relative dynamics between the spacecraft within the three-body system. Formation keeping performance is quantified by monitoring shape and size changes of the triangular formation. The analysis has been performed under five degrees of freedom to define the geometry, the orientation and the location of the triangle in the synodic rotating frame.

Prospects for tracking spacecrafts within 2 million Km of Earth with phased array antennas

NASA Technical Reports Server (NTRS)

Amoozegar, F.; Jamnejad, V.; Cesarone, R.

2003-01-01

Recent advances in space technology for Earth observations, global communications, and positioning systems have created heavy traffic at a variety of orbits. These include smart sensors in low Earth orbits (LEO), internet satellites in LEO and GEO orbits, Earth observing satellites in high Earth orbits (HEO), observatory class satellites at Lagrangian libration points, and those heading for deep space.

Spacecraft transfer trajectory design exploiting resonant orbits in multi-body environments

NASA Astrophysics Data System (ADS)

Vaquero Escribano, Tatiana Mar

Historically, resonant orbits have been employed in mission design for multiple planetary flyby trajectories and, more recently, as a source of long-term orbital stability. For instance, in support of a mission concept in NASA's Outer Planets Program, the Jupiter Europa Orbiter spacecraft is designed to encounter two different resonances with Europa during the 'endgame' phase, leading to Europa orbit insertion on the final pass. In 2011, the Interstellar Boundary Explorer spacecraft was inserted into a stable out-of-plane lunar-resonant orbit, the first of this type for a spacecraft in a long-term Earth orbit. However, resonant orbits have not yet been significantly explored as transfer mechanisms between non-resonant orbits in multi-body systems. This research effort focuses on incorporating resonant orbits into the design process to potentially enable the construction of more efficient or even novel transfer scenarios. Thus, the goals in this investigation are twofold: i) to expand the orbit architecture in multi-body environments by cataloging families of resonant orbits, and ii) to assess the role of such families in the design of transfer trajectories with specific patterns and itineraries. The benefits and advantages of employing resonant orbits in the design process are demonstrated through a variety of astrodynamics applications in several multi-body systems. In the Earth-Moon system, locally optimal transfer trajectories from low Earth orbit to selected libration point orbits are designed by leveraging conic arcs and invariant manifolds associated with resonant orbits. Resonant manifolds in the Earth-Moon system offer trajectories that tour the entire space within reasonable time intervals, facilitating the design of libration point orbit tours as well as Earth-Moon cyclers. In the Saturnian system, natural transitions between resonant and libration point orbits are sought and the problem of accessing Hyperion from orbits that are resonant with Titan is also examined. To add versatility to the proposed design method, a system translation technique enables the straightforward transition of solutions from the Earth-Moon system to any Sun-planet or planet-moon three-body system. The circular restricted three-body problem serves as a basis to quickly generate solutions that meet specific requirements, but candidate transfer trajectories are then transitioned to an ephemeris model for validation.

Impulsive time-free transfers between halo orbits

NASA Astrophysics Data System (ADS)

Hiday, L. A.; Howell, K. C.

1992-08-01

A methodology is developed to design optimal time-free impulsive transfers between three-dimensional halo orbits in the vicinity of the interior L1 libration point of the sun-earth/moon barycenter system. The transfer trajectories are optimal in the sense that the total characteristics velocity required to implement the transfer exhibits a local minimum. Criteria are established whereby the implementation of a coast in the initial orbit, a coast in the final orbit, or dual coasts accomplishes a reduction in fuel expenditure. The optimality of a reference two-impulse transfer can be determined by examining the slope at the endpoints of a plot of the magnitude of the primer vector on the reference trajectory. If the initial and final slopes of the primer magnitude are zero, the transfer trajectory is optimal; otherwise, the execution of coasts is warranted. The optimal time of flight on the time-free transfer, and consequently, the departure and arrival locations on the halo orbits are determined by the unconstrained minimization of a function of two variables using a multivariable search technique. Results indicate that the cost can be substantially diminished by the allowance for coasts in the initial and final libration-point orbits.

Impulsive Time-Free Transfers Between Halo Orbits

NASA Astrophysics Data System (ADS)

Hiday-Johnston, L. A.; Howell, K. C.

1996-12-01

A methodology is developed to design optimal time-free impulsive transfers between three-dimensional halo orbits in the vicinity of the interior L 1 libration point of the Sun-Earth/Moon barycenter system. The transfer trajectories are optimal in the sense that the total characteristic velocity required to implement the transfer exhibits a local minimum. Criteria are established whereby the implementation of a coast in the initial orbit, a coast in the final orbit, or dual coasts accomplishes a reduction in fuel expenditure. The optimality of a reference two-impulse transfer can be determined by examining the slope at the endpoints of a plot of the magnitude of the primer vector on the reference trajectory. If the initial and final slopes of the primer magnitude are zero, the transfer trajectory is optimal; otherwise, the execution of coasts is warranted. The optimal time of flight on the time-free transfer, and consequently, the departure and arrival locations on the halo orbits are determined by the unconstrained minimization of a function of two variables using a multivariable search technique. Results indicate that the cost can be substantially diminished by the allowance for coasts in the initial and final libration-point orbits.

Earth to Moon Transfer: Direct vs Via Libration Points (L1, L2)

NASA Technical Reports Server (NTRS)

Condon, Gerald L.; Wilson, Samuel W.

2004-01-01

For some three decades, the Apollo-style mission has served as a proven baseline technique for transporting flight crews to the Moon and back with expendable hardware. This approach provides an optimal design for expeditionary missions, emphasizing operational flexibility in terms of safely returning the crew in the event of a hardware failure. However, its application is limited essentially to low-latitude lunar sites, and it leaves much to be desired as a model for exploratory and evolutionary programs that employ reusable space-based hardware. This study compares the performance requirements for a lunar orbit rendezvous mission type with one using the cislunar libration point (L1) as a stopover and staging point for access to arbitrary sites on the lunar surface. For selected constraints and mission objectives, it contrasts the relative uniformity of performance cost when the L1 staging point is used with the wide variation of cost for the Apollo-style lunar orbit rendezvous.

Transport and Capture of Comets

NASA Astrophysics Data System (ADS)

Ross, S. D.; Koon, W. S.; Lo, M. W.; Marsden, J. E.

2001-11-01

The dynamics of comets and other solar system objects which have a three-body energy close to that of the collinear libration points are known to exhibit a complicated array of behaviors such as rapid transition between the interior and exterior Hill's regions, temporary capture, and collision. The invariant manifold structures of the collinear libration points for the restricted three-body problem, which exist for a range of energies, provide the framework for understanding these transport phenomena from a geometric point of view. In particular, the stable and unstable invariant manifold "tubes" associated to libration point orbits are the phase space conduits transporting material to and from the smaller primary body (e.g., Jupiter), and between primary bodies for separate three-body systems (e.g., Saturn and Jupiter). This point of view has worked well in describing the planar circular restricted three-body problem. The current work seeks to extend the results to three degrees of freedom. This work was supported by the National Science Foundation Grant No. KDI/ATM-9873133 under a contract with the Jet Propulsion Laboratory, NASA.

Inclined asymmetric librations in exterior resonances

NASA Astrophysics Data System (ADS)

Voyatzis, G.; Tsiganis, K.; Antoniadou, K. I.

2018-04-01

Librational motion in Celestial Mechanics is generally associated with the existence of stable resonant configurations and signified by the existence of stable periodic solutions and oscillation of critical (resonant) angles. When such an oscillation takes place around a value different than 0 or π , the libration is called asymmetric. In the context of the planar circular restricted three-body problem, asymmetric librations have been identified for the exterior mean motion resonances (MMRs) 1:2, 1:3, etc., as well as for co-orbital motion (1:1). In exterior MMRs the massless body is the outer one. In this paper, we study asymmetric librations in the three-dimensional space. We employ the computational approach of Markellos (Mon Not R Astron Soc 184:273-281, https://doi.org/10.1093/mnras/184.2.273, 1978) and compute families of asymmetric periodic orbits and their stability. Stable asymmetric periodic orbits are surrounded in phase space by domains of initial conditions which correspond to stable evolution and librating resonant angles. Our computations were focused on the spatial circular restricted three-body model of the Sun-Neptune-TNO system (TNO = trans-Neptunian object). We compare our results with numerical integrations of observed TNOs, which reveal that some of them perform 1:2 resonant, inclined asymmetric librations. For the stable 1:2 TNO librators, we find that their libration seems to be related to the vertically stable planar asymmetric orbits of our model, rather than the three-dimensional ones found in the present study.

Locally optimal transfer trajectories between libration point orbits using invariant manifolds

NASA Astrophysics Data System (ADS)

Davis, Kathryn E.

2009-12-01

Techniques from dynamical systems theory and primer vector theory have been applied to the construction of locally optimal transfer trajectories between libration point orbits. When two libration point orbits have different energies, it has been found that the unstable manifold of the first orbit can be connected to the stable manifold of the second orbit with a bridging trajectory. A bounding sphere centered on the secondary, with a radius less than the radius of the sphere of influence of the secondary, was used to study the stable and unstable manifold trajectories. It was numerically demonstrated that within the bounding sphere, the two-body parameters of the unstable and stable manifold trajectories could be analyzed to locate low transfer costs. It was shown that as the two-body parameters of an unstable manifold trajectory more closely matched the two-body parameters of a stable manifold trajectory, the total DeltaV necessary to complete the transfer decreased. Primer vector theory was successfully applied to a transfer to determine the optimal maneuvers required to create the bridging trajectory that connected the unstable manifold of the first orbit to the stable manifold of the second orbit. Transfer trajectories were constructed between halo orbits in the Sun-Earth and Earth-Moon three-body systems. Multiple solutions were found between the same initial and final orbits, where certain solutions retraced interior portions of the trajectory. All of the trajectories created satisfied the conditions for optimality. The costs of transfers constructed using invariant manifolds were compared to the costs of transfers constructed without the use of invariant manifolds, when data was available. In all cases, the total cost of the transfers were significantly lower when invariant manifolds were used in the transfer construction. In many cases, the transfers that employed invariant manifolds were three to four times more efficient, in terms of fuel expenditure, than the transfer that did not. The decrease in transfer cost was accompanied by an increase in transfer time of flight. Transfers constructed in the Earth-Moon system were shown to be particularly viable for lunar navigation and communication constellations, as excellent coverage of the lunar surface can be achieved during the transfer.

An Investigation of Spinup Dynamics of Axial Gyrostats Using Elliptic Integrals and the Method of Averaging

DTIC Science & Technology

1991-01-01

is a gyrostat near one of the five libration points . She identified the equilibria and determined their stability regions. Also, Mavraga- nis [71] has...defines a family of periodic orbits , depending on how close the all-spun motion is to an equilibrium point of the equations of motion for a single...determined by the relationship between the mission orbit and the object the platform is supposed to track. As a limiting case, one might wish to point

DOE Office of Scientific and Technical Information (OSTI.GOV)

Seiler, M.; Seiß, M.; Hoffmann, H.

The reconstruction of the orbital evolution of the propeller structure Blériot orbiting in Saturn’s A ring from recurrent observations in Cassini ISS images yielded a considerable offset motion from the expected Keplerian orbit. This offset motion can be composed by three sinusoidal harmonics with amplitudes and periods of 1845, 152, 58 km and 11.1, 3.7, and 2.2 years, respectively. In this paper we present results from N -body simulations, where we integrated the orbital evolution of a moonlet, which is placed at the radial position of Blériot under the gravitational action of the Saturnian satellites. Our simulations yield that, especiallymore » the gravitational interactions with Prometheus, Pandora, and Mimas are forcing the moonlet to librate with the right frequencies, but the libration amplitudes are too small to explain the observations. Thus, further mechanisms are needed to explain the amplitudes of the forced librations—e.g., moonlet–ring interactions. Here, we develop a model, where the moonlet is allowed to be slightly displaced with respect to its created gaps breaking the point symmetry and causing a repulsive force in this way. As a result, the evolution of the moonlet’s longitude can be described by a harmonic oscillator. In the presence of external forcing by the outer moons, the libration amplitudes get the more amplified the closer the forcing frequency is to the eigenfrequency of the disturbed propeller oscillator. Applying our model to Blériot, it is possible to reproduce a libration period of 13 years with an amplitude of about 2000 km.« less

Libration Point Orbit Utilization for Tactical Advantage in Communications, Surveillance, and Risk Mitigation

DTIC Science & Technology

2014-10-27

Ephemeris model in the orbit analysis software Satellite Took Kit ( STK ). As the first step, a study was conducted to find the visibility coverage using...northern L1 and L3 halo orbits. Figure 55. Average visibility by latitude at different ephemeris epochs for an L1 orbiter from STK analysis . Figure...56. Average visibility by latitude at different ephemeris epochs for an L3 orbiter from STK analysis . Figure 57. Average percent visibility of the

The long-period librations of large synchronous icy moons

NASA Astrophysics Data System (ADS)

Yseboodt, Marie; Van Hoolst, Tim

2014-11-01

A moon in synchronous rotation has longitudinal librations because of its non-spherical mass distribution and its elliptical orbit around the planet. We study the long-period librations of the Galilean satellites and Titan and include deformation effects and the existence of a subsurface ocean. We take into account the fact that the orbit is not keplerian and has other periodicities than the main period of orbital motion around Jupiter or Saturn due to perturbations by the Sun, other planets and moons. An orbital theory is used to compute the orbital perturbations due to these other bodies. For Titan we also take into account the large atmospheric torque at the semi-annual period of Saturn around the Sun.We numerically evaluate the amplitude and phase of the long-period librations for many interior structure models of the icy moons constrained by the mass, radius and gravity field.

An Astronomical Glossary.

DTIC Science & Technology

1980-02-12

planet across the limb of the Sun at the end of a transit. Elements of an Orbit - See orbital elements . Elevation - The height of a point on the...That component of libration due to variations in the geometric position of the Earth relative to the Moon. 71 ś" Orbital Elements - The quantities which...completely describe the size, shape, and orientation of an object’s orbit as well as its location in it. The classical set consists of the semi-major

Phobos' gravity field and its influence on its orbit and physical librations

NASA Technical Reports Server (NTRS)

Borderies, N.; Yoder, C. F.

1990-01-01

A model describing the physical libration in longitude and latitude for Phobos is derived. The major effect is the well-known longitude variation with the anomalistic orbital period and amplitude. Several additional meter-sized periodic librations in longitude exist. The latitude variation is dominated by the forced precession of Phobos' figure axis with the precession of Phobos' orbital plane. The contribution of Phobos' topography to its gravity field is estimated using the control network model of Duxbury and Callahan (1989).

Fuel-optimal, low-thrust transfers between libration point orbits

NASA Astrophysics Data System (ADS)

Stuart, Jeffrey R.

Mission design requires the efficient management of spacecraft fuel to reduce mission cost, increase payload mass, and extend mission life. High efficiency, low-thrust propulsion devices potentially offer significant propellant reductions. Periodic orbits that exist in a multi-body regime and low-thrust transfers between these orbits can be applied in many potential mission scenarios, including scientific observation and communications missions as well as cargo transport. In light of the recent discovery of water ice in lunar craters, libration point orbits that support human missions within the Earth-Moon region are of particular interest. This investigation considers orbit transfer trajectories generated by a variable specific impulse, low-thrust engine with a primer-vector-based, fuel-optimizing transfer strategy. A multiple shooting procedure with analytical gradients yields rapid solutions and serves as the basis for an investigation into the trade space between flight time and consumption of fuel mass. Path and performance constraints can be included at node points along any thrust arc. Integration of invariant manifolds into the design strategy may also yield improved performance and greater fuel savings. The resultant transfers offer insight into the performance of the variable specific impulse engine and suggest novel implementations of conventional impulsive thrusters. Transfers incorporating invariant manifolds demonstrate the fuel savings and expand the mission design capabilities that are gained by exploiting system symmetry. A number of design applications are generated.

Constraints on Titan rotation from Cassini radar

NASA Astrophysics Data System (ADS)

Bills, B. G.; Stiles, B. W.; Kirk, R. L.

2014-12-01

We give an update on efforts to model the rotation of Titan, subject to constraints from Cassini radar observations. The data we are currently using includes 670 tie-points, each of which is a pair of inertial positions of a single surface point, relative to the center of mass of Titan, and the corresponding pair of observation times. The positional accuracy is of order 1 km, in each Cartesian component. A reasonably good fit to the observations is obtained with a simple model which has a fixed spin pole and a rotation rate which is a sum of a constant value and a single sinusoidal oscillation. A better fit is obtained if we insist that Titan should behave as a synchronous rotator, in the dynamical sense of keeping its axis of least inertia oriented toward Saturn. At the level of accuracy required to fit the Cassini radar data, synchronous rotation is notably different than having a uniform rate of rotation. In this case, we need to model time variations in the orbital mean longitude, which is the longitude of periapse, plus the mean anomaly. That angle varies on a wide range of times scales, including Titan's periapse precession period (703 years), Saturn's heliocentric orbital period (29.47 years), perturbations from relatively large satellites Iapetus (79.3 days), and a 4:3 mean motion resonant interaction with Hyperion (640 and 6850 days), and a linear increase at Titan's mean orbital period (15.9455 day). Our rotation model for Titan has 4 free parameters. Two of them specify the orientation of the fixed spin pole, and the other two are the effective free libration period and viscous damping time. Our dynamical model includes a damped forced longitudinal libration, in which gravitational torques attempt to align the axis of least inertia with the instantaneous direction to Saturn. For a rigid tri-axial body, with Titan's moments of inertia, the free oscillation period for longitudinal librations would be 850 days. For a decoupled elastic shell, the effective period is likely somewhat less. Variations in angular position of Saturn, as seen from Titan, with periods shorter than the free libration period, will not be accurately tracked. Thus the short period (one and two cycles per orbit) forced librations will be very small (~50 m), and are, in any event, not well sampled in the data.

Design of the stabilizing control of the orbital motion in the vicinity of the collinear libration point L1 using the analytical representation of the invariant manifold

NASA Astrophysics Data System (ADS)

Maliavkin, G. P.; Shmyrov, A. S.; Shmyrov, V. A.

2018-05-01

Vicinities of collinear libration points of the Sun-Earth system are currently quite attractive for the space navigation. Today, various projects on placing of spacecrafts observing the Sun in the L1 libration point and telescopes in L2 have been implemented (e.g. spacecrafts "WIND", "SOHO", "Herschel", "Planck"). Collinear libration points being unstable leads to the problem of stabilization of a spacecraft's motion. Laws of stabilizing motion control in vicinity of L1 point can be constructed using the analytical representation of a stable invariant manifold. Efficiency of these control laws depends on the precision of the representation. Within the model of Hill's approximation of the circular restricted three-body problem in the rotating geocentric coordinate system one can obtain the analytical representation of an invariant manifold filled with bounded trajectories in a form of series in terms of powers of the phase variables. Approximate representations of the orders from the first to the fourth inclusive can be used to construct four laws of stabilizing feedback motion control under which trajectories approach the manifold. By virtue of numerical simulation the comparison can be made: how the precision of the representation of the invariant manifold influences the efficiency of the control, expressed by energy consumptions (characteristic velocity). It shows that using approximations of higher orders in constructing the control laws can significantly reduce the energy consumptions on implementing the control compared to the linear approximation.

Long Term Missions at the Sun-Earth Libration Point L1: ACE, SOHO, and WIND

NASA Technical Reports Server (NTRS)

Roberts, Craig E.

2011-01-01

Three heliophysics missions -- the Advanced Composition Explorer (ACE), Solar Heliospheric Observatory (SOHO), and the Global Geoscience WIND -- have been orbiting the Sun-Earth interior libration point L1 continuously since 1997, 1996, and 2004, respectively. ACE and WIND (both NASA missions) and SOHO (an ESA-NASA joint mission) are all operated from the NASA Goddard Space Flight Center (GSFC). While ACE and SOHO have been dedicated libration point orbiters since their launches, WIND has had also a remarkable 10-year career flying a deep-space, multiple lunar-flyby trajectory prior to 2004. That era featured 36 targeted lunar flybys with excursions to both L1 and L2 before its final insertion in L1 orbit. A figure depicts the orbits of the three spacecraft, showing projections of the orbits onto the orthographic planes of a solar rotating ecliptic frame of reference. The SOHO orbit is a quasi-periodic halo orbit, where the frequencies of the in-plane and out-of-plane motions are practically equal. Such an orbit is seen to repeat itself with a period of approximately 178 days. For ACE and WIND, the frequencies of the in-plane and out-of-plane motions are unequal, giving rise to the characteristic Lissajous motion. ACE's orbit is of moderately small amplitude, whereas WIND's orbit is a large-amplitude Lissajous of dimensions close to those of the SOHO halo orbit. As motion about the collinear points is inherently unstable, stationkeeping maneuvers are necessary to prevent orbital decay and eventual escape from the L1 region. Though the three spacecraft are dissimilar (SOHO is a 3-axis stabilized Sun pointer, WIND is a spin-stabilized ecliptic pole pointer, and ACE is also spin-stabilized with its spin axis maintained between 4 and 20 degrees of the Sun), the stationkeeping technique for the three is fundamentally the same. The technique consists of correcting the energy of the orbit via a delta-V directed parallel or anti-parallel to the Spacecraft-to-Sun line. SOHO achieves this using thrusters oriented in line with the solar direction. WIND achieves the delta-V via pulsing radial thrusters when aligned with the Sun. ACE uses axial thrusters to apply delta-V with a component that is 94% or more aligned with the ACE-Sun line. Sunward thrust adds energy to the orbit preventing decay back toward Earth. Thrust directed anti-Sunward takes energy out of the L1 orbit, thereby preventing escape from the Earth-Moon system into independent heliocentric orbit. Libration point orbit stationkeeping delta-V costs grow exponentially with time elapsed from the last maneuver performed. The doubling time constant is approximately 16 days. For the sake of fuel conservation, and for limiting the absolute magnitude of propulsion performance errors, stationkeeping maneuvers should be performed before the delta-V grows too large; for our purposes 'too large' is considered to be greater than 0.5 m/sec. In practice, the typical interval between burns for this trio is about three months, and the typical delta-V is much smaller than 0.5 m/sec. Typical annual stationkeeping costs have been around 1.0 m/sec for ACE and WIND, and much less than that for SOHO. All three spacecraft have ample fuel remaining; barring contingencies all three could, in principle, be maintained at L1 for decades to come. This paper will review the L1 orbits and the mission history of ACE, WIND, and SOHO, and describe the stationkeeping techniques and orbit maneuver experience. The Lissajous phase control that was practiced for ACE during the period from 1999 to 2001 will also be briefly discussed. The final section will consider the future of these ongoing missions.

Multi-Body Orbit Architectures for Lunar South Pole Coverage

NASA Technical Reports Server (NTRS)

Grebow, D. J.; Ozimek, M. T.; Howell, K. C.; Folta, D. C.

2006-01-01

A potential ground station at the lunar south pole has prompted studies of orbit architectures that ensure adequate coverage. Constant communications can be achieved with two spacecraft in different combinations of Earth-Moon libration point orbits. Halo and vertical families, as well as other orbits near L1 and L2 are considered. The investigation includes detailed results using nine different orbits with periods ranging from 7 to 16 days. Natural solutions are generated in a full ephemeris model, including solar perturbations. A preliminary station-keeping analysis is also completed.

Lissajous Orbit Control for the Deep Space Climate Observatory Sun-Earth L1 Libration Point Mission

NASA Technical Reports Server (NTRS)

Roberts, Craig; Case, Sarah; Reagoso, John

2015-01-01

DSCOVR Lissajous Orbit sized such that orbit track never extends beyond 15 degrees from Earth-Sun line (as seen from Earth). Requiring delta-V maneuvers, control orbit to obey a Solar Exclusion Zone (SEZ) cone of half-angle 4 degrees about the Earth-Sun line. Spacecraft should never be less than 4 degrees from solar center as seen from Earth. Following Lissajous Orbit Insertion (LOI), DSCOVR should be in an opening phase that just skirts the 4-degree SEZ. Maximizes time to the point where a closing Lissajous will require avoidance maneuvers to keep it out of the SEZ. Station keeping maneuvers should take no more than 15 minutes.

Orbit determination error analysis and comparison of station-keeping costs for Lissajous and halo-type libration point orbits and sensitivity analysis using experimental design techniques

NASA Technical Reports Server (NTRS)

Gordon, Steven C.

1993-01-01

Spacecraft in orbit near libration point L1 in the Sun-Earth system are excellent platforms for research concerning solar effects on the terrestrial environment. One spacecraft mission launched in 1978 used an L1 orbit for nearly 4 years, and future L1 orbital missions are also being planned. Orbit determination and station-keeping are, however, required for these orbits. In particular, orbit determination error analysis may be used to compute the state uncertainty after a predetermined tracking period; the predicted state uncertainty levels then will impact the control costs computed in station-keeping simulations. Error sources, such as solar radiation pressure and planetary mass uncertainties, are also incorporated. For future missions, there may be some flexibility in the type and size of the spacecraft's nominal trajectory, but different orbits may produce varying error analysis and station-keeping results. The nominal path, for instance, can be (nearly) periodic or distinctly quasi-periodic. A periodic 'halo' orbit may be constructed to be significantly larger than a quasi-periodic 'Lissajous' path; both may meet mission requirements, but perhaps the required control costs for these orbits are probably different. Also for this spacecraft tracking and control simulation problem, experimental design methods can be used to determine the most significant uncertainties. That is, these methods can determine the error sources in the tracking and control problem that most impact the control cost (output); it also produces an equation that gives the approximate functional relationship between the error inputs and the output.

Cislunar Near Rectilinear Halo Orbit for Human Space Exploration

NASA Technical Reports Server (NTRS)

Whitley, Ryan; Martinez, Roland; Condon, Gerald; Williams, Jacob; Lee, David; Davis, Diane; Barton, Gregg; Bhatt, Sagar; Jang, Jiann-Woei; Clark, Fred;

TYCHO: Demonstrator and operational satellite mission to Earth-Moon-Libration point EML-4 for communication relay provision as a service

NASA Astrophysics Data System (ADS)

Hornig, Andreas; Homeister, Maren

2015-03-01

In the current wake of mission plans to the Moon and to Earth-Moon Libration points (EML) by several agencies and organizations, TYCHO identifies the key role of telecommunication provision for the future path of lunar exploration. It demonstrates an interesting extension to existing communication methods to the Moon and beyond by combining innovative technology with a next frontier location and the commercial space communication sector. It is evident that all communication systems will rely on direct communication to Earth ground stations. In case of EML-2 missions around HALO orbits or bases on the far side of the Moon, it has to be extended by communication links via relay stations. The innovative approach is that TYCHO provides this relay communication to those out-of-sight lunar missions as a service. TYCHO will establish a new infrastructure for future missions and even create a new market for add-on relay services. The TMA-0 satellite is TYCHO's first phase and a proposed demonstrator mission to the Earth-Moon Libration point EML-4. It demonstrates relay services needed for automated exploratory and manned missions (Moon bases) on the rim (>90°E and >90°W) and far side surface, to lunar orbits and even to EML-2 halo orbits (satellites and space stations). Its main advantage is the permanent availability of communication coverage. This will provide full access to scientific and telemetry data and furthermore to crucial medical monitoring and safety. The communication subsystem is a platform for conventional communication but also a test-bed for optical communication with high data-rate LASER links to serve the future needs of manned bases and periodic burst data-transfer from lunar poles. The operational TMA-1 satellite is a stand-alone mission integrated into existing space communication networks to provide open communication service to external lunar missions. Therefore the long-time stable libration points EML-4 and -5 are selected to guarantee an operation time of up to 10 years. It also enables measurements of the libration point environment with the scientific payloads. This includes sensors for space dust, solar and cosmic radiation activity for satellite lifetime estimation and lunar crew protection by providing early-warning systems. The paper describes the mission concept and the pre-design of the demonstrator satellite according to the operational mission requirements, advantages and benefits of this service. The concept was awarded with the Space Generation Advisory Council and OHB Scholarship in 2011 and the concept study is conducted at the Institute of Space Systems (IRS) [1] of the University of Stuttgart and OHB-System, Bremen [2].

Formations Near the Libration Points: Design Strategies Using Natural and Non-Natural Arcs

NASA Technical Reports Server (NTRS)

Howell, K. C.; Marchand, B. G.

2004-01-01

Space based observatory and interferometry missions, such as Terrestrial Planet Finder (TPF), Stellar Imager, and MAXIM, have sparked great interest in multi-spacecraft formation flight in the vicinity of the Sun-Earth/Moon (SEM) libration points. The initial phase of this research considered the formation keeping problem from the perspective of continuous control as applied to non-natural formations. In the present study, closer inspection of the flow, corresponding to the stable and center manifolds near the reference orbit, reveals some interesting natural relative motions as well as some discrete control strategies for deployment. A hybrid control strategy is also employed that combines both the natural formation dynamics with non-natural motions via input feedback linearization techniques.

Spaceflight mechanics 1992; Proceedings of the 2nd AAS/AIAA Meeting, Colorado Springs, CO, Feb. 24-26, 1992. Pts. 1 & 2

NASA Astrophysics Data System (ADS)

Diehl, Roger E.; Schinnerer, Ralph G.; Williamson, Walton E.; Boden, Daryl G.

The present conference discusses topics in orbit determination, tethered satellite systems, celestial mechanics, guidance optimization, flexible body dynamics and control, attitude dynamics and control, Mars mission analyses, earth-orbiting mission analysis/debris, space probe mission analyses, and orbital computation numerical analyses. Attention is given to electrodynamic forces for control of tethered satellite systems, orbiting debris threats to asteroid flyby missions, launch velocity requirements for interceptors of short range ballistic missiles, transfers between libration-point orbits in the elliptic restricted problem, minimum fuel spacecraft reorientation, orbital guidance for hitting a fixed point at maximum speed, efficient computation of satellite visibility periods, orbit decay and reentry prediction for space debris, and the determination of satellite close approaches.

Spaceflight mechanics 1992; Proceedings of the 2nd AAS/AIAA Meeting, Colorado Springs, CO, Feb. 24-26, 1992. Pts. 1 & 2

NASA Technical Reports Server (NTRS)

Diehl, Roger E. (Editor); Schinnerer, Ralph G. (Editor); Williamson, Walton E. (Editor); Boden, Daryl G. (Editor)

1992-01-01

The present conference discusses topics in orbit determination, tethered satellite systems, celestial mechanics, guidance optimization, flexible body dynamics and control, attitude dynamics and control, Mars mission analyses, earth-orbiting mission analysis/debris, space probe mission analyses, and orbital computation numerical analyses. Attention is given to electrodynamic forces for control of tethered satellite systems, orbiting debris threats to asteroid flyby missions, launch velocity requirements for interceptors of short range ballistic missiles, transfers between libration-point orbits in the elliptic restricted problem, minimum fuel spacecraft reorientation, orbital guidance for hitting a fixed point at maximum speed, efficient computation of satellite visibility periods, orbit decay and reentry prediction for space debris, and the determination of satellite close approaches.

Trajectory analysis of transfers between L4 and L5 and low lunar orbit

NASA Technical Reports Server (NTRS)

1988-01-01

The flight characteristics and spacecraft performance during missions involving flight between the equilateral libration points and the Moon are discussed. The conclusions drawn will show that a minimum energy trajectory is the most efficient transfer technique for this type of flight.

Dynamics and control of three-body tethered system in large elliptic orbits

NASA Astrophysics Data System (ADS)

Shi, Gefei; Zhu, Zhanxia; Zhu, Zheng H.

2018-03-01

This paper investigates the dynamic characteristics a three-body tethered satellite system in large elliptic orbits and the control strategy to suppress the libration of the system in orbital transfer process. The system is modeled by a two-piece dumbbell model in the domain of true anomaly. The model consists of one main satellite and two subsatellites connected with two straight, massless and inextensible tethers. Two control strategies based on the sliding mode control are developed to control the libration to the zero state and the steady state respectively. The results of numerical simulations show that the proposed control scheme has good performance in controlling the libration motion of a three-body tethered satellite system in an elliptic orbit with large eccentricity by limited control inputs. Furthermore, Hamiltonians in both states are examined and it shows that less control input is required to control the libration motion to the steady state than that of zero state.

Optimal transfers between libration-point orbits in the elliptic restricted three-body problem

NASA Astrophysics Data System (ADS)

Hiday, Lisa Ann

1992-09-01

A strategy is formulated to design optimal impulsive transfers between three-dimensional libration-point orbits in the vicinity of the interior L(1) libration point of the Sun-Earth/Moon barycenter system. Two methods of constructing nominal transfers, for which the fuel cost is to be minimized, are developed; both inferior and superior transfers between two halo orbits are considered. The necessary conditions for an optimal transfer trajectory are stated in terms of the primer vector. The adjoint equation relating reference and perturbed trajectories in this formulation of the elliptic restricted three-body problem is shown to be distinctly different from that obtained in the analysis of trajectories in the two-body problem. Criteria are established whereby the cost on a nominal transfer can be improved by the addition of an interior impulse or by the implementation of coastal arcs in the initial and final orbits. The necessary conditions for the local optimality of a time-fixed transfer trajectory possessing additional impulses are satisfied by requiring continuity of the Hamiltonian and the derivative of the primer vector at all interior impulses. The optimality of a time-free transfer containing coastal arcs is surmised by examination of the slopes at the endpoints of a plot of the magnitude of the primer vector over the duration of the transfer path. If the initial and final slopes of the primer magnitude are zero, the transfer trajectory is optimal; otherwise, the execution of coasts is warranted. The position and timing of each interior impulse applied to a time-fixed transfer as well as the direction and length of coastal periods implemented on a time-free transfer are specified by the unconstrained minimization of the appropriate variation in cost utilizing a multivariable search technique. Although optimal solutions in some instances are elusive, the time-fixed and time-free optimization algorithms prove to be very successful in diminishing costs on nominal transfer trajectories. The inclusion of coastal arcs on time-free superior and inferior transfers results in significant modification of the transfer time of flight caused by shifts in departure and arrival locations on the halo orbits.

Sun-Earth L1 Region Halo-To-Halo Orbit and Halo-To-LisaJous Orbit Transfers

NASA Technical Reports Server (NTRS)

Roberts, Craig E.; DeFazio, Robert

2004-01-01

Practical techniques for designing transfer trajectories between Libration Point Orbits (LPOs) are presented. Motivation for development of these techniques was provided by a hardware contingency experienced by the Solar Heliospheric Observatory (SOHO), a joint mission of the European Space Agency (ESA) and the National Aeronautics and Space Administration (NASA) orbiting the L1 point of the Sun-Earth system. A potential solution to the problem involved a transfer from SOHO s periodic halo orbit to a new LPO of substantially different dimensions. Assuming the SOHO halo orbit as the departure orbit, several practical LPO transfer techniques were developed to obtain new Lissajous or periodic halo orbits that satisfy mission requirements and constraints. While not implemented for the SOHO mission, practical LPO transfer techniques were devised that are generally applicable to current and future LPO missions.

End of Life Disposal for Three Libration Point Missions through Manipulation of the Jacobi Constant and Zero Velocity Curves

NASA Technical Reports Server (NTRS)

Petersen, Jeremy; Brown, Jonathan

2015-01-01

Flight Dynamics Facility (FDF) located at NASA Goddard Space Flight Center (GSFC) provides the flight dynamics expertise for three Sun-Earth Moon L1 missions. Advanced Composition Explorer (ACE) launched August 1997 Solar and Heliospheric Observatory (SOHO) launched December 1995 Global Geospace Science WIND satellite launched November 1994 entered Lagrange point orbit in 2004.

Orbit Maintenance and Navigation of Human Spacecraft at Cislunar Near Rectilinear Halo Orbits

NASA Technical Reports Server (NTRS)

Davis, Diane; Bhatt, Sagar; Howell, Kathleen; Jang, Jiann-Woei; Whitley, Ryan; Clark, Fred; Guzzetti, Davide; Zimovan, Emily; Barton, Gregg

2017-01-01

Multiple studies have concluded that Earth-Moon libration point orbits are attractive candidates for staging operations. The Near Rectilinear Halo Orbit (NRHO), a member of the Earth-Moon halo orbit family, has been singularly demonstrated to meet multi-mission architectural constraints. In this paper, the challenges associated with operating human spacecraft in the NRHO are evaluated. Navigation accuracies and human vehicle process noise effects are applied to various station keeping strategies in order to obtain a reliable orbit maintenance algorithm. Additionally, the ability to absorb missed burns, construct phasing maneuvers to avoid eclipses and conduct rendezvous and proximity operations are examined.

Transfer to the Collinear Libration Point L3 in the Sun-Earth+Moon System

NASA Technical Reports Server (NTRS)

Hou, Xi-yun; Tang, Jing-shi; Liu, Lin

2007-01-01

The collinear libration point L3 of the sun-earth+moon system is an ideal place for some space missions. Although there has been a great amount of work concerning the applications of the other two collinear libration points L1 and L2, little work has been done about the point L3. In this paper, the dynamics of the libration points was briefly introduced first. Then a way to transfer the spacecraft to the collinear libration point L3 via the invariant manifolds of the other two collinear libration points was proposed. Theoretical works under the model of circular restricted three-body problem were done. For the sun-earth+moon system, this model is a good approximation. The results obtained are useful when a transfer trajectory under the real solar system is designed.

An Approach to Optimal Control of Electrodynamic Tethers in a Stochastically Varying Drag Environment

DTIC Science & Technology

2011-05-06

and used to help address some of the complications and drawbacks of chemical propulsion systems. One such technology is electric propulsion, which...in and out of the orbital plane around its equilibrium point. The motion is similar to a swinging pendulum . These librations are due to the

The rotation of Io

NASA Astrophysics Data System (ADS)

Henrard, Jacques

2005-11-01

The paper develops, in the framework of Hamiltonian mechanics, a theory of the rotation of Io, considered as a rigid body. The theory includes the perturbation due to Jupiter (considered as an oblate body) and the indirect perturbations due to the other Galilean satellites. In order to describe the orbit of Io around Jupiter, we use the synthetic theory of Lainey [2002, PhD dissertation, Observatoire de Paris], the result of a frequency analysis of a numerically integrated jovian system. The direct effects of the other Galilean satellites are found to be negligible, but their indirect effects are important. Our theory is consistent with the rigid body model and with Lainey's description of the orbit of Io, at least down to 10 rad (0.2 arc-second). Of course the effects of the nonrigidity of Io and of a probable liquid core should be considered. We find a mean obliquity of 7.619×10 rad (157 arc-second) and the period of the three free librations to be 13.25 days (free libration in longitude), 159.39 days (free libration in latitude), and 229.85 days (free wobble). Fourier series are produced describing, in the body frame, the motion of the polar axis of Jupiter, the motion of the unit vector pointing toward Jupiter, and the "motion of the pole" (the motion of the angular momentum with respect to the axis of largest inertia). Free librations (depending on three arbitrary parameters) are also computed.

CARE AND FEEDING OF FROGS

DOE Office of Scientific and Technical Information (OSTI.GOV)

Pan, Margaret; Chiang, Eugene, E-mail: mpan@astro.berkeley.edu

2012-01-15

'Propellers' are features in Saturn's A ring associated with moonlets that open partial gaps. They exhibit non-Keplerian motion (Tiscareno et al.); the longitude residuals of the best-observed propeller, 'Bleriot', appear consistent with a sinusoid of period {approx}4 years. Pan and Chiang proposed that propeller moonlets librate in 'frog resonances' with co-orbiting ring material. By analogy with the restricted three-body problem, they treated the co-orbital material as stationary in the rotating frame and neglected non-co-orbital material. Here we use simple numerical experiments to extend the frog model, including feedback due to the gap's motion, and drag associated with the Lindblad diskmore » torques that cause Type I migration. Because the moonlet creates the gap, we expect the gap centroid to track the moonlet, but only after a time delay t{sub delay}, the time for a ring particle to travel from conjunction with the moonlet to the end of the gap. We find that frog librations can persist only if t{sub delay} exceeds the frog libration period P{sub lib}, and if damping from Lindblad torques balances driving from co-orbital torques. If t{sub delay} << Pl{sub ib}, then the libration amplitude damps to zero. In the case of Bleriot, the frog resonance model can reproduce the observed libration period P{sub lib} {approx_equal} 4 yr. However, our simple feedback prescription suggests that Bleriot's t{sub delay} {approx} 0.01P{sub lib}, which is inconsistent with the observed libration amplitude of 260 km. We urge more accurate treatments of feedback to test the assumptions of our toy models.« less

Anti-sway control of tethered satellite systems using attitude control of the main satellite

NASA Astrophysics Data System (ADS)

Yousefian, Peyman; Salarieh, Hassan

2015-06-01

In this study a new method is introduced to suppress libration of a tethered satellite system (TSS). It benefits from coupling between satellites and tether libration dynamics. The control concept uses the main satellite attitude maneuvers to suppress librational motion of the tether, and the main satellite's actuators for attitude control are used as the only actuation in the system. The study considers planar motion of a two body TSS system in a circular orbit and it is assumed that the tether's motion will not change it. Governing dynamic equations of motion are derived using the extended Lagrange method. Controllability of the system around the equilibrium state is studied and a linear LQG controller is designed to regulate libration of the system. Tether tension and satellite attitude are assumed as only measurable outputs of the system. The Extended Kalman Filter (EKF) is used to estimate states of the system to be used as feedback to the controller. The designed controller and observer are implemented to the nonlinear plant and simulations demonstrate that the controller lead to reduction of the tether libration propoerly. By the way, because the controller is linear, it is applicable only at low amplitudes in the vicinity of equilibrium point. To reach global stability, a nonlinear controller is demanded.

Non-collinear libration points in ER3BP with albedo effect and oblateness

NASA Astrophysics Data System (ADS)

Idrisi, M. Javed; Ullah, M. Shahbaz

2018-06-01

In this paper we establish a relation between direct radiations (generally called radiation factor) and reflected radiations (albedo) to show their effects on the existence and stability of non-collinear libration points in the elliptic restricted three-body problem taking into account the oblateness of smaller primary. It is discussed briefly when α =0 and σ =0, the non-collinear libration points form an isosceles triangle with the primaries and as e increases the libration points L_{4,5} move vertically downward (α , σ and e represents the radiation factor, oblateness factor and eccentricity of the primaries respectively). If α = 0 but σ ≠ 0, the libration points slightly displaced to the right-side from its previous location and form scalene triangle with the primaries and go vertically downward as e increases. If α ≠ 0 and σ ≠ 0, the libration points L_{4,5} form scalene triangle with the primaries and as e increases L_{4,5} move downward and displaced to the left-side. Also, the libration points L_{4,5} are stable for the critical mass parameter μ ≤ μ c.

Mission Architecture Comparison for Human Lunar Exploration

NASA Technical Reports Server (NTRS)

Geffre, Jim; Robertson, Ed; Lenius, Jon

2006-01-01

The Vision for Space Exploration outlines a bold new national space exploration policy that holds as one of its primary objectives the extension of human presence outward into the Solar System, starting with a return to the Moon in preparation for the future exploration of Mars and beyond. The National Aeronautics and Space Administration is currently engaged in several preliminary analysis efforts in order to develop the requirements necessary for implementing this objective in a manner that is both sustainable and affordable. Such analyses investigate various operational concepts, or mission architectures , by which humans can best travel to the lunar surface, live and work there for increasing lengths of time, and then return to Earth. This paper reports on a trade study conducted in support of NASA s Exploration Systems Mission Directorate investigating the relative merits of three alternative lunar mission architecture strategies. The three architectures use for reference a lunar exploration campaign consisting of multiple 90-day expeditions to the Moon s polar regions, a strategy which was selected for its high perceived scientific and operational value. The first architecture discussed incorporates the lunar orbit rendezvous approach employed by the Apollo lunar exploration program. This concept has been adapted from Apollo to meet the particular demands of a long-stay polar exploration campaign while assuring the safe return of crew to Earth. Lunar orbit rendezvous is also used as the baseline against which the other alternate concepts are measured. The first such alternative, libration point rendezvous, utilizes the unique characteristics of the cislunar libration point instead of a low altitude lunar parking orbit as a rendezvous and staging node. Finally, a mission strategy which does not incorporate rendezvous after the crew ascends from the Moon is also studied. In this mission strategy, the crew returns directly to Earth from the lunar surface, and is thus referred to as direct return. Figures of merit in the areas of safety and mission success, mission effectiveness, extensibility, and affordability are used to evaluate and compare the lunar orbit rendezvous, libration point rendezvous, and direct return architectures, and this paper summarizes the results of those assessments.

Adaptive surrogate model based multi-objective transfer trajectory optimization between different libration points

NASA Astrophysics Data System (ADS)

Peng, Haijun; Wang, Wei

2016-10-01

An adaptive surrogate model-based multi-objective optimization strategy that combines the benefits of invariant manifolds and low-thrust control toward developing a low-computational-cost transfer trajectory between libration orbits around the L1 and L2 libration points in the Sun-Earth system has been proposed in this paper. A new structure for a multi-objective transfer trajectory optimization model that divides the transfer trajectory into several segments and gives the dominations for invariant manifolds and low-thrust control in different segments has been established. To reduce the computational cost of multi-objective transfer trajectory optimization, a mixed sampling strategy-based adaptive surrogate model has been proposed. Numerical simulations show that the results obtained from the adaptive surrogate-based multi-objective optimization are in agreement with the results obtained using direct multi-objective optimization methods, and the computational workload of the adaptive surrogate-based multi-objective optimization is only approximately 10% of that of direct multi-objective optimization. Furthermore, the generating efficiency of the Pareto points of the adaptive surrogate-based multi-objective optimization is approximately 8 times that of the direct multi-objective optimization. Therefore, the proposed adaptive surrogate-based multi-objective optimization provides obvious advantages over direct multi-objective optimization methods.

Secondary resonances and the boundary of effective stability of Trojan motions

NASA Astrophysics Data System (ADS)

Páez, Rocío Isabel; Efthymiopoulos, Christos

2018-02-01

One of the most interesting features in the libration domain of co-orbital motions is the existence of secondary resonances. For some combinations of physical parameters, these resonances occupy a large fraction of the domain of stability and rule the dynamics within the stable tadpole region. In this work, we present an application of a recently introduced `basic Hamiltonian model' H_b for Trojan dynamics (Páez and Efthymiopoulos in Celest Mech Dyn Astron 121(2):139, 2015; Páez et al. in Celest Mech Dyn Astron 126:519, 2016): we show that the inner border of the secondary resonance of lowermost order, as defined by H_b, provides a good estimation of the region in phase space for which the orbits remain regular regardless of the orbital parameters of the system. The computation of this boundary is straightforward by combining a resonant normal form calculation in conjunction with an `asymmetric expansion' of the Hamiltonian around the libration points, which speeds up convergence. Applications to the determination of the effective stability domain for exoplanetary Trojans (planet-sized objects or asteroids) which may accompany giant exoplanets are discussed.

Natural motion around the Martian moon Phobos: the dynamical substitutes of the Libration Point Orbits in an elliptic three-body problem with gravity harmonics

NASA Astrophysics Data System (ADS)

Zamaro, M.; Biggs, J. D.

2015-07-01

The Martian moon Phobos is becoming an appealing destination for future scientific missions. The orbital dynamics around this planetary satellite is particularly complex due to the unique combination of both small mass-ratio and length-scale of the Mars-Phobos couple: the resulting sphere of influence of the moon is very close to its surface, therefore both the classical two-body problem and circular restricted three-body problem (CR3BP) do not provide an accurate approximation to describe the spacecraft's dynamics in the vicinity of Phobos. The aim of this paper is to extend the model of the CR3BP to consider the orbital eccentricity and the highly-inhomogeneous gravity field of Phobos, by incorporating the gravity harmonics series expansion into an elliptic R3BP, named ER3BP-GH. Following this, the dynamical substitutes of the Libration Point Orbits (LPOs) are computed in this more realistic model of the relative dynamics around Phobos, combining methodologies from dynamical systems theory and numerical continuation techniques. Results obtained show that the structure of the periodic and quasi-periodic LPOs differs substantially from the classical case without harmonics. Several potential applications of these natural orbits are presented to enable unique low-cost operations in the proximity of Phobos, such as close-range observation, communication, and passive radiation shielding for human spaceflight. Furthermore, their invariant manifolds are demonstrated to provide high-performance natural landing and take-off pathways to and from Phobos' surface, and transfers from and to Martian orbits. These orbits could be exploited in upcoming and future space missions targeting the exploration of this Martian moon.

Trajectory design for Saturnian Ocean Worlds orbiters using multidimensional Poincaré maps

NASA Astrophysics Data System (ADS)

Davis, Diane Craig; Phillips, Sean M.; McCarthy, Brian P.

2018-02-01

Missions based on low-energy orbits in the vicinity of planetary moons, such as Titan or Enceladus, involve significant end-to-end trajectory design challenges due to the gravitational effects of the distant larger primary. To address these challenges, the current investigation focuses on the visualization and use of multidimensional Poincaré maps to perform preliminary design of orbits with significant out-of-plane components, including orbits that provide polar coverage. Poincaré maps facilitate the identification of families of solutions to a given orbit problem and provide the ability to easily respond to changing inputs and requirements. A visual-based design process highlights a variety of trajectory options near Saturn's ocean worlds, including both moon-centered orbits and libration point orbits.

Proposed gravity-gradient dynamics experiments in lunar orbit using the RAE-B spacecraft

NASA Technical Reports Server (NTRS)

Blanchard, D. L.; Walden, H.

1973-01-01

A series of seven gravity-gradient dynamics experiments is proposed utilizing the Radio Astronomy Explorer (RAE-B) spacecraft in lunar orbit. It is believed that none of the experiments will impair the spacecraft structure or adversely affect the continuation of the scientific mission of the satellite. The first experiment is designed to investigate the spacecraft dynamical behavior in the absence of libration damper action and inertia. It requires stable gravity-gradient capture of the spacecraft in lunar orbit with small amplitude attitude librations as a prerequisite. Four subsequent experiments involve partial retraction, ultimately followed by full redeployment, of one or two of the 230-meter booms forming the lunar-directed Vee-antenna. These boom length change operations will induce moderate amplitude angular librations of the spacecraft.

Spacecraft formation keeping near the libration points of the Sun-Earth/Moon system

NASA Astrophysics Data System (ADS)

Marchand, Belinda G.

Multi-spacecraft formations, evolving near the vicinity of the libration points of the Sun-Earth/Moon system, have drawn increased interest for a variety of applications. This is particularly true for space based interferometry missions such as Terrestrial Planet Finder (TPF) and the Micro Arcsecond X-Ray Imaging Mission (MAXIM). Recent studies in formation flight have focused, primarily, on the control of formations that evolve in the immediate vicinity of the Earth. However, the unique dynamical structure near the libration points requires that the effectiveness and feasibility of these methods be re-examined. The present study is divided into two main topics. First, a dynamical systems approach is employed to develop a better understanding of the natural uncontrolled formation dynamics in this region of space. The focus is formations that evolve near halo orbits and Lissajous trajectories, near the L1 and L2 libration points of the Sun-Earth/Moon system. This leads to the development of a Floquet controller designed to simplify the process of identifying naturally existing formations as well as the associated stable manifolds for deployment. The initial analysis is presented in the Circular Restricted Three-Body Problem, but the results are later transitioned into the more complete Ephemeris model. The next subject of interest in this investigation is non-natural formations. That is, formations that are not consistent with the natural dynamical flow near the libration points. Mathematically, precise formation keeping of a given nominal configuration requires continuous control. Hence, a detailed analysis is presented to contrast the effectiveness and issues associated with linear optimal control and feedback linearization methods. Of course, continuous operation of the thrusters, may not represent a feasible option for a particular mission. If discrete formation keeping is implemented, however, the formation keeping goal will be subject to increased tracking errors relative to the nominal path. With this in mind, the final phase of the analysis presented here is centered on discrete formation keeping. The initial analysis is devoted to both linear state and radial targeters. The results from these two methodologies are later employed as a starting solution for an optimal impulsive control algorithm.

Using Cassini CIRS Data to Constrain Enceladus' Libration State

NASA Technical Reports Server (NTRS)

Hurford, T. A.; Helfenstein, P.; Spencer, J. R.; Nimmo, F.

2009-01-01

Given the non-spherical shape of Enceladus, the satellite may experience gravitational torques that will cause it to physically librate as it orbits Saturn. Physical Libration would produce a diurnal oscillation in the longitude of Enceladus' tidal bulge, which could have a profound effect on the diurnal stresses experienced by the surface of the satellite. Although Cassini ISS has placed an observational upper limit on Enceladus' libration amplitude, small amplitude librations may have geologically significant consequences. For example, a physical libration will affect heat production. along the tiger stripes as produced by tidal shear heating. We have modeled the expected power en-litted along the tiger stripes for various types of physical libration and have quantified which types of physical libration best reproduce the observed power flux as detailed in Cassini CIRS data. We find that including a physical libration does allow better fits to the observations and we have identified regions of the libration phase space that where these fits are optimized. A physical libration has important implications for tidal dissipation within Enceladus and if identified may provide an additional constraint on its interior mass distribution.

Using Cassini CIRS Data to Constrain Enceladus' Libration State

NASA Technical Reports Server (NTRS)

Hurford, T. A.; Helfenstein, P.; Spencer, J. R.; Nimmo, P.

2010-01-01

Given the non-spherical shape of Enceladus, the satellite may experience gravitational torques that will cause it to physically librate as it orbits Saturn. Physical libration would produce a diurnal oscillation in the longitude of Enceladus' tidal bulge, which could have a profound effect on the diurnal stresses experienced by the surface of the satellite. Although Cassini ISS has placed an observational upper limit on Enceladus' libration amplitude, small amplitude librations may have geologically significant consequences. For example, a physical libration will affect heat production along the tiger stripes as produced by tidal shear heating. We have modeled the expected power emitted along the tiger stripes for various types of physical libration and have quantified which types of physical libration best reproduce the observed power f1ux as detailed in Cassini CIRS data. We find that including a physical libration does allow better fits to the observations and we have identified regions of the libration phase space that where these fits are optimized. A physical libration has important implications for tidal dissipation within Ence1adus and if identified may provide an additional constraint on its interior mass distribution.

Understanding the Sun-Earth Libration Point Orbit Formation Flying Challenges For WFIRST and Starshade

NASA Technical Reports Server (NTRS)

Webster, Cassandra M.; Folta, David C.

2017-01-01

In order to fly an occulter in formation with a telescope at the Sun-Earth L2 (SEL2) Libration Point, one must have a detailed understanding of the dy-namics that govern the restricted three body system. For initial purposes, a linear approximation is satisfactory, but operations will require a high-fidelity modeling tool along with strategic targeting methods in order to be successful. This paper focuses on the challenging dynamics of the transfer trajectories to achieve the relative positioning of two spacecraft to fly in formation at SEL2, in our case, the Wide-Field Infrared Survey Telescope (WFIRST) and a proposed Starshade. By modeling the formation transfers using a high fidelity tool, an accurate V approximation can be made to as-sist with the development of the subsystem design required for a WFIRST and Starshade formation flight mission.

ARTEMIS Mission Overview: From Concept to Operations

NASA Technical Reports Server (NTRS)

Folta, David; Sweetser, Theodore

2011-01-01

ARTEMIS (Acceleration, Reconnection, Turbulence and Electrodynamics of the Moon's Interaction with the Sun) repurposed two spacecraft to extend their useful science (Angelopoulos, 2010) by moving them via lunar gravity assists from elliptical Earth orbits to L1 and L2 Earth-Moon libration orbits and then to lunar orbits by exploiting the Earth-Moon-Sun dynamical environment. This paper describes the complete design from conceptual plans using weak stability transfer options and lunar gravity assist to the implementation and operational support of the Earth-Moon libration and lunar orbits. The two spacecraft of the ARTEMIS mission will have just entered lunar orbit at this paper's presentation.

Librations and obliquity of Mercury from the BepiColombo laser altimetry, radio science and camera experiments

NASA Astrophysics Data System (ADS)

Pfyffer, G.; van Hoolst, T.; Dehant, V. M.

2010-12-01

Through its anomalously high uncompressed density implying a metal fraction of 60% or more by mass, Mercury represents an extreme outcome of planetary formation in the inner solar system. The space missions MESSENGER and BepiColombo are expected to advance largely our knowledge of the structure, formation, and evolution of Mercury. In particular, insight into Mercury's deep interior will be obtained from observations of the obliquity, the 88-day forced libration, the planetary induced librations and the degree-two coefficients of the gravity field of Mercury. We report here on aspects of the observational strategy of ESA’s BepiColombo mission to determine the libration amplitude and obliquity, taking into account the space as well as the ground segment of the experiment. Repeated photographic measurements of selected target positions on the surface of Mercury are central to the strategy to determine the obliquity and libration in the frame of the BepiColombo mission, but a significant constraint is posed by the fact that the planetary surface can only be photographed under very strict illumination conditions. We therefore study the possibility to use the information embedded in the groundtrack crossings (crosstracks) of the BepiColombo laser altimeter (BELA) in addition to the primary photographic data in order to estimate the librations and obliquity of Mercury. An advantage of the laser altimetry data is that it does not depend on the solar incidence angle on the surface nor on the presence of specific surface features as required for the camera data in the camera rotation experiment. Both laser and photographic measurements were simulated in a realistic set-up in order to estimate the accuracy of the reconstruction of the orientation and rotational motion of the planet as a function of the amount of measurements made, the number of different targets and crosstrack points considered and their locations on the surface of the planet. Such an analysis requires the use of an accurate model of the rotation of Mercury, which takes into account longitudinal librations additional to the main 88 day libration due to planetary perturbations on Mercury's orbit. Our simulations show that the achievable level of accuracy on the libration amplitude and obliquity will only be sufficient to constrain the size and physical state of the core of Mercury if certain conditions are satisfied. If the orbiter follows the ESA baseline mission scenario, and at least 25 landmarks are imaged at least twice over the mission duration (360 days), the annual libration amplitude and obliquity can be determined with sufficient accuracy. Also the Jupiter induced libration amplitude can pose an additional constraint on the interior of the planet. We will discuss the relative contributions of the different methods will enable us to determine the optimum combinations of the observations with consequences for the mission planning and the instrument performances.

Benchmark Problems for Space Mission Formation Flying

NASA Technical Reports Server (NTRS)

Carpenter, J. Russell; Leitner, Jesse A.; Folta, David C.; Burns, Richard

2003-01-01

To provide a high-level focus to distributed space system flight dynamics and control research, several benchmark problems are suggested for space mission formation flying. The problems cover formation flying in low altitude, near-circular Earth orbit, high altitude, highly elliptical Earth orbits, and large amplitude lissajous trajectories about co-linear libration points of the Sun-Earth/Moon system. These problems are not specific to any current or proposed mission, but instead are intended to capture high-level features that would be generic to many similar missions that are of interest to various agencies.

Active and Passive Sensing from Geosynchronous and Libration Orbits

NASA Technical Reports Server (NTRS)

Schoeberl, Mark; Raymond, Carol; Hildebrand, Peter

2003-01-01

The development of the LEO (EOS) missions has led the way to new technologies and new science discoveries. However, LEO measurements alone cannot cost effectively produce high time resolution measurements needed to move the science to the next level. Both GEO and the Lagrange points, L1 and L2, provide vantage points that will allow higher time resolution measurements. GEO is currently being exploited by weather satellites, but the sensors currently operating at GEO do not provide the spatial or spectral resolution needed for atmospheric trace gas, ocean or land surface measurements. It is also may be possible to place active sensors in geostationary orbit. It seems clear, that the next era in earth observation and discovery will be opened by sensor systems operating beyond near earth orbit.

Thersites: a `jumping' Trojan?

NASA Astrophysics Data System (ADS)

Tsiganis, K.; Dvorak, R.; Pilat-Lohinger, E.

2000-02-01

In this paper, we examine the dynamical evolution of the asteroid (1868) Thersites, a member of the Trojan belt. Thersites is librating around the Lagrangian point L_4, following, however, a chaotic orbit. The equations of motion for Thersites as well as for a distribution of neighboring initial conditions are integrated numerically for 50 million years in the Outer Solar System model (OSS), which consists of the Sun and the four giant planets. Our results indicate that the probability that this asteroid will eventually escape from the Trojan swarm is rather high. In fact, 20% from our initial distribution escaped within the integration time. Many of the remaining ones also show characteristic `jumps' in the orbital elements, especially the inclination. Secular resonances involving the nodes of the outer planets are found to be responsible for this chaotic behavior. The width of libration and eccentricity values that lead to grossly unstable orbits are calculated and compared with previously known results on the stability of the Trojans. Finally, a very interesting behavior has been observed for one of the escaping asteroids as he `jumped' from L_4 to L_5 where he remained performing a highly inclined libration for ~ 2 Myrs before escaping from the Trojan swarm. According to Homer, Thersites was not only the ugliest of all Greeks that took part in the Trojan war, but also had the most intolerable personality. His nasty habit of making fun of everybody cost him his life, as the last person for whom he spoke ironically about was Achilles, the mightiest warrior of all Greeks, who killed Thersites with just one punch!

Tides in a body librating about a spin-orbit resonance: generalisation of the Darwin-Kaula theory

NASA Astrophysics Data System (ADS)

Frouard, Julien; Efroimsky, Michael

2017-09-01

The Darwin-Kaula theory of bodily tides is intended for celestial bodies rotating without libration. We demonstrate that this theory, in its customary form, is inapplicable to a librating body. Specifically, in the presence of libration in longitude, the actual spectrum of Fourier tidal modes differs from the conventional spectrum rendered by the Darwin-Kaula theory for a nonlibrating celestial object. This necessitates derivation of formulae for the tidal torque and the tidal heating rate, that are applicable under libration. We derive the tidal spectrum for longitudinal forced libration with one and two main frequencies, generalisation to more main frequencies being straightforward. (By main frequencies we understand those emerging due to the triaxiality of the librating body.) Separately, we consider a case of free libration at one frequency (once again, generalisation to more frequencies being straightforward). We also calculate the tidal torque. This torque provides correction to the triaxiality-caused physical libration. Our theory is not self-consistent: we assume that the tidal torque is much smaller than the permanent-triaxiality-caused torque, so the additional libration due to tides is much weaker than the main libration due to the permanent triaxiality. Finally, we calculate the tidal dissipation rate in a body experiencing forced libration at the main mode, or free libration at one frequency, or superimposed forced and free librations.

The structure of non-hierarchical triple system stability regions

NASA Astrophysics Data System (ADS)

Martynova, A. I.; Orlov, V. V.; Rubinov, A. V.

2009-08-01

A detailed study of the two-dimensional initial conditions region section in the planar three-body problem is performed. The initial conditions for the three well-known stable periodic orbits (the Schubart’s orbit, the Broucke’s orbit and the eight-like orbit) belong to this section. Continuous stability regions (for the fixed integration interval) generated by these periodic orbits are found. Zones of the quick stability violation are outlined. The analysis of some concrete trajectories coming from various stability regions is performed. In particular, trajectories possessing varying number of “eights” formed by moving triple system components are discovered. Orbits with librations are also found. The new periodic orbit originated from the zone siding with the Schubart’s orbit region is discovered. This orbit has reversibility points (each of the outer bodies possess a reversibility point) and two points of close double approach of the central body to each of the outer bodies. The influence of the numerical integration accuracy on the results is studied. The stability regions structure is preserved during calculations with different values of the precision parameter, numerical integration methods and regularization algorithms of the equations of motion.

Resonance Occupation in the Kuiper Belt: Case Examples of the 5:2 and Trojan Resonances

NASA Astrophysics Data System (ADS)

Chiang, E. I.; Jordan, A. B.; Millis, R. L.; Buie, M. W.; Wasserman, L. H.; Elliot, J. L.; Kern, S. D.; Trilling, D. E.; Meech, K. J.; Wagner, R. M.

2003-07-01

As part of our ongoing Deep Ecliptic Survey (DES) of the Kuiper belt, we report on the occupation of the 1:1 (Trojan), 4:3, 3:2, 7:4, 2:1, and 5:2 Neptunian mean motion resonances (MMRs). The previously unrecognized occupation of the 1:1 and 5:2 MMRs is not easily understood within the standard model of resonance sweeping by a migratory Neptune over an initially dynamically cold belt. Among all resonant Kuiper belt objects (KBOs), the three observed members of the 5:2 MMR discovered by DES possess the largest semimajor axes (a~55.4 AU), the highest eccentricities (e~0.4), and substantial orbital inclinations (i~10deg). Objects (38084) 1999HB12 and possibly 2001KC77 can librate with modest amplitudes of ~90° within the 5:2 MMR for at least 1 Gyr. Their trajectories cannot be explained by close encounters with Neptune alone, given the latter's current orbit. The dynamically hot orbits of such 5:2 resonant KBOs, unlike hot orbits of previously known resonant KBOs, may imply that these objects were preheated to large inclination and large eccentricity prior to resonance capture by a migratory Neptune. Our first discovered Neptunian Trojan, 2001QR322, may not owe its existence to Neptune's migration at all. The trajectory of 2001QR322 is remarkably stable; the object can undergo tadpole-type libration about Neptune's leading Lagrange (L4) point for at least 1 Gyr with a libration amplitude of 24°. Trojan capture probably occurred while Neptune accreted the bulk of its mass. For an assumed albedo of 12%-4%, our Trojan is ~130-230 km in diameter. Model-dependent estimates place the total number of Neptune Trojans resembling 2001QR322 at ~20-60. Their existence helps to rule out violent orbital histories for Neptune.

Dynamics of Multibody Systems Near Lagrangian Points

NASA Astrophysics Data System (ADS)

Wong, Brian

This thesis examines the dynamics of a physically connected multi-spacecraft system in the vicinity of the Lagrangian points of a Circular Restricted Three-Body System. The spacecraft system is arranged in a wheel-spoke configuration with smaller and less massive satellites connected to a central hub using truss/beams or tether connectors. The kinematics of the system is first defined, and the kinetic, gravitational potential energy and elastic potential energy of the system are derived. The Assumed Modes Method is used to discretize the continuous variables of the system, and a general set of ordinary differential equations describing the dynamics of the connectors and the central hub are obtained using the Lagrangian method. The flexible body dynamics of the tethered and truss connected systems are examined using numerical simulations. The results show that these systems experienced only small elastic deflections when they are naturally librating or rotating at moderate angular velocities, and these deflections have relatively small effect on the attitude dynamics of the systems. Based on these results, it is determined that the connectors can be modeled as rigid when only the attitude dynamics of the system is of interest. The equations of motion of rigid satellites stationed at the Lagrangian points are linearized, and the stability conditions of the satellite are obtained from the linear equations. The required conditions are shown to be similar to those of geocentric satellites. Study of the linear equations also revealed the resonant conditions of rigid Lagrangian point satellites, when a librational natural frequency of the satellite matches the frequency of its station-keeping orbit leading to large attitude motions. For tethered satellites, the linear analysis shows that the tethers are in stable equilibrium when they lie along a line joining the two primary celestial bodies of the Three-Body System. Numerical simulations are used to study the long term dynamics of two sample rigid bodies when they are in different periodic orbits around a collinear point, and the tether librations of a two-tether system in the same orbits. The results show that the rigid satellites and the tethered system experience greater attitude motions when they are in larger periodic orbits. The dynamics of variable length systems are also studied in order to determine the control cost associated with moving the end bodies in a gapless spiral to cover the area spanned by the system. The control cost is relatively low during tether deployment, and negligible effort is required to maintain the angular velocity of the tethered system after deployment. A set of recommendations for the applications of Lagrangian-point physically-connected systems are presented as well as some future research directions are suggested.

ON THE DYNAMICS AND TIDAL DISSIPATION RATE OF THE WHITE DWARF IN 4U 1820-30

DOE Office of Scientific and Technical Information (OSTI.GOV)

Prodan, Snezana; Murray, Norman, E-mail: sprodan@cita.utoronto.ca

It has been suggested that the 170 day period in the light curve of the low-mass X-ray binary 4U 1820-30 arises from the presence of a third body with a large inclination to the binary orbit. We show that this long-period motion arises if the system is librating around the stable fixed point in a Kozai resonance. We demonstrate that mass transfer drives the system toward this fixed point and calculate, both analytically and via numerical integrations, that the period of libration is of order 170 days when the mutual inclination is near the Kozai critical value. The non-zero eccentricitymore » of the binary, combined with tidal dissipation, implies that the rate of change of the binary period would be slower than, or even of opposite sign to, that implied by standard mass transfer models. If the 170 day period results from libration, then, contrary to appearances, the orbital period of the inner binary is increasing with time; in that case, (e/0.009){sup 2} Q/k{sub 2} {approx}> 2.5 Multiplication-Sign 10{sup 9}, where k{sub 2} Almost-Equal-To 0.01 is the tidal Love number and e = 0.009 is the fiducial eccentricity of the inner binary. It appears unlikely that the observed negative period derivative results from the smaller than expected (but positive) value of P-dot combined with the previously suggested acceleration of the system in the gravitational field of the host globular cluster NGC 6624. The discrepancy between the observed and the expected period derivative requires further investigation.« less

Applications of Multi-Body Dynamical Environments: The ARTEMIS Transfer Trajectory Design

NASA Technical Reports Server (NTRS)

Folta, David C.; Woodard, Mark; Howell, Kathleen; Patterson, Chris; Schlei, Wayne

2010-01-01

The application of forces in multi-body dynamical environments to pennit the transfer of spacecraft from Earth orbit to Sun-Earth weak stability regions and then return to the Earth-Moon libration (L1 and L2) orbits has been successfully accomplished for the first time. This demonstrated transfer is a positive step in the realization of a design process that can be used to transfer spacecraft with minimal Delta-V expenditures. Initialized using gravity assists to overcome fuel constraints; the ARTEMIS trajectory design has successfully placed two spacecraft into EarthMoon libration orbits by means of these applications.

Dynamics of Equilibrium Points in a Uniformly Rotating Second-Order and Degree Gravitational Field

NASA Astrophysics Data System (ADS)

Feng, Jinglang; Hou, Xiyun

2017-07-01

Using tools such as periodic orbits and invariant manifolds, the global dynamics around equilibrium points (EPs) in a rotating second-order and degree gravitational field are studied. For EPs on the long axis, planar and vertical periodic families are computed, and their stability properties are investigated. Invariant manifolds are also computed, and their relation to the first-order resonances is briefly discussed. For EPs on the short axis, planar and vertical periodic families are studied, with special emphasis on the genealogy of the planar periodic families. Our studies show that the global dynamics around EPs are highly similar to those around libration points in the circular restricted three-body problem, such as spatial halo orbits, invariant manifolds, and the genealogy of planar periodic families.

Applying the OTV to lunar logistics

NASA Technical Reports Server (NTRS)

Willcockson, W. H.

1988-01-01

The Orbit Transfer Vehicle (OTV), representing the next generation of upper stages, has recently been studied in a Phase A concept definition study managed by NASA's Marshall Space Flight Center. The vehicle has been previously defined as strictly an orbit-to-orbit type transfer device. Recently its application to the task of lunar surface logistics was investigated. Transfer options to the surface were considered which included direct transfer, and transfer via lunar orbit as well as the L1 libration point. The subsystem modifications required to enable lunar landings were established for the following elements: aerobrake, main propulsion system, landing legs, primary structure, and avionics. It is concluded that the majority of the basic systems required for efficient transfer to the lunar surface are already contained in the OTV.

Contingency study for the third international Sun-Earth Explorer (ISEE-3) satellite

NASA Technical Reports Server (NTRS)

Dunham, D. W.

1979-01-01

The third satellite of the international Sun-Earth Explorer program was inserted into a periodic halo orbit about L sub 1, the collinear libration point between the Sun and the Earth-Moon barycenter. A plan is presented that was developed to enable insertion into the halo orbit in case there was a large underperformance of the Delta second or third stage during the maneuver to insert the spacecraft into the transfer trajectory. After one orbit of the Earth, a maneuver would be performed near perigee to increase the energy of the orbit. A relatively small second maneuver would put the spacecraft in a transfer trajectory to the halo orbit, into which it could be inserted for a total cost within the fuel budget. Overburns (hot transfer trajectory insertions) were also studied.

Geological Implications of a Physical Libration on Enceladus

NASA Technical Reports Server (NTRS)

Hurford, T. A.; Bills, B. G.; Helfenstein, P.; Greenberg, R.; Hoppa, G. V.; Hamilton, D. P.

2008-01-01

Given the non-spherical shape of Enceladus (Thomas et al., 2007), the satellite will experience gravitational torques that will cause it to physically librate as it orbits Saturn. Physical libration would produce a diurnal oscillation in the longitude of Enceladus tidal bulge which, could have a profound effect on the diurnal stresses experienced by the surface of the satellite. Although Cassini ISS has placed an observational upper limit on Enceladus libration amplitude of F < 1.5deg (Porco et al., 2006), smaller amplitudes can still have geologically significant consequences. Here we present the first detailed description of how physical libration affects tidal stresses and how those stresses then might affect geological processes including crack formation and propagation, south polar eruption activity, and tidal heating. Our goal is to provide a framework for testing the hypothesis that geologic features on Enceladus are produced by tidal stresses from diurnal physical and optical librations of the satellite.

The strange case of the missing apocentric librators in the 3:2 resonance. [in asteroidal belt

NASA Technical Reports Server (NTRS)

Ip, W.-H.

1976-01-01

From a comparison of the 2:1 and 3:2 resonances (in the asteroidal belt) two possible explanations to the absence of 3:2 apocentric librators are suggested. The first one is that such 3:2 resonant motion is dynamically unstable. The second interpretation requires the absence of near-circular orbits originally at 4 AU. The latter view, if correct, is inconsistent with cosmogonic models which predict the original orbits of the asteroids to be nearly circular.

Normal modes of synchronous rotation

NASA Astrophysics Data System (ADS)

Varadi, Ferenc; Musotto, Susanna; Moore, William; Schubert, Gerald

2005-07-01

The dynamics of synchronous rotation and physical librations are revisited in order to establish a conceptually simple and general theoretical framework applicable to a variety of problems. Our motivation comes from disagreements between the results of numerical simulations and those of previous theoretical studies, and also because different theoretical studies disagree on basic features of the dynamics. We approach the problem by decomposing the orientation matrix of the body into perfectly synchronous rotation and deviation from the equilibrium state. The normal modes of the linearized equations are computed in the case of a circular satellite orbit, yielding both the periods and the eigenspaces of three librations. Libration in longitude decouples from the other two, vertical modes. There is a fast vertical mode with a period very close to the average rotational period. It corresponds to tilting the body around a horizontal axis while retaining nearly principal-axis rotation. In the inertial frame, this mode appears as nutation and free precession. The other vertical mode, a slow one, is the free wobble. The effects of the nodal precession of the orbit are investigated from the point of view of Cassini states. We test our theory using numerical simulations of the full equations of the dynamics and discuss the disagreements among our study and previous ones. The numerical simulations also reveal that in the case of eccentric orbits large departures from principal-axis rotation are possible due to a resonance between free precession and wobble. We also revisit the history of the Moon's rotational state and show that it switched from one Cassini state to another when it was at 46.2 Earth radii. This number disagrees with the value 34.2 derived in a previous study.

Automating Initial Guess Generation for High Fidelity Trajectory Optimization Tools

NASA Technical Reports Server (NTRS)

Villa, Benjamin; Lantoine, Gregory; Sims, Jon; Whiffen, Gregory

2013-01-01

Many academic studies in spaceflight dynamics rely on simplified dynamical models, such as restricted three-body models or averaged forms of the equations of motion of an orbiter. In practice, the end result of these preliminary orbit studies needs to be transformed into more realistic models, in particular to generate good initial guesses for high-fidelity trajectory optimization tools like Mystic. This paper reviews and extends some of the approaches used in the literature to perform such a task, and explores the inherent trade-offs of such a transformation with a view toward automating it for the case of ballistic arcs. Sample test cases in the libration point regimes and small body orbiter transfers are presented.

The Future of Human Exploration

NASA Technical Reports Server (NTRS)

Cooke, Doug

2001-01-01

This slide presentation reviews the near term future of human space exploration in terms of possible mission scenarios, propulsion technologies, orbital dynamics that lead to Low-Energy Transfer from Earth-Moon LI to Solar Libration Points and Return Potential Staging Point for Human Mars Missions. It also examines the required evolution of mission architecture, solar electric propulsion concept, vehicle concepts for future Mars missions, and an overview of a Mars Mission, Also in this presentation are pictures of several historic personages and occasions, and a view of a Mars Meteorite (i.e., ALH84001.0)

Three Dimensional Orbital Stability About the Earth-Moon Equilateral Libration Points.

DTIC Science & Technology

1980-12-01

need to be rotated to the ecliptic . If e is the obliquity of the ecliptic , then the transformation matrix for this is: t F e, ’ C]u 11E -12 IF I) I...the use of the above transformation matrix. The frame for the analysis of the problem will be an Earth-centered ecliptic nonrotating rectangular system...The X-axis will point toward the vernal equinox and the Z-axis will be perpendicular to the ecliptic having the XY-plane coincident with the ecliptic

Simulating the Librational Behaviour of Propeller Moons In The Saturnian Ring System

NASA Astrophysics Data System (ADS)

Seiler, Michael; Seiss, Martin; Hoffmann, Holger; Spahn, Frank

2016-10-01

The propeller structure Blériot orbiting in the outer A ring of the Saturnian ring system has been one of the tremendous discoveries of the spacecraft Cassini [Tiscareno et al., 2010, ApJL]. The reconstruction of the orbital evolution of Blériot from recurrent observations in the ISS images yielded a systematic offset motion from the expected Keplerian orbit. This offset motion can be well described by three sinusoidal harmonics with amplitudes and periods of 1845, 152, 58 km and 11.1, 3.7 and 2.2 years, respectively [Sremčević et al., 2014, EPSC]. Oscillatory deviations from the Keplerian orbit are a known phenomenon for the Saturnian moons, which can be explained by resonant interactions with other moons [Spitale et al., 2006, AJ] and which look similar to the observation of Blériot.In this work we present our results from N-Body simulations, where we integrated the orbital evolution of a test particle, orbiting at the radial position of the propeller Blériot and 15 other moons of Saturn. Our simulation yield, that gravitational interactions with the larger moons result in reasonable and observable frequencies, but the resulting amplitudes of the librations are by far too small to explain the observations. Further mechanisms are needed, to amplify the amplitudes of the forced librations -- as e.g. by moonlet-ring interactions. Inspired by the recent work of Pan and Chiang [2010, ApJL; 2012, AJ] we introduce an alternative, physically more reasonable model. In our model, the moonlet is allowed to be slightly displaced with respect to its created gaps, resulting in a repulsive force. As a result, the moonlet's longitude starts to oscillate. In the presence of the additional external forcing by the outer moons the libration amplitude gets amplified, if the forcing frequency is close to the eigenfrequency of the system. Applying our model to Blériot, we can indeed reproduce a libration period of 13 years with an amplitude of about 2000 km.

Solar wind parameters and magnetospheric coupling studies

NASA Technical Reports Server (NTRS)

King, Joseph H.

1986-01-01

This paper presents distributions, means, and standard deviations of the fluxes of solar wind protons, momentum, and energy as observed near earth during the solar quiet and active years 1976 and 1979. Distributions of ratios of energies (Alfven Mach number, plasma beta) and distributions of interplanetary magnetic field orientations are also given. Finally, the uncertainties associated with the use of the libration point orbiting ISEE-3 spacecraft as a solar wind monitor are discussed.

Dynamics of Equilibrium Points in a Uniformly Rotating Second-Order and Degree Gravitational Field

DOE Office of Scientific and Technical Information (OSTI.GOV)

Feng, Jinglang; Hou, Xiyun, E-mail: jinglang@nju.edu.cn, E-mail: silence@nju.edu.cn

2017-07-01

Using tools such as periodic orbits and invariant manifolds, the global dynamics around equilibrium points (EPs) in a rotating second-order and degree gravitational field are studied. For EPs on the long axis, planar and vertical periodic families are computed, and their stability properties are investigated. Invariant manifolds are also computed, and their relation to the first-order resonances is briefly discussed. For EPs on the short axis, planar and vertical periodic families are studied, with special emphasis on the genealogy of the planar periodic families. Our studies show that the global dynamics around EPs are highly similar to those around libration points in the circularmore » restricted three-body problem, such as spatial halo orbits, invariant manifolds, and the genealogy of planar periodic families.« less

Flights between a neighborhoods of unstable libration points of Sun-Earth system

NASA Astrophysics Data System (ADS)

Surkova, Valerya; Shmyrov, Vasily

2018-05-01

In this paper we study the problem of constructing impulse flights between neighborhoods of unstable collinear libration points of the Sun-Earth system [1]. Such maneuvering in near-Earth space may prove to be in demand in modern space navigation. For example, such a maneuvering was done by the space vehicle GENESIS. Three test points are chosen for the implementation of the impulse control, in order to move to a neighborhood of the libration point L2. It is shown that the earlier on the exit from the vicinity of the libration point L1 impulse control was realized, the sooner the neighborhood L2 was achieved. Separated from this problem, the problem of optimal control in the neighborhood of L2 was considered and a form of stabilizing control is presented.

Contingency plans for the ISEE-3 libration-point mission

NASA Technical Reports Server (NTRS)

Dunham, D. W.

1979-01-01

During the planning stage of the International Sun-Earth Explorer-3 (ISEE-3) mission, a recovery strategy was developed in case the Delta rocket underperformed during the launch phase. If a large underburn had occurred, the ISEE-3 spacecraft would have been allowed to complete one revolution of its highly elliptical earth orbit. The recovery plan called for a maneuver near perigee to increase the energy of the off-nominal orbit; a relatively small second maneuver would then insert the spacecraft into a new transfer trajectory toward the desired halo orbit target, and a third maneuver would place the spacecraft in the halo orbit. Results of the study showed that a large range of underburns could be corrected for a total nominal velocity deviation cost within the ISEE-3 fuel budget.

High Fidelity Modeling of SRP and Its Effect on the Relative Motion of Starshade and WFIRST

NASA Technical Reports Server (NTRS)

Farres, Ariadna; Webster, Cassandra; Folta, Dave

2018-01-01

In this paper we perform a detailed analysis of how Solar Radiation Pressure (SRP) affects the relative motion of two spacecrafts, the Wide-Field Infrared Survey Telescope (WFIRST) and Starshade, orbiting in the vicinity of the Sun-Earth L2. While WFIRST orbits about its own Libration Point Orbit (LPO), Starshade will fly a specific trajectory to align with WFIRST and observe a Design Reference Mission of pre-determined target stars. In this analysis, we focus on the transfer orbit for Starshade from one observation to the other. We will describe how SRP affects the dynamics of the Starshade relative to WFIRSTand how relevant this effect is in order to get an accurate estimate of the total difference in velocity (delta v).

A Direct Method for Fuel Optimal Maneuvers of Distributed Spacecraft in Multiple Flight Regimes

NASA Technical Reports Server (NTRS)

Hughes, Steven P.; Cooley, D. S.; Guzman, Jose J.

2005-01-01

We present a method to solve the impulsive minimum fuel maneuver problem for a distributed set of spacecraft. We develop the method assuming a non-linear dynamics model and parameterize the problem to allow the method to be applicable to multiple flight regimes including low-Earth orbits, highly-elliptic orbits (HEO), Lagrange point orbits, and interplanetary trajectories. Furthermore, the approach is not limited by the inter-spacecraft separation distances and is applicable to both small formations as well as large constellations. Semianalytical derivatives are derived for the changes in the total AV with respect to changes in the independent variables. We also apply a set of constraints to ensure that the fuel expenditure is equalized over the spacecraft in formation. We conclude with several examples and present optimal maneuver sequences for both a HE0 and libration point formation.

Launch Window Trade Analysis for the James Webb Space Telescope

NASA Technical Reports Server (NTRS)

Yu, Wayne H.; Richon, Karen

2014-01-01

The James Webb Space Telescope (JWST) is a large-scale space telescope mission designed to study fundamental astrophysical questions ranging from the formation of the universe to the origin of planetary systems and the origins of life. JWSTs orbit design is a Libration Point Orbit (LPO) around the Sun-Earth/Moon (SEM) L2 point for a planned mission lifetime of 10.5 years. The launch readiness period for JWST is from Oct 1st, 2018 November 30th, 2018. This paper presents the first launch window analysis for the JWST observatory using finite-burn modeling; previous analysis assumed a single impulsive midcourse correction to achieve the mission orbit. The physical limitations of the JWST hardware stemming primarily from propulsion, communication and thermal requirements alongside updated mission design requirements result in significant launch window within the launch readiness period. Future plans are also discussed.

James Webb Space Telescope Launch Window Trade Analysis

NASA Technical Reports Server (NTRS)

Yu, Wayne; Richon, Karen

2014-01-01

The James Webb Space Telescope (JWST) is a large-scale space telescope mission designed to study fundamental astrophysical questions ranging from the formation of the universe to the origin of planetary systems and the origins of life. JWSTs orbit design is a Libration Point Orbit (LPO) around the Sun-EarthMoon (SEM) L2 point for a planned mission lifetime of 10.5 years. The launch readiness period for JWST is from Oct 1st, 2018 November 30th, 2018. This paper presents the first launch window analysis for the JWST observatory using finite-burn modeling; previous analysis assumed a single impulsive midcourse correction to achieve the mission orbit. The physical limitations of the JWST hardware stemming primarily from propulsion, communication and thermal requirements alongside updated mission design requirements result in significant launch window within the launch readiness period. Future plans are also discussed.

Dynamic Portrait of the Retrograde 1:1 Mean Motion Resonance

NASA Astrophysics Data System (ADS)

Huang, Yukun; Li, Miao; Li, Junfeng; Gong, Shengping

2018-06-01

Asteroids in mean motion resonances with giant planets are common in the solar system, but it was not until recently that several asteroids in retrograde mean motion resonances with Jupiter and Saturn were discovered. A retrograde co-orbital asteroid of Jupiter, 2015 BZ509 is confirmed to be in a long-term stable retrograde 1:1 mean motion resonance with Jupiter, which gives rise to our interests in its unique resonant dynamics. In this paper, we investigate the phase-space structure of the retrograde 1:1 resonance in detail within the framework of the circular restricted three-body problem. We construct a simple integrable approximation for the planar retrograde resonance using canonical contact transformation and numerically employ the averaging procedure in closed form. The phase portrait of the retrograde 1:1 resonance is depicted with the level curves of the averaged Hamiltonian. We thoroughly analyze all possible librations in the co-orbital region and uncover a new apocentric libration for the retrograde 1:1 resonance inside the planet’s orbit. We also observe the significant jumps in orbital elements for outer and inner apocentric librations, which are caused by close encounters with the perturber.

End of Life Disposal for Three Libration Point Missions through Manipulation of the Jacobi Constant and Zero Velocity Curves

NASA Technical Reports Server (NTRS)

Peterson, Jeremy D.; Brown, Jonathan M.

2015-01-01

The aim of this investigation is to determine the feasibility of mission disposal by inserting the spacecraft into a heliocentric orbit along the unstable manifold and then manipulating the Jacobi constant to prevent the spacecraft from returning to the Earth-Moon system. This investigation focuses around L1 orbits representative of ACE, WIND, and SOHO. It will model the impulsive delta-V necessary to close the zero velocity curves after escape through the L1 gateway in the circular restricted three body model and also include full ephemeris force models and higher fidelity finite maneuver models for the three spacecraft.

Libration of arguments of circumbinary-planet orbits at resonance

NASA Astrophysics Data System (ADS)

Schubart, Joachim

2017-06-01

The paper refers to fictitious resonant orbits of planet type that surround both components of a binary system. In case of 16 studied examples a suitable choice of the starting values leads to a process of libration of special angular arguments and to an evolution with an at least temporary stay of the planet in the resonant orbit. The ratio of the periods of revolution of the binary and a planet is equal to 1:5. Eight orbits depend on the ratio 1:5 of the masses of the binary components, but two other ratios appear as well. The basis of this study is the planar, elliptic or circular restricted problem of three bodies, but remarks at the end of the text refer to a four-body problem.

Research on the transfers to Halo orbits from the view of invariant manifolds

NASA Astrophysics Data System (ADS)

Xu, Ming; Tan, Tian; Xu, ShiJie

2012-04-01

This paper discusses the evolutions of invariant manifolds of Halo orbits by low-thrust and lunar gravity. The possibility of applying all these manifolds in designing low-thrust transfer, and the presence of single-impulse trajectories under lunar gravity are also explained. The relationship between invariant manifolds and the altitude of the perigee is investigated using a Poincaré map. Six types of single-impulse transfer trajectories are then attained from the geometry of the invariant manifolds. The evolutions of controlled manifolds are surveyed by the gradient law of Jacobi energy, and the following conclusions are drawn. First, the low thrust (acceleration or deceleration) near the libration point is very inefficient that the spacecraft free-flies along the invariant manifolds. The purpose is to increase its velocity and avoid stagnation near the libration point. Second, all controlled manifolds are captured because they lie inside the boundary of Earth's gravity trap in the configuration space. The evolutions of invariant manifolds under lunar gravity are indicated from the relationship between the lunar phasic angle and the altitude of the perigee. Third and last, most of the manifolds have preserved their topologies in the circular restricted three-body problem. However, the altitudes of the perigee of few manifolds are quite non-continuous, which can be used to generate single- impulse flyby trajectories.

Autonomous Navigation Using Celestial Objects

NASA Technical Reports Server (NTRS)

Folta, David; Gramling, Cheryl; Leung, Dominic; Belur, Sheela; Long, Anne

1999-01-01

In the twenty-first century, National Aeronautics and Space Administration (NASA) Enterprises envision frequent low-cost missions to explore the solar system, observe the universe, and study our planet. Satellite autonomy is a key technology required to reduce satellite operating costs. The Guidance, Navigation, and Control Center (GNCC) at the Goddard Space Flight Center (GSFC) currently sponsors several initiatives associated with the development of advanced spacecraft systems to provide autonomous navigation and control. Autonomous navigation has the potential both to increase spacecraft navigation system performance and to reduce total mission cost. By eliminating the need for routine ground-based orbit determination and special tracking services, autonomous navigation can streamline spacecraft ground systems. Autonomous navigation products can be included in the science telemetry and forwarded directly to the scientific investigators. In addition, autonomous navigation products are available onboard to enable other autonomous capabilities, such as attitude control, maneuver planning and orbit control, and communications signal acquisition. Autonomous navigation is required to support advanced mission concepts such as satellite formation flying. GNCC has successfully developed high-accuracy autonomous navigation systems for near-Earth spacecraft using NASA's space and ground communications systems and the Global Positioning System (GPS). Recently, GNCC has expanded its autonomous navigation initiative to include satellite orbits that are beyond the regime in which use of GPS is possible. Currently, GNCC is assessing the feasibility of using standard spacecraft attitude sensors and communication components to provide autonomous navigation for missions including: libration point, gravity assist, high-Earth, and interplanetary orbits. The concept being evaluated uses a combination of star, Sun, and Earth sensor measurements along with forward-link Doppler measurements from the command link carrier to autonomously estimate the spacecraft's orbit and reference oscillator's frequency. To support autonomous attitude determination and control and maneuver planning and control, the orbit determination accuracy should be on the order of kilometers in position and centimeters per second in velocity. A less accurate solution (one hundred kilometers in position) could be used for acquisition purposes for command and science downloads. This paper provides performance results for both libration point orbiting and high Earth orbiting satellites as a function of sensor measurement accuracy, measurement types, measurement frequency, initial state errors, and dynamic modeling errors.

Stochastic analysis of the control of the movement of the spacecraft in the vicinity of the colinear libration point by means of the forces of luminous pressure

NASA Technical Reports Server (NTRS)

Lukyanov, S. S.

1983-01-01

This paper is dedicated to the possible investigation of the utilization of the solar radiation pressure for the spacecraft motion control in the vicinity of collinear libration point of planar restricted ring problem of three bodies. The control is realized by changing the solar sail area at its permanent orientation. In this problem the influence of the trajectory errors and the errors of the execution control is accounted. It is worked out, the estimation method of the solar sail sizes, which are necessary for spacecraft keeping in the vicinity of collinear libration point during the certain time with given probability. The main control parameters were calculated for some examples in case of libration points of the Sun-Earth and Earth-Moon systems.

Identification of New Orbits to Enable Future Missions for the Exploration of the Martian Moon Phobos

NASA Astrophysics Data System (ADS)

Zamaro, Mattia; Biggs, James D.

One of the paramount stepping stones towards NASA's long-term goal of undertaking human missions to Mars is the exploration of the Martian moons. In this paper, a showcase of various classes of non-Keplerian orbits are identified and a number of potential mission applications in the Mars-Phobos system are proposed. These applications include: low-thrust hovering around Phobos for close-range observations; Libration Point Orbits in enhanced three-body dynamics to enable unique low-cost operations for space missions in the proximity of Phobos; their manifold structure for high-performance landing/take-off maneuvers to and from Phobos' surface; Quasi-Satellite Orbits for long-period station-keeping and maintenance. In particular, these orbits could exploit Phobos' occulting bulk as a passive radiation shield during future manned flights to Mars to reduce human exposure to radiation. Moreover, the latter orbits can be used as an orbital garage, requiring no orbital maintenance, where a spacecraft could make planned pit-stops during a round-trip mission to Mars.

The capture of lunar materials in low lunar orbit

NASA Technical Reports Server (NTRS)

Floyd, M. A.

1981-01-01

A scenario is presented for the retrieval of lunar materials sent into lunar orbit to be used as raw materials in space manufacturing operations. The proposal is based on the launch of material from the lunar surface by an electromagnetic mass driver and the capture of this material in low lunar orbit by a fleet of mass catchers which ferry the material to processing facilities when full. Material trajectories are analyzed using the two-body equations of motion, and intercept requirements and the sensitivity of the system to launch errors are determined. The present scenario is shown to be superior to scenarios that place a single mass catcher at the L2 libration point due to increased operations flexibility, decreased mass driver performance requirements and centralized catcher servicing.

Proof-of-Concept Trajectory Designs for a Multi-Spacecraft, Low-Thrust Heliocentric Solar Weather Buoy Mission

NASA Technical Reports Server (NTRS)

Muller, Ronald; Franz, Heather; Roberts, Craig; Folta, Dave

2005-01-01

A new solar weather mission has been proposed, involving a dozen or more small spacecraft spaced at regular, constant intervals in a mutual heliocentric circular orbit between the orbits of Earth and Venus. These solar weather buoys (SWBs) would carry instrumentation to detect and measure the material in solar flares, solar energetic particle events, and coronal mass ejections as they flowed past the buoys, serving both as science probes and as a radiation early warning system for the Earth and interplanetary travelers to Mars. The baseline concept involves placing a mothercraft carrying the SWBs into a staging orbit at the Sun-Earth L1 libration point. The mothercraft departs the L1 orbit at the proper time to execute a trailing-edge lunar flyby near New Moon, injecting it into a heliocentric orbit with its perihelion interior to Earth s orbit. An alternative approach would involve the use of a Double Lunar Swingby (DLS) orbit, rather than the L1 orbit, for staging prior to this flyby. After injection into heliocentric orbit, the mothercraft releases the SWBs-all equipped with low-thrust pulsed plasma thrusters (PPTs)-whereupon each SWB executes a multi-day low-thrust finite bum around perihelion, lowering aphelion such that each achieves an elliptical phasing orbit of different orbital period from its companions. The resulting differences in angular rates of motion cause the spacecraft to separate. While the lead SWB achieves the mission orbit following an insertion burn at its second perihelion passage, the remaining SWBs must complete several revolutions in their respective phasing orbits to establish them in the mission orbit with the desired longitudinal spacing. The complete configuration for a 14 SWB scenario using a single mothercraft is achieved in about 8 years, and the spacing remains stable for at least a further 6 years. Flight operations can be simplified, and mission risk reduced, by employing two mothercraft instead of one. In this scenario: the second mothercraft stays in a libration-point or DLS staging orbit until the first mothercraft has achieved nearly 180 separation from the Earth. The timing of the second mothercraft's subsequent lunar flyby is planned such that this spacecraft will be located 180 from the first mothercraft upon completion of its heliocentric circularization maneuvers. Both groups of satellites then only have to spread out over 180 to obtain full 360 coverage around the Sun.

Mimas: Constraints on Origin and Evolution from Libration Data

NASA Astrophysics Data System (ADS)

Neveu, Marc; Rhoden, Alyssa R.

2016-10-01

In stark contrast with its neighbor moon Enceladus, Mimas is surprisingly geologically quiet, despite an orbital configuration prone to levels of tidal dissipation 30 times higher. While Mimas' lack of activity could be due to a stiff, frigid interior, libration data from the Cassini spacecraft suggest its interior is not homogeneous [1]. Here, we present 1-D models of Mimas' thermal and structural evolution under two accretion scenarios: primordial, undifferentiated formation in the Saturnian subnebula [2]; and late, layered formation from a debris ring created by the disruption of one or more previous moons [3]. In the primordial scenario, our simulations yield two possible outcomes. If tidal dissipation proceeds at levels higher than those obtained using an Andrade rheology [4], Mimas differentiates and an ocean persists until the present day. This should quickly circularize its orbit, but the current orbit is eccentric. In addition, Mimas lacks surface fractures that should result from strong tidal stresses in an ice shell atop an ocean [5]. If dissipation proceeds at lower levels obtained using a Maxwell rheology, it is too weak to drive differentiation; this does not match the observed libration [1]. In the late accretion scenario, Mimas forms already differentiated. As a result, even its deepest ice is within only 100 km of the frigid surface, and poorly insulated by overlying thermally conductive crystalline ice. Thus, all ice remains cold and poorly dissipative, even if dissipation is an order of magnitude above that provided by the Andrade rheology [4]. If Mimas' rocky core is slightly non-hydrostatic [1], this matches the observed libration. We conclude that Mimas' libration is compatible with a late origin from a debris ring, but not with primordial accretion. Consistent with findings from many authors (e.g. [6]), these models cannot produce an ocean on Enceladus unless its orbital eccentricity is higher than observed.References:[1] Tajeddine et al. (2014) Science 346, 322[2] Peale (1999) Annu Rev Astron Astrophys 37, 533[3] Charnoz et al. (2011) Icarus 216, 535[4] McCarthy & Cooper (2016) EPSL 443, 185[5] Rhoden et al., JGR: Planets, submitted[6] Roberts & Nimmo (2008) Icarus 194, 675

Zero, minimum and maximum relative radial acceleration for planar formation flight dynamics near triangular libration points in the Earth-Moon system

NASA Astrophysics Data System (ADS)

Salazar, F. J. T.; Masdemont, J. J.; Gómez, G.; Macau, E. E.; Winter, O. C.

2014-11-01

Assume a constellation of satellites is flying near a given nominal trajectory around L4 or L5 in the Earth-Moon system in such a way that there is some freedom in the selection of the geometry of the constellation. We are interested in avoiding large variations of the mutual distances between spacecraft. In this case, the existence of regions of zero and minimum relative radial acceleration with respect to the nominal trajectory will prevent from the expansion or contraction of the constellation. In the other case, the existence of regions of maximum relative radial acceleration with respect to the nominal trajectory will produce a larger expansion and contraction of the constellation. The goal of this paper is to study these regions in the scenario of the Circular Restricted Three Body Problem by means of a linearization of the equations of motion relative to the periodic orbits around L4 or L5. This study corresponds to a preliminar planar formation flight dynamics about triangular libration points in the Earth-Moon system. Additionally, the cost estimate to maintain the constellation in the regions of zero and minimum relative radial acceleration or keeping a rigid configuration is computed with the use of the residual acceleration concept. At the end, the results are compared with the dynamical behavior of the deviation of the constellation from a periodic orbit.

Space Trajectory Error Analysis Program (STEAP) for halo orbit missions. Volume 2: Programmer's manual

NASA Technical Reports Server (NTRS)

Byrnes, D. V.; Carney, P. C.; Underwood, J. W.; Vogt, E. D.

1974-01-01

The six month effort was responsible for the development, test, conversion, and documentation of computer software for the mission analysis of missions to halo orbits about libration points in the earth-sun system. The software consisting of two programs called NOMNAL and ERRAN is part of the Space Trajectories Error Analysis Programs. The program NOMNAL targets a transfer trajectory from earth on a given launch date to a specified halo orbit on a required arrival date. Either impulsive or finite thrust insertion maneuvers into halo orbit are permitted by the program. The transfer trajectory is consistent with a realistic launch profile input by the user. The second program ERRAN conducts error analyses of the targeted transfer trajectory. Measurements including range, doppler, star-planet angles, and apparent planet diameter are processed in a Kalman-Schmidt filter to determine the trajectory knowledge uncertainty.

Heteroclinic connections between periodic orbits and resonance transitions in celestial mechanics

NASA Astrophysics Data System (ADS)

Koon, Wang Sang; Lo, Martin W.; Marsden, Jerrold E.; Ross, Shane D.

2000-06-01

In this paper we apply dynamical systems techniques to the problem of heteroclinic connections and resonance transitions in the planar circular restricted three-body problem. These related phenomena have been of concern for some time in topics such as the capture of comets and asteroids and with the design of trajectories for space missions such as the Genesis Discovery Mission. The main new technical result in this paper is the numerical demonstration of the existence of a heteroclinic connection between pairs of periodic orbits: one around the libration point L1 and the other around L2, with the two periodic orbits having the same energy. This result is applied to the resonance transition problem and to the explicit numerical construction of interesting orbits with prescribed itineraries. The point of view developed in this paper is that the invariant manifold structures associated to L1 and L2 as well as the aforementioned heteroclinic connection are fundamental tools that can aid in understanding dynamical channels throughout the solar system as well as transport between the ``interior'' and ``exterior'' Hill's regions and other resonant phenomena.

Orbital Injection of the SEDSAT Satellite: Tethered Systems Dynamics and Flight Data Analysis

NASA Technical Reports Server (NTRS)

Lorenzini, Enrico C.; Gullahorn, Gordon E.; Cosmo, Mario L.; Ruiz, Manuel; Pelaez, Jesus

1996-01-01

This report deals with the following topics which are all related to the orbital injection of the SEDSAT satellite: Dynamics and Stability of Tether Oscillations after the First Cut. The dynamics of the tether after the first cut (i.e., without the Shuttle attached to it) is investigated. The tether oscillations with the free end are analyzed in order to assess the stability of the rectilinear configuration in between the two tether cuts; analysis of Unstable Modes. The unstable modes that appear for high libration angles are further investigated in order to determine their occurrences and the possible transition from bound librations to rotations; Orbital Release Strategies for SEDSAT. A parametric analysis of the orbital decay rate of the SEDSAT satellite after the two tether cuts has been carried out as a function of the following free parameters: libration amplitude at the end of deployment, deviation angle from LV at the first cut, and orbital anomaly at the second cut. The values of these parameters that provide a minimum orbital decay rate of the satellite (after the two cuts) have been computed; and Dynamics and Control of SEDSAT. The deployment control law has been modified to cope with the new ejection velocity of the satellite from the Shuttle cargo bay. New reference profiles have been derived as well as new control parameters. Timing errors at the satellite release as a function of the variations of the initial conditions and the tension model parameters have been estimated for the modified control law.

Guidebook for analysis of tether applications

NASA Technical Reports Server (NTRS)

Carroll, J. A.

1985-01-01

This guidebook is intended as a tool to facilitate initial analyses of proposed tether applications in space. Topics disscussed include: orbit and orbit transfer equations; orbital perturbations; aerodynamic drag; thermal balance; micrometeoroids; gravity gradient effects; tether control strategies; momentum transfer; orbit transfer by tethered release/rendezvous; impact hazards for tethers; electrodynamic tether principles; and electrodynamic libration control issues.

Abort Options for Human Missions to Earth-Moon Halo Orbits

NASA Technical Reports Server (NTRS)

Jesick, Mark C.

2013-01-01

Abort trajectories are optimized for human halo orbit missions about the translunar libration point (L2), with an emphasis on the use of free return trajectories. Optimal transfers from outbound free returns to L2 halo orbits are numerically optimized in the four-body ephemeris model. Circumlunar free returns are used for direct transfers, and cislunar free returns are used in combination with lunar gravity assists to reduce propulsive requirements. Trends in orbit insertion cost and flight time are documented across the southern L2 halo family as a function of halo orbit position and free return flight time. It is determined that the maximum amplitude southern halo incurs the lowest orbit insertion cost for direct transfers but the maximum cost for lunar gravity assist transfers. The minimum amplitude halo is the most expensive destination for direct transfers but the least expensive for lunar gravity assist transfers. The on-orbit abort costs for three halos are computed as a function of abort time and return time. Finally, an architecture analysis is performed to determine launch and on-orbit vehicle requirements for halo orbit missions.

Proceedings from the 2nd International Symposium on Formation Flying Missions and Technologies

NASA Technical Reports Server (NTRS)

2004-01-01

Topics discussed include: The Stellar Imager (SI) "Vision Mission"; First Formation Flying Demonstration Mission Including on Flight Nulling; Formation Flying X-ray Telescope in L2 Orbit; SPECS: The Kilometer-baseline Far-IR Interferometer in NASA's Space Science Roadmap Presentation; A Tight Formation for Along-track SAR Interferometry; Realization of the Solar Power Satellite using the Formation Flying Solar Reflector; SIMBOL-X : Formation Flying for High-Energy Astrophysics; High Precision Optical Metrology for DARWIN; Close Formation Flight of Micro-Satellites for SAR Interferometry; Station-Keeping Requirements for Astronomical Imaging with Constellations of Free-Flying Collectors; Closed-Loop Control of Formation Flying Satellites; Formation Control for the MAXIM Mission; Precision Formation Keeping at L2 Using the Autonomous Formation Flying Sensor; Robust Control of Multiple Spacecraft Formation Flying; Virtual Rigid Body (VRB) Satellite Formation Control: Stable Mode-Switching and Cross-Coupling; Electromagnetic Formation Flight (EMFF) System Design, Mission Capabilities, and Testbed Development; Navigation Algorithms for Formation Flying Missions; Use of Formation Flying Small Satellites Incorporating OISL's in a Tandem Cluster Mission; Semimajor Axis Estimation Strategies; Relative Attitude Determination of Earth Orbiting Formations Using GPS Receivers; Analysis of Formation Flying in Eccentric Orbits Using Linearized Equations of Relative Motion; Conservative Analytical Collision Probabilities for Orbital Formation Flying; Equations of Motion and Stability of Two Spacecraft in Formation at the Earth/Moon Triangular Libration Points; Formations Near the Libration Points: Design Strategies Using Natural and Non-Natural Ares; An Overview of the Formation and Attitude Control System for the Terrestrial Planet Finder Formation Flying Interferometer; GVE-Based Dynamics and Control for Formation Flying Spacecraft; GNC System Design for a New Concept of X-Ray Distributed Telescope; GNC System for the Deployment and Fine Control of the DARWIN Free-Flying Interferometer; Formation Algorithm and Simulation Testbed; and PLATFORM: A Formation Flying, RvD and Robotic Validation Test-bench.

Secular dynamics of an exterior test particle: the inverse Kozai and other eccentricity-inclination resonances

NASA Astrophysics Data System (ADS)

Vinson, Benjamin R.; Chiang, Eugene

2018-03-01

The behaviour of an interior test particle in the secular three-body problem has been studied extensively. A well-known feature is the Lidov-Kozai resonance in which the test particle's argument of periastron librates about ±90° and large oscillations in eccentricity and inclination are possible. Less explored is the inverse problem: the dynamics of an exterior test particle and an interior perturber. We survey numerically the inverse secular problem, expanding the potential to hexadecapolar order and correcting an error in the published expansion. Four secular resonances are uncovered that persist in full N-body treatments (in what follows, ϖ and Ω are the longitudes of periapse and of ascending node, ω is the argument of periapse, and subscripts 1 and 2 refer to the inner perturber and the outer test particle): (i) an orbit-flipping quadrupole resonance requiring a non-zero perturber eccentricity e1, in which Ω2 - ϖ1 librates about ±90°; (ii) a hexadecapolar resonance (the `inverse Kozai' resonance) for perturbers that are circular or nearly so and inclined by I ≃ 63°/117°, in which ω2 librates about ±90° and which can vary the particle eccentricity by Δe2 ≃ 0.2 and lead to orbit crossing; (iii) an octopole `apse-aligned' resonance at I ≃ 46°/107° wherein ϖ2 - ϖ1 librates about 0° and Δe2 grows with e1; and (iv) an octopole resonance at I ≃ 73°/134° wherein ϖ2 + ϖ1 - 2Ω2 librates about 0° and Δe2 can be as large as 0.3 for small but non-zero e1. Qualitatively, the more eccentric the perturber, the more the particle's eccentricity and inclination vary; also, more polar orbits are more chaotic. Our solutions to the inverse problem have potential application to the Kuiper belt and debris discs, circumbinary planets, and hierarchical stellar systems.

Effect of mass variation on dynamics of tethered system in orbital maneuvering

NASA Astrophysics Data System (ADS)

Sun, Liang; Zhao, Guowei; Huang, Hai

2018-05-01

In orbital maneuvering, the mass variation due to fuel consumption has an obvious impact on the dynamics of tethered system, which cannot be neglected. The contributions of the work are mainly shown in two aspects: 1) the improvement of the model; 2) the analysis of dynamics characteristics. As the mass is variable, and the derivative of the mass is directly considered in the traditional Lagrange equation, the expression of generalized force is complicated. To solve this problem, the coagulated derivative is adopted in the paper; besides, the attitude dynamics equations derived in this paper take into account the effect of mass variation and the drift of orbital trajectory at the same time. The bifurcation phenomenon, the pendular motion angular frequency, and amplitudes of tether vibration revealed in this paper can provide a reference for the parameters and controller design in practical engineering. In the article, a dumbbell model is adopted to analyze the dynamics of tethered system, in which the mass variation of base satellite is fully considered. Considering the practical application, the case of orbital transfer under a transversal thrust is mainly studied. Besides, compared with the analytical solutions of librational angles, the effects of mass variation on stability and librational characteristic are studied. Finally, in order to make an analysis of the effect on vibrational characteristic, a lumped model is introduced, which reveals a strong coupling of librational and vibrational characteristics.

Minimum impulse three-body trajectories.

NASA Technical Reports Server (NTRS)

D'Amario, L.; Edelbaum, T. N.

1973-01-01

A rapid and accurate method of calculating optimal impulsive transfers in the restricted problem of three bodies has been developed. The technique combines a multi-conic method of trajectory integration with primer vector theory and an accelerated gradient method of trajectory optimization. A unique feature is that the state transition matrix and the primer vector are found analytical without additional integrations or differentiations. The method has been applied to the determination of optimal two and three impulse transfers between the L2 libration point and circular orbits about both the earth and the moon.

Earth to Moon Transfers - Direct vs Via Libration Points (L1, L2)

NASA Technical Reports Server (NTRS)

Condon, Gerald L.; Wilson, Sam

2002-01-01

Recommend Direct Remote Ocean Area impact disposal for caseswithout hazardous (e.g., radioactive) material on LTV kickstage Controlled Earth contact. Relatively small disposal AV. Avoids close encounter with Moon. Trajectories can be very sensitive to initial conditions (at disposalmaneuver).V to correct for errors is small. Recommend Heliocentric Orbit disposal for cases with hazardousmaterial on LTV kickstage. No Earth or Lunar disposal issues (e.g.. impact location, debris footprint,litter). Relatively low disposal AV cost. Further study required to determine possibility of re-contact with Earth.

NASA Human Spaceflight Architecture Team Cis-Lunar Analysis

NASA Technical Reports Server (NTRS)

Lupisella, M.; Bobskill, M. R.

2012-01-01

The Cis-Lunar Destination Team of NASA's Human Spaceflight Architecture Teait1 (HAT) has been perfom1ing analyses of a number of cis-lunar locations to infom1 architecture development, transportation and destination elements definition, and operations. The cis-lunar domain is defined as that area of deep space under the gravitation influence of the earth-moon system, including a set of orbital locations (low earth orbit (LEO]. geosynchronous earth orbit [GEO]. highly elliptical orbits [HEO]); earth-moon libration or "Lagrange·· points (EMLl through EMLS, and in particular, EMLI and EML2), and low lunar orbit (LLO). We developed a set of cis-lunar mission concepts defined by mission duration, pre-deployment, type of mission, and location, to develop mission concepts and the associated activities, capabilities, and architecture implications. To date, we have produced two destination operations J concepts based on present human space exploration architectural considerations. We have recently begun defining mission activities that could be conducted within an EM LI or EM L2 facility.

Development of the program visualizing the lunar physical libration with Visual Basic

NASA Astrophysics Data System (ADS)

Zagidullin, Arthur; Petrova, Natalia

Study of the Moon, of its spin-orbital characteristics and parameters of the lunar interior is one of the traditional fields of the Kazan astronomical school. However, despite the incredible successes in space investigations of the planets and of the Moon, in last years the interest to celestial mechanics, ephemerides astronomy and astrometry is significantly decreased, especially among the young scientists and students. Therefore, it is encouraging to see the work of the third-year student, which is devoted to the study of the physical libration of the Moon. This report presents the results of the first stage of the above study associated with the study of Cassini's laws in the rotation of the Moon and the visualization of these laws by means the programming language Visual Basic. The Earth moves on the Moon's orbit in selenocentric frame. Dynamic coordinate system is based on the principal axes of inertia of the Moon. The x-axis is directed along the largest principal axis of inertia A, the axis z is a dynamic pole of the Moon associated with the smallest principal axis of inertia C. According to the first Cassini’s law the lunar pole is inclined at a constant angle approximately equal to 1.5 degree. The ascending node of the orbit is coincides with descending node of the lunar equator (the second Cassini’s law) and, as a result, the ecliptic pole lies between the orbit pole and spin pole. Therefore the three vectors directed from the lunar centre of mass to orbit pole, ecliptic pole and spin pole form a single plane. The third Cassini’s law reflects the uniform rotation of the Moon synchronised with orbital motion of the Moon around the Earth (in the selenocentric frame the Earth moves around the Moon). It’s necessary a significant time to calculate the corresponding coordinates of points, which move synchronously on the orbit and on the equator. In any time t the Earth moves with the mean velocity n and forms the angle n*t in the orbit plane. At the same time, according to the third law, the axis x forms the same angle varphi = n*t in equatorial plane. In other words the longest axis of the Moon is always "looking" at the Earth. The latter action, which the developed program executes, is a demonstration of the effects of several, the most powerful, harmonics of the physical libration. Unfortunately, Visual Basic opportunities are severely limited for creating three-dimensional images. Because of this we could not to support real scale in angles and time. This work was supported by RFBR grant No. 13-02-00792.

Solar sail trajectory design in the Earth-Moon circular restricted three body problem

NASA Astrophysics Data System (ADS)

Das, Ashwati

The quest to explore the Moon has helped resolve scientific questions, has spurred leaps in technology development, and has revealed Earth's celestial companion to be a gateway to other destinations. With a renewed focus on returning to the Moon in this decade, alternatives to chemical propulsion systems are becoming attractive methods to efficiently use scarce resources and support extended mission durations. Thus, an investigation is conducted to develop a general framework, that facilitates propellant-free Earth-Moon transfers by exploiting sail dynamics in combination with advantageous transfer options offered in the Earth-Moon circular restricted multi-body dynamical model. Both periodic orbits in the vicinity of the Earth-Moon libration points, and lunar-centric long-term capture orbits are incorporated as target destinations to demonstrate the applicability of the general framework to varied design scanarios, each incorporating a variety of complexities and challenges. The transfers are comprised of three phases - a spiral Earth escape, a transit period, and, finally, the capture into a desirable orbit in the vicinity of the Moon. The Earth-escape phase consists of spiral trajectories constructed using three different sail steering strategies - locally optimal, on/off and velocity tangent. In the case of the Earth-libration point transfers, naturally occurring flow structures (e.g., invariant manifolds) arising from the mutual gravitational interaction of the Earth and Moon are exploited to link an Earth departure spiral with a destination orbit. In contrast, sail steering alone is employed to establish a link between the Earth-escape phase and capture orbits about the Moon due to a lack of applicable natural structures for the required connection. Metrics associated with the transfers including flight-time and the influence of operational constraints, such as occultation events, are investigated to determine the available capabilities for Earth-Moon transfers given current sail technology levels. Although the implemented steering laws suffice to generate baseline paths, infeasible turn rate demands placed on the sail are also investigated to explore the technical hurdles in designing Earth-Moon transfers. The methodologies are suitable for a variety of mission scenarios and sail configurations, rendering the resulting trajectories valuable for a diverse range of applications.

Lunar libration point flight dynamics study

NASA Technical Reports Server (NTRS)

1969-01-01

Two satellite concepts, Halo and Hummingbird, for a lunar libration point satellite to be used as a tracking and communications link with the far side of the moon were evaluated. Study areas included flight dynamics, communications, attitude control, propulsion, and system integration. Both concepts were proved feasible, but Halo was shown to be the better concept.

The cislunar low-thrust trajectories via the libration point

NASA Astrophysics Data System (ADS)

Qu, Qingyu; Xu, Ming; Peng, Kun

2017-05-01

The low-thrust propulsion will be one of the most important propulsion in the future due to its large specific impulse. Different from traditional low-thrust trajectories (LTTs) yielded by some optimization algorithms, the gradient-based design methodology is investigated for LTTs in this paper with the help of invariant manifolds of LL1 point and Halo orbit near the LL1 point. Their deformations under solar gravitational perturbation are also presented to design LTTs in the restricted four-body model. The perturbed manifolds of LL1 point and its Halo orbit serve as the free-flight phase to reduce the fuel consumptions as much as possible. An open-loop control law is proposed, which is used to guide the spacecraft escaping from Earth or captured by Moon. By using a two-dimensional search strategy, the ON/OFF time of the low-thrust engine in the Earth-escaping and Moon-captured phases can be obtained. The numerical implementations show that the LTTs achieved in this paper are consistent with the one adopted by the SMART-1 mission.

Control of asteroid retrieval trajectories to libration point orbits

NASA Astrophysics Data System (ADS)

Ceriotti, Matteo; Sanchez, Joan Pau

2016-09-01

The fascinating idea of shepherding asteroids for science and resource utilization is being considered as a credible concept in a not too distant future. Past studies identified asteroids which could be efficiently injected into manifolds which wind onto periodic orbits around collinear Lagrangian points of the Sun-Earth system. However, the trajectories are unstable, and errors in the capture maneuver would lead to complete mission failure, with potential danger of collision with the Earth, if uncontrolled. This paper investigates the controllability of some asteroids along the transfers and the periodic orbits, assuming the use of a solar-electric low-thrust system shepherding the asteroid. Firstly, an analytical approach is introduced to estimate the stability of the trajectories from a dynamical point of view; then, a numerical control scheme based on a linear quadratic regulator is proposed, where the gains are optimized for each trajectory through a genetic algorithm. A stochastic simulation with a Monte Carlo approach is used to account for different perturbed initial conditions and the epistemic uncertainty on the asteroid mass. Results show that only a small subset of the considered combinations of trajectories/asteroids are reliably controllable, and therefore controllability must be taken into account in the selection of potential targets.

Dynamical evolution of a fictitious population of binary Neptune Trojans

NASA Astrophysics Data System (ADS)

Brunini, Adrián

2018-03-01

We present numerical simulations of the evolution of a synthetic population of Binary Neptune Trojans, under the influence of the solar perturbations and tidal friction (the so-called Kozai cycles and tidal friction evolution). Our model includes the dynamical influence of the four giant planets on the heliocentric orbit of the binary centre of mass. In this paper, we explore the evolution of initially tight binaries around the Neptune L4 Lagrange point. We found that the variation of the heliocentric orbital elements due to the libration around the Lagrange point introduces significant changes in the orbital evolution of the binaries. Collisional processes would not play a significant role in the dynamical evolution of Neptune Trojans. After 4.5 × 109 yr of evolution, ˜50 per cent of the synthetic systems end up separated as single objects, most of them with slow diurnal rotation rate. The final orbital distribution of the surviving binary systems is statistically similar to the one found for Kuiper Belt Binaries when collisional evolution is not included in the model. Systems composed by a primary and a small satellite are more fragile than the ones composed by components of similar sizes.

Rendezvous missions to temporarily captured near Earth asteroids

NASA Astrophysics Data System (ADS)

Brelsford, S.; Chyba, M.; Haberkorn, T.; Patterson, G.

2016-04-01

Missions to rendezvous with or capture an asteroid present significant interest both from a geophysical and safety point of view. They are key to the understanding of our solar system and are stepping stones for interplanetary human flight. In this paper, we focus on a rendezvous mission with 2006 RH120, an asteroid classified as a Temporarily Captured Orbiter (TCO). TCOs form a new population of near Earth objects presenting many advantages toward that goal. Prior to the mission, we consider the spacecraft hibernating on a Halo orbit around the Earth-Moon's L2 libration point. The objective is to design a transfer for the spacecraft from the parking orbit to rendezvous with 2006 RH120 while minimizing the fuel consumption. Our transfers use indirect methods, based on the Pontryagin Maximum Principle, combined with continuation techniques and a direct method to address the sensitivity of the initialization. We demonstrate that a rendezvous mission with 2006 RH120 can be accomplished with low delta-v. This exploratory work can be seen as a first step to identify good candidates for a rendezvous on a given TCO trajectory.

Effect of Stellar Wind and Poynting-Robertson Drag on Photogravitational Elliptic Restricted Three Body Problem

NASA Astrophysics Data System (ADS)

Chakraborty, A.; Narayan, A.

2018-03-01

The existence and linear stability of the planar equilibrium points for photogravitational elliptical restricted three body problem is investigated in this paper. Assuming that the primaries, one of which is radiating are rotating in an elliptical orbit around their common center of mass. The effect of the radiation pressure, forces due to stellar wind and Poynting-Robertson drag on the dust particles are considered. The location of the five equilibrium points are found using analytical methods. It is observed that the collinear equilibrium points L 1, L 2 and L 3 do not lie on the line joining the primaries but are shifted along the y-coordinate. The instability of the libration points due to the presence of the drag forces is demonstrated by Lyapunov's first method of stability.

Space manufacturing facilities: Space colonies; Proceedings of the Princeton Conference, Princeton University, Princeton, N.J., May 7-9, 1975

NASA Technical Reports Server (NTRS)

Grey, J.

1977-01-01

Reports submitted to the conference encompass: administration and law relating to inhabited space facilities and colonies; space manufacturing and processing; organization and construction of space habitats and management of space colony farms; winning and acquisition of lunar and asteroidal materials for sustaining autonomous space colonies. Attention is given to trajectories between earth, low earth orbit, earth-moon libration points (specifically L5), circumlunar parking orbits, and trajectories in translunar space; effects of low gravity and zero gravity on human physiology and on materials processing; architecture and landscaping for space colonies; closed ecosystems of space colonies. Varieties of human cultures and value hierarchies around the earth are examined for broader perspectives on the social organization of space colonies.

Earth Shadows and the SEV Angle of MAP's Lissajous Orbit At L2

NASA Technical Reports Server (NTRS)

Edery, Ariel

2002-01-01

The Microwave Anisotropy Probe (MAP) launched successfully on June 30, 2001 and is presently in a Lissajous orbit about the Sun-Earth libration point L2. To avoid Earth shadows at L2, the Sun-Earth-Vehicle (SEV) angle of MAP has to be greater than 0.5 deg for an extended mission of four years. An equation is derived for the SEV angle in terms of the phase angle, frequencies and amplitudes of the Lissajous. The SEV angle is shown to oscillate with a period of 90.4 days within an amplitude envelope of period 13.9 years. A range of phase angles that avoids shadows is identified. MAP'S present phase angle is within this range and will avoid shadows for approximately 5.8 years.

Mercury's spin-orbit model and signature of C/MR2

NASA Astrophysics Data System (ADS)

Rambaux, N.; Bois, E.

2003-04-01

The upcoming missions, MESSENGER (Solomon etal 2001, Planet. Space Sci 49) and Bepi Colombo (Milani etal 2001, Planet. Space Sci 49) with onboard instrumentation capable of measuring the rotational parameters stimulate the objective to reach an accurate theory of the rotational motion of Mercury. Our work deals with the physical and dynamical causes that induce librations around an equilibrium state defined by the 3:2 spin-orbit resonance of Mercury. In order to integrate the spin-orbit motion of Mercury, we have used our gravitational model of the solar System including the Moon's spin-orbit motion. This model, called SONYR (acronym of Spin-Orbit N-bodY Relativistic model), was previously built by Bois, Journet and Vokrouhlicky in accordance with the requirements of the Lunar Laser Ranging observational accuracy (see for instance a review by Bois 2000, C. R. Acad. Sci. Série IV, or Bois and Vokrouhlický 1995). Using the model, the present study is devoted to the main perturbations acting on the spin-orbit motion of Mercury such as the planetary interactions (and their hierarchy) and the dynamical figure of the planet. The effect of the torque of Venus is 105 times smaller in magnitude than the one due to the Sun. Moreover, the complete rotation of Mercury exhibits two proper frequencies, namely 15.825 and 1089 years, and one secular variation of 271043 years which is due to the nodal precession between the equatorial plane of Mercury and its orbital plane. It is the second synchronism of Mercury mentioned by Beletski in 1986. We have made into evidence that the 3:2 resonance of Mercury is preserved by this second synchronism, which can be understood as a spin-orbit secular resonance. We have shown that the secular resonance variable ψ - Ω librates with a frequency of 1089 years. Our model integration starts with an initial obliquity of 1.65 arcminute (re-evaluate from the Cassini state) and gives an amplitude of libration in longitude of the order of 20 arcseconds, which is in agreement with Balogh and Giamperi (2002, Rep. Prog. Phys. 65). Besides, we have computed in the Hermean librations the impact of the variation of the greatest principal moment of inertia, cm2. The maximal signature on the obliquity is then 1.4 mas (milliarsecond) on the 176 day period, and the one on the libration in longitude is 0.4 mas on the 87.9 day period, resulting from an increase of the cm2 value of 1%. These values have to be understood as upper bounds of such signatures. These two effects permit to contribute to precise the relationship between the cm2 coefficient and the internal structure of Mercury. References : Balog, A., and Giamperi, G., 2002, Rep. Prog. Phys. 65, 529-560. Beletski, V, 1986, "Essais sur le Mouvement des Corps Cosmiques", Mir (ed), Moscou. Bois, E., 2000, C. R. Acad. Sci. Paris, t. 1, Série IV, 809-823. Bois, E., and Vokrouhlický, D., 1995, Astronomy and Astrophysics 300, 559-567. Milani, A., Vokrouhlicky, D., and Bonanno, C., 2001, Planet. Space Sci 49, 1579. Solomon, etal, 2001, Planet. Space Sci 49, 1445.

To development of analytical theory of rotational motion of the Moon

NASA Astrophysics Data System (ADS)

Barkin, Yu. V.; Ferrandiz, J. M.; Navarro, J. F.

2009-04-01

Resume. In the work the analytical theory of forced librations of the Moon considered as a celestial body with a liquid core and rigid non-spherical mantle is developed. For the basic variables: Andoyer, Poincare and Eulerian angles, and also for various dynamic characteristics of the Moon the tables for amplitudes, periods and phases of perturbations of the first order have been constructed. Resonant periods of free librations have been estimated. The influence of a liquid core results in decreasing of the period of free librations in longitude approximately on 0.316 day, and in change of the period of free pole wobble of the Moon on 25.8 days. In the first approximation the liquid core does not render influence on the value of Cassini's inclination and on the period of precession of the angular momentum vector. However it causes an additional "quasi-diurnal" librations with period about 27.165 days. In comparison with model of rigid non-spherical of the Moon the presence of a liquid core should result in increase of amplitudes of the Moon librations in longitude on 0.06 %. 1 Development of analytical theory of rotational motion of the Moon with liquid core and rigid mantle. The work has been realized in following stages. 1. Canonical equations of rotation of the Moon with liquid core and elastic mantle in Andoyer and Poincare variables have been constructed. Developments of second harmonic of force function of the Moon in pointed variables have been obtained for accurate trigonometric presentation of perturbations of the Moon orbital motion. 2. Two approaches (two methods) of construction of analytical theory have been developed. These approaches use different principles for eliminating of singularities for axial rotation of the Moon. One is based on direct application of Andoyer variables by changing of notations of moments of inertia [1]. Second is based on application of Poincare elements. For comparison both approaches are developed. 3. The main equation for determination of Cassini's inclination and its solution has been obtained in the case of accurate orbit of the Moon. An dynamical explanation of Cassini's laws has been done for model of the Moon with liquid core [2]. 4. Compact formulae for perturbations of the first (and second) order have been constructed for general used variables and for different kinematical and dynamical characteristics of the Moon (23 variables and characteristics: Andoyer-Poincare variables, classical variables, components of angular velocity and angular momentums of the Moon and its core). 5. Analytical formulae for 4 periods of free librations of the Moon have been constructed: for librations in longitude, in pole wobble, for free precession, and "quasi-diurnal" librations, caused by the liquid core. 6. The dynamical effects in the Moon rotation, caused by secular orbital perturbations of the Earth and Sun, have been studied. 2 Structure perturbations of the first order and their tabulation. For example, perturbations (periodic and of mixed type) in inclination ?and in node h of angular momentum of the Moon are determined by formulae: ? = ?0 + ‘ ???(1) cosθv, h = ? + ‘ ¥?¥h?(1) sinθ?. Here ?0 = 1033′50" is the Cassini's inclination of the Moon; ??(1), h?(1)are constant coefficients; θv = v1lM + v2lS + v3F + v4D, ? = (v1,v2,v3,v4)Tare combinations of known classical arguments of the Moon orbital theory; v1,v2,v3 and v4 are integer. 3 Influence of the liquid core and its ellipticity ɛ on amplitudes of the Moon forced and free librations. An influence of the liquid core and its ellipticity is determined by positive correction to amplitudes of librations for model of the rigid Moon. If the amplitudes of librations of rigid Moon we note as 1, so the corresponding amplitudes of librations of the Moon with the liquid core will be characterized by parameter 1 + L, where correction for liquid core is determined by formula L = Cc(1- ɛ2)•C ? Cc•C = 0.5996 × 10-3, where Cand Ccis the polar moments of inertia of the Moon and its core;ɛ = (a2 - b2)• (a2 + b2)? (a - b)•a is an ellipticity of equatorial ellipse of core cavity with semi-axes a and b. So all amplitudes of librations in longitude due to the liquid core are increased on 0.06%. A small effect of ellipticity has more smaller order. Here as example we present formula for perturbations of the first order of the Moon in longitude: (1) 21-+-L λ = 6n0 I C22Ã- ‘ ‘ D (1) (? )- D(-1) (? ) Ã- (- 1)?5-?1.?2.?3+2.?4.?5--0----?1.?2.?3-2.?4.?25-0-sin(v1lM + v2lS + v3F + v4D ) ¥?¥>0 ?5 (v1nM + v2nS + v3nF + v4nD) I = C•(mr2) is the dimensionless moment of inertia of the Moon (m and rare it's the mass and mean radius). Kinoshita's inclination functions D?1.?2.?3.?4.?5(±1)(? 0) are determined by known formulae through the value of Cassini's angle? = 1033′50". v1nM + v2nS + v3nF + v4nD = ˙θv1,v2,v3,v4 are derivatives with respect to the time of corresponding linear combinations of classical arguments of lunar orbit theory; nM,nS,nF and nD are velocities of changes of these arguments; C22 is the selenopotential coefficient; n02 = fm⊕•a3, a is an unperturbed value of semi-axis major of lunar orbit, fis a gravitational constant. The perturbations of the first order for others variables and considered dynamical characteristics have the structure similar to the formula for ˜λ(1). In given table 1 we present amplitudes of forced librations in longitude of intermediate Andoyer plane λ?1,?2,?3,?4 (in arc seconds) and perturbations of angular velocity of the Moon axial rotation ??1,?2,?3,?4 (in units10-4nF). T?1,?2,?3,?4are periods of corresponding perturbations. Table 1. Main perturbations in the Moon librations in longitude. ?1 ?2 ?3 ?4 T?1,?2,?3,?4 λ?1,?2,?3,?4 0 1 0 0 365.26 81"02 1 0 0 0 27.555 -15"65 1 -1 0 -1 -3232.9 9"85 2 0 0 -2 205.89 9"69 1 0 0 -2 31.81 4"15 1 0 0 -1 411.78 -2"98 2 0 -2 0 -1095.2 -1"86 2 -1 0 -2 471.89 0"74 0 0 0 2 14.77 -0"61 The results of tabulations of amplitudes of perturbations in the Moon rotation give good agreement with earlier constructed theories for its rigid model. Barkin's work partially was financially accepted by Spanish grants, Japanese-Russian grant N-07-02-91212 and by RFBR grant N 08-02-00367. References [1] Barkin, Yu. (1987) An Analytical Theory of the Lunar Rotational Motion. In: Figure and Dynamics of the Earth, Moon and Planets/ Proceedings of the Int. Symp. (Prague, Czechoslovakia, Sept. 15-20, 1986)/ Monogr. Ser. of UGTK, Prague. pp. 657-677. [2] Ferrandiz, J., Barkin, Yu. (2003) New approach to development of Moon rotation theory. Procced. of Inter. Conf. "Astrometry, Geodynamics and Solar System Dynamics". Journees 2003 (Sept. 22-25, 2003, St. Peters., Russia). IPA RAS, 199-200.

Variations in Rotation Rate and Polar Motion of a Non-hydrostatic Titan

NASA Astrophysics Data System (ADS)

Van Hoolst, T.; Coyette, A.; Baland, R. M.

2017-12-01

Observations of the rotation of large synchronously rotating satellites such as Titan can help to probe their interior. Previous studies (Van Hoolst et al. 2013, Richard et al. 2014, Coyette et al. 2016) mostly assume that Titan is in hydrostatic equilibrium, although several measurements indicate that it deviates from such a state. Here we investigate the effect of non-hydrostatic equilibrium and of flow in the subsurface ocean on the rotation of Titan. We consider (1) the periodic changes in Titan's rotation rate with a period equal to Titan's orbital period (diurnal librations) as a result of the gravitational torque exerted by Saturn, (2) the periodic changes in Titan's rotation rate with a main period equal to half the orbital period of Saturn (seasonal librations) and due to the dynamic variations in the atmosphere of Titan and (3) the periodic changes of the axis of rotation with respect to the figure axis of Titan (polar motion) with a main period equal to the orbital period of Saturn and due to the dynamic variations in the atmosphere of Titan. The non-hydrostatic mass distribution significantly influences the amplitude of the diurnal and seasonal librations. It is less important for polar motion, which is sensitive to flow in the subsurface ocean. The smaller than synchronous rotation rate measured by Cassini (Meriggiola 2016) can be explained by the atmospheric forcing.

The Space Review

NASA Technical Reports Server (NTRS)

Thronson, Harley; Lester, Dan; Hatfield, Skip

2011-01-01

Human space flight in the US and other space-faring countries is faced with a twin challenge that is likely to persist for many years: flat or declining budgets along with an expectation of continuing, significant achievements. A partial solution may involve increased participation by multiple commercial competitors with the promise - albeit yet to be fully demonstrated - of much-reduced costs. That said, most commercial goals are concentrated on low-Earth orbit (LEO) for the time being, leaving human trips beyond Earth orbit (BED) as governmental initiatives. The past decade, beginning with the 1999/2000 Decadal Planning Team (DPT)/NASA Exploration Team (NExT) human space flight studies for the White House Office of Management and Budget (http://history.nasa.gov/DPT/DPT.htm), can arguably be described as a Golden Age of engineering design, strategic planning, technology capability prioritization, and development programs on the International Space Station (ISS). However, cynics have criticized the same period as little more than PowerPoint presentations, and unfocused technology investments with only limited progress toward a goal of human space flight beyond the immediate vicinity of the Earth. We disagree with the cynics. Experience with the ISS on increasingly sophisticated capabilities have prepared international partners to deploy a major "stepping stone" for human space flight: a habitation system in free space beyond low-Earth orbit. Such an achievement would be a major milestone in human space flight and, very likely, an essential demonstration site for subsequent, very ambitious exploration missions such as to Mars. Developing critical capabilities for human voyages beyond LEO, such as Earth-Moon libration points, offers, as just one example, easy return to Earth within days (see, e.g., Farquhar 1971 (Aeronautics & Astronautics, July, p. 59ff), Thronson, Lester, and Talay 2011 (http://www.thespacereview.com/article/1756/1), and Lester 2012 (http://www.thespacereview.com/article/1650/1). Use of Earth-Moon libration points as sites for early demonstrations of capabilities necessary for human missions to Mars, for example, contrasts sharply with using missions to near-Earth asteroids (NEAs) for that purpose.

Space Trajectory Error Analysis Program (STEAP) for halo orbit missions. Volume 1: Analytic and user's manual

NASA Technical Reports Server (NTRS)

Byrnes, D. V.; Carney, P. C.; Underwood, J. W.; Vogt, E. D.

1974-01-01

Development, test, conversion, and documentation of computer software for the mission analysis of missions to halo orbits about libration points in the earth-sun system is reported. The software consisting of two programs called NOMNAL and ERRAN is part of the Space Trajectories Error Analysis Programs (STEAP). The program NOMNAL targets a transfer trajectory from Earth on a given launch date to a specified halo orbit on a required arrival date. Either impulsive or finite thrust insertion maneuvers into halo orbit are permitted by the program. The transfer trajectory is consistent with a realistic launch profile input by the user. The second program ERRAN conducts error analyses of the targeted transfer trajectory. Measurements including range, doppler, star-planet angles, and apparent planet diameter are processed in a Kalman-Schmidt filter to determine the trajectory knowledge uncertainty. Execution errors at injection, midcourse correction and orbit insertion maneuvers are analyzed along with the navigation uncertainty to determine trajectory control uncertainties and fuel-sizing requirements. The program is also capable of generalized covariance analyses.

Innovations in mission architectures for exploration beyond low Earth orbit

NASA Technical Reports Server (NTRS)

Cooke, D. R.; Joosten, B. J.; Lo, M. W.; Ford, K. M.; Hansen, R. J.

2003-01-01

Through the application of advanced technologies and mission concepts, architectures for missions beyond Earth orbit have been dramatically simplified. These concepts enable a stepping stone approach to science driven; technology enabled human and robotic exploration. Numbers and masses of vehicles required are greatly reduced, yet the pursuit of a broader range of science objectives is enabled. The scope of human missions considered range from the assembly and maintenance of large aperture telescopes for emplacement at the Sun-Earth libration point L2, to human missions to asteroids, the moon and Mars. The vehicle designs are developed for proof of concept, to validate mission approaches and understand the value of new technologies. The stepping stone approach employs an incremental buildup of capabilities, which allows for future decision points on exploration objectives. It enables testing of technologies to achieve greater reliability and understanding of costs for the next steps in exploration. c2003 American Institute of Aeronautics and Astronautics. Published by Elsevier Science Ltd. All rights reserved.

On the stability of dust orbits in mean-motion resonances perturbed by from an interstellar wind

NASA Astrophysics Data System (ADS)

Pástor, Pavol

2014-09-01

Circumstellar dust particles can be captured in a mean-motion resonance (MMR) with a planet and simultaneously be affected by non-gravitational effects. It is possible to describe the secular variations of a particle orbit in the MMR analytically using averaged resonant equations. We derive the averaged resonant equations from the equations of motion in near-canonical form. The secular variations of the particle orbit depending on the orientation of the orbit in space are taken into account. The averaged resonant equations can be derived/confirmed also from Lagrange's planetary equations. We apply the derived theory to the case when the non-gravitational effects are the Poynting-Robertson effect, the radial stellar wind, and an interstellar wind. The analytical and numerical results obtained are in excellent agreement. We found that the types of orbits correspond to libration centers of the conservative problem. The averaged resonant equations can lead to a system of equations which holds for stationary points in a subset of resonant variables. Using this system we show analytically that for the considered non-gravitational effects, all stationary points should correspond to orbits which are stationary in interplanetary space after an averaging over a synodic period. In an exact resonance, the stationary orbits are stable. The stability is achieved by a periodic repetition of the evolution during the synodic period. Numerical solutions of this system show that there are no stationary orbits for either the exact or non-exact resonances.

Dissipation in a tidally perturbed body librating in longitude

NASA Astrophysics Data System (ADS)

Efroimsky, Michael

2018-05-01

Internal dissipation in a tidally perturbed librating body differs in several respects from the tidal dissipation in a steadily spinning rotator. First, libration changes the spectral distribution of tidal damping across the tidal modes, as compared to the case of steady spin. This changes both the tidal heating rate and the tidal torque. Second, while a non-librating rotator experiences alternating deformation only due to the potential force exerted on it by the perturber, a librating body is also subject to a toroidal force proportional to the angular acceleration. Third, while the centrifugal force in a steadily spinning body renders only a permanent deformation (which defines the oblateness when the body cools down), in a librating body this force contains two alternating components-one purely radial, another a degree-2 potential force. Both contribute to heating, as well as to the tidal torque and potential (and, thereby, to the orbital evolution). We develop a formalism needed to describe dissipation in a homogeneous terrestrial body performing small-amplitude libration in longitude. This formalism incorporates as its part a linear rheological law defining the response of the rotator's material to forcing. While the developed formalism can work with an arbitrary linear rheology, we consider a simple example of a Maxwell material. We demonstrate that, independent of the rheology, forced libration in longitude can provide a considerable and even leading-and sometimes overwhelming-input in the tidal heating. Based on the observed parameters, this input amounts to 52% in Phobos, 33% in Mimas, 23% in Enceladus, and 96% in Epimetheus. This supports the hypothesis by Makarov and Efroimsky (2014) that the additional tidal damping due to forced libration may have participated in the early heating up of some of the large moons. As one possibility, such a moon could have been chipped by collisions-whereby it acquired a higher permanent triaxiality and, therefore, a higher forced-libration magnitude and, consequently, a higher heating rate. After the moon warms up, its permanent triaxiality decreases, and so does the tidal heating rate.

Large longitude libration of Mercury reveals a molten core.

PubMed

Margot, J L; Peale, S J; Jurgens, R F; Slade, M A; Holin, I V

2007-05-04

Observations of radar speckle patterns tied to the rotation of Mercury establish that the planet occupies a Cassini state with obliquity of 2.11 +/- 0.1 arc minutes. The measurements show that the planet exhibits librations in longitude that are forced at the 88-day orbital period, as predicted by theory. The large amplitude of the oscillations, 35.8 +/- 2 arc seconds, together with the Mariner 10 determination of the gravitational harmonic coefficient C22, indicates that the mantle of Mercury is decoupled from a core that is at least partially molten.

Contingency Planning for the Microwave Anisotropy Probe Mission

NASA Technical Reports Server (NTRS)

Mesarch, Michael A.; Rohrbaugh, David; Schiff, Conrad; Bauer, Frank (Technical Monitor)

2002-01-01

The Microwave Anisotropy Probe (MAP) utilized a phasing loop/lunar encounter strategy to achieve a small amplitude Lissajous orbit about the Sun-Earth/Moon L2 libration point. The use of phasing loops was key in minimizing MAP's overall deltaV needs while also providing ample opportunities for contingency resolution. This paper will discuss the different contingencies and responses studied for MAP. These contingencies included accommodating excessive launch vehicle errors (beyond 3 sigma), splitting perigee maneuvers to achieve ground station coverage through the Deep Space Network (DSN), delaying the start of a perigee maneuver, aborting a perigee maneuver in the middle of execution, missing a perigee maneuver altogether, and missing the lunar encounter (crucial to achieving the final Lissajous orbit). It is determined that using a phasing loop approach permits many opportunities to correct for a majority of these contingencies.

Establishing the moon as a spectral radiance standard

USGS Publications Warehouse

Kieffer, H.H.; Wildey, R.L.

1996-01-01

A new automated observatory dedicated to the radiometry of the moon has been constructed to provide new radiance information for calibration of earth-orbiting imaging instruments, particularly Earth Observing System instruments. Instrumentation includes an imaging photometer with 4.5-in. resolution on a fully digital mount and a full-aperture radiance calibration source. Interference filters within 0.35-0.95 ??m correspond to standard stellar magnitude systems, accommodate wavelengths of lunar spectral contrast, and approximate some band-passes of planned earth-orbiting instruments (ASTER, Landsat-7 ETM, MISR, MODIS, and SeaWIFS). The same equipment is used for lunar and stellar observations, with the use of an aperture stop in lunar imaging to comply with Nyquist's theorem and lengthen exposure times to avoid scintillation effects. A typical robotic night run involves observation of about 60 photometric standard stars and the moon; about 10 of the standard stars are observed repeatedly to determine atmospheric extinction, and the moon is observed several times. Observations are to be made on every photometric night during the bright half of the month for at least 4.5 years to adequately cover phase and libration variation. Each lunar image is reduced to absolute exoatmospheric radiance and reprojected to a fixed selenographic grid system. The collection of these images at various librations and phase angles will be reduced to photometric models for each of the approximately 120 000 points in the lunar grid for each filter. Radiance models of the moon can then be produced for the precise geometry of an orbiting instrument observation. Expected errors are under 1% relative and 2.5% absolute. A second telescope operating from 1.0 to 2.5 ??m is planned.

Use of Invariant Manifolds for Transfers Between Three-Body Systems

NASA Technical Reports Server (NTRS)

Beckman, Mark; Howell, Kathleen

2003-01-01

The Lunar L1 and L2 libration points have been proposed as gateways granting inexpensive access to interplanetary space. To date, only individual solutions to the transfer between three-body systems have been found. The methodology to solve the problem for arbitrary three-body systems and entire families of orbits does not exist. This paper presents the initial approaches to solve the general problem for single and multiple impulse transfers. Two different methods of representing and storing 7-dimensional invariant manifold data are presented. Some particular solutions are presented for the transfer problem, though the emphasis is on developing methodology for solving the general problem.

Representations of Invariant Manifolds for Applications in Three-Body Systems

NASA Technical Reports Server (NTRS)

Howell, K.; Beckman, M.; Patterson, C.; Folta, D.

2004-01-01

The Lunar L1 and L2 libration points have been proposed as gateways granting inexpensive access to interplanetary space. To date, only individual solutions to the transfer between three-body systems have been found. The methodology to solve the problem for arbitrary three-body systems and entire families of orbits is currently being studied. This paper presents an initial approach to solve the general problem for single and multiple impulse transfers. Two different methods of representing and storing the invariant manifold data are presented. Some particular solutions are presented for two types of transfer problems, though the emphasis is on developing the methodology for solving the general problem.

Estimating Mass Parameters of Doubly Synchronous Binary Asteroids

NASA Astrophysics Data System (ADS)

Davis, Alex; Scheeres, Daniel J.

2017-10-01

The non-spherical mass distributions of binary asteroid systems lead to coupled mutual gravitational forces and torques. Observations of the coupled attitude and orbital dynamics can be leveraged to provide information about the mass parameters of the binary system. The full 3-dimensional motion has 9 degrees of freedom, and coupled dynamics require the use of numerical investigation only. In the current study we simplify the system to a planar ellipsoid-ellipsoid binary system in a doubly synchronous orbit. Three modes are identified for the system, which has 4 degrees of freedom, with one degree of freedom corresponding to an ignorable coordinate. The three modes correspond to the three major librational modes of the system when it is in a doubly synchronous orbit. The linearized periods of each mode are a function of the mass parameters of the two asteroids, enabling measurement of these parameters based on observations of the librational motion. Here we implement estimation techniques to evaluate the capabilities of this mass measurement method. We apply this methodology to the Trojan binary asteroid system 617 Patroclus and Menoetius (1906 VY), the final flyby target of the recently announced LUCY Discovery mission. This system is of interest because a stellar occultation campaign of the Patroclus and Menoetius system has suggested that the asteroids are similarly sized oblate ellipsoids moving in a doubly-synchronous orbit, making the system an ideal test for this investigation. A number of missed observations during the campaign also suggested the possibility of a crater on the southern limb of Menoetius, the presence of which could be evaluated by our mass estimation method. This presentation will review the methodology and potential accuracy of our approach in addition to evaluating how the dynamical coupling can be used to help understand light curve and stellar occultation observations for librating binary systems.

Orbits in elementary, power-law galaxy bars - 1. Occurrence and role of single loops

NASA Astrophysics Data System (ADS)

Struck, Curtis

2018-05-01

Orbits in galaxy bars are generally complex, but simple closed loop orbits play an important role in our conceptual understanding of bars. Such orbits are found in some well-studied potentials, provide a simple model of the bar in themselves, and may generate complex orbit families. The precessing, power ellipse (p-ellipse) orbit approximation provides accurate analytic orbit fits in symmetric galaxy potentials. It remains useful for finding and fitting simple loop orbits in the frame of a rotating bar with bar-like and symmetric power-law potentials. Second-order perturbation theory yields two or fewer simple loop solutions in these potentials. Numerical integrations in the parameter space neighbourhood of perturbation solutions reveal zero or one actual loops in a range of such potentials with rising rotation curves. These loops are embedded in a small parameter region of similar, but librating orbits, which have a subharmonic frequency superimposed on the basic loop. These loops and their librating companions support annular bars. Solid bars can be produced in more complex potentials, as shown by an example with power-law indices varying with radius. The power-law potentials can be viewed as the elementary constituents of more complex potentials. Numerical integrations also reveal interesting classes of orbits with multiple loops. In two-dimensional, self-gravitating bars, with power-law potentials, single-loop orbits are very rare. This result suggests that gas bars or oval distortions are unlikely to be long-lived, and that complex orbits or three-dimensional structure must support self-gravitating stellar bars.

Triangular Libration Points in the CR3BP with Radiation, Triaxiality and Potential from a Belt

NASA Astrophysics Data System (ADS)

Singh, Jagadish; Taura, Joel John

2017-07-01

In this paper the equations of motion of the circular restricted three body problem is modified to include radiation of the bigger primary, triaxiality of the smaller primary; and gravitational potential created by a belt. We have obtained that due to the perturbations, the locations of the triangular libration points and their linear stability are affected. The points move towards the bigger primary due to the resultant effect of the perturbations. Triangular libration points are stable for 0<μ<μc0<μ<μc and unstable for μc≤μ≤12μc≤μ≤12, where μcμc is the critical mass ratio affected by the perturbations. The radiation of the bigger primary and triaxiality of the smaller primary have destabilizing propensities, whereas the potential created by the belt has stabilizing propensity. This model could be applied in the study of the motion of a dust particle near radiating -triaxial binary system surrounded by a belt.

Analysis of the long and short-period terms due the nonsphericity of the central body: applications for Mercury

NASA Astrophysics Data System (ADS)

Carvalho, J. P. S.

2017-10-01

In this work, we present an approach taking into account the single-averaged equations and unaveraged equations to investigate the dynamics of artificial satellites on the effect due to the non-spherical shape of the planet Mercury. An analysis considering the long-period terms and another taking into account the short-period terms is presented. The numerical integrations of the equations developed are performed using the Maple software. We consider the numerical values of the most updated spherical harmonic coefficients in the literature. Emphasis is given to analyze the effect of the C22 term in the dynamics of the spacecraft. We show that the two techniques are in agreement (average or not average). We found orbits that librates around an equilibrium point with small variation of the orbital elements, in particular the eccentricity and argument of the pericenter. We also note that the C22 term contributes to reduce the growth of the orbital eccentricity.

Solar Electric Propulsion Vehicle Design Study for Cargo Transfer to Earth-moon L1

NASA Technical Reports Server (NTRS)

Sarver-Verhey, Timothy R.; Kerslake, Thomas W.; Rawlin, Vincent K.; Falck, Robert D.; Dudzinski, Leonard J.; Oleson, Steven R.

2002-01-01

A design study for a cargo transfer vehicle using solar electric propulsion was performed for NASA's Revolutionary Aerospace Systems Concepts program. Targeted for 2016, the solar electric propulsion (SEP) transfer vehicle is required to deliver a propellant supply module with a mass of approximately 36 metric tons from Low Earth Orbit to the first Earth-Moon libration point (LL1) within 270 days. Following an examination of propulsion and power technology options, a SEP transfer vehicle design was selected that incorporated large-area (approx. 2700 sq m) thin film solar arrays and a clustered engine configuration of eight 50 kW gridded ion thrusters mounted on an articulated boom. Refinement of the SEP vehicle design was performed iteratively to properly estimate the required xenon propellant load for the out-bound orbit transfer. The SEP vehicle performance, including the xenon propellant estimation, was verified via the SNAP trajectory code. Further efforts are underway to extend this system model to other orbit transfer missions.

The dynamics and control of large flexible space structures. Volume 3, part B: The modelling, dynamics, and stability of large Earth pointing orbiting structures

NASA Technical Reports Server (NTRS)

Bainum, P. M.; Kumar, V. K.

1980-01-01

The dynamics and stability of large orbiting flexible beams, and platforms and dish type structures oriented along the local horizontal are treated both analytically and numerically. It is assumed that such structures could be gravitationally stabilized by attaching a rigid light-weight dumbbell at the center of mass by a spring loaded hinge which also could provide viscous damping. For the beam, the small amplitude inplane pitch motion, dumbbell librational motion, and the anti-symmetric elastic modes are all coupled. The three dimensional equations of motion for a circular flat plate and shallow spherical shell in orbit with a two-degree-of freedom gimballed dumbbell are also developed and show that only those elastic modes described by a single nodal diameter line are influenced by the dumbbell motion. Stability criteria are developed for all the examples and a sensitivity study of the system response characteristics to the key system parameters is carried out.

Utilization of multi-body trajectories in the Sun-Earth-Moon system

NASA Technical Reports Server (NTRS)

Farquhar, R. W.

1980-01-01

An overview of three uncommon trajectory concepts for space missions in the Sun-Earth-Moon System is presented. One concept uses a special class of libration-point orbits called 'halo orbits.' It is shown that members of this orbit family are advantageous for monitoring the solar wind input to the Earth's magnetosphere, and could also be used to establish a continuous communications link between the Earth and the far side of the Moon. The second concept employs pretzel-like trajectories to explore the Earth's geomagnetic tail. These trajectories are formed by using the Moon to carry out a prescribed sequence of gravity-assist maneuvers. Finally, there is the 'boomerang' trajectory technique for multiple-encounter missions to comets and asteroids. In this plan, Earth-swingby maneuvers are used to retarget the original spacecraft trajectory. The boomerang method could be used to produce a triple-encounter sequence which includes flybys of comets Halley and Tempel-2 as well as the asteroid Geographos.

An approach for finding long period elliptical orbits for precursor SEI missions

NASA Technical Reports Server (NTRS)

Fraietta, Michael F.; Bond, Victor R.

1993-01-01

Precursors for Solar System Exploration Initiative (SEI) missions may require long period elliptical orbits about a planet. These orbits will typically have periods on the order of tens to hundreds of days. Some potential uses for these orbits may include the following: studying the effects of galactic cosmic radiation, parking orbits for engineering and operational test of systems, and ferrying orbits between libration points and low altitude orbits. This report presents an approach that can be used to find these orbits. The approach consists of three major steps. First, it uses a restricted three-body targeting algorithm to determine the initial conditions which satisfy certain desired final conditions in a system of two massive primaries. Then the initial conditions are transformed to an inertial coordinate system for use by a special perturbation method. Finally, using the special perturbation method, other perturbations (e.g., sun third body and solar radiation pressure) can be easily incorporated to determine their effects on the nominal trajectory. An algorithm potentially suitable for on-board guidance will also be discussed. This algorithm uses an analytic method relying on Chebyshev polynomials to compute the desired position and velocity of the satellite as a function of time. Together with navigation updates, this algorithm can be implemented to predict the size and timing for AV corrections.

The Suess-Urey mission (return of solar matter to Earth).

PubMed

Rapp, D; Naderi, F; Neugebauer, M; Sevilla, D; Sweetnam, D; Burnett, D; Wiens, R; Smith, N; Clark, B; McComas, D; Stansbery, E

1996-01-01

The Suess-Urey (S-U) mission has been proposed as a NASA Discovery mission to return samples of matter from the Sun to the Earth for isotopic and chemical analyses in terrestrial laboratories to provide a major improvement in our knowledge of the average chemical and isotopic composition of the solar system. The S-U spacecraft and sample return capsule will be placed in a halo orbit around the L1 Sun-Earth libration point for two years to collect solar wind ions which implant into large passive collectors made of ultra-pure materials. Constant Spacecraft-Sun-Earth geometries enable simple spin stabilized attitude control, simple passive thermal control, and a fixed medium gain antenna. Low data requirements and the safety of a Sun-pointed spinner, result in extremely low mission operations costs.

Assessment of uncertainty in ROLO lunar irradiance for on-orbit calibration

USGS Publications Warehouse

Stone, T.C.; Kieffer, H.H.; Barnes, W.L.; Butler, J.J.

2004-01-01

A system to provide radiometric calibration of remote sensing imaging instruments on-orbit using the Moon has been developed by the US Geological Survey RObotic Lunar Observatory (ROLO) project. ROLO has developed a model for lunar irradiance which treats the primary geometric variables of phase and libration explicitly. The model fits hundreds of data points in each of 23 VNIR and 9 SWIR bands; input data are derived from lunar radiance images acquired by the project's on-site telescopes, calibrated to exoatmospheric radiance and converted to disk-equivalent reflectance. Experimental uncertainties are tracked through all stages of the data processing and modeling. Model fit residuals are ???1% in each band over the full range of observed phase and libration angles. Application of ROLO lunar calibration to SeaWiFS has demonstrated the capability for long-term instrument response trending with precision approaching 0.1% per year. Current work involves assessing the error in absolute responsivity and relative spectral response of the ROLO imaging systems, and propagation of error through the data reduction and modeling software systems with the goal of reducing the uncertainty in the absolute scale, now estimated at 5-10%. This level is similar to the scatter seen in ROLO lunar irradiance comparisons of multiple spacecraft instruments that have viewed the Moon. A field calibration campaign involving NASA and NIST has been initiated that ties the ROLO lunar measurements to the NIST (SI) radiometric scale.

Dynamical analysis of rendezvous and docking with very large space infrastructures in non-Keplerian orbits

NASA Astrophysics Data System (ADS)

Colagrossi, Andrea; Lavagna, Michèle

2018-03-01

A space station in the vicinity of the Moon can be exploited as a gateway for future human and robotic exploration of the solar system. The natural location for a space system of this kind is about one of the Earth-Moon libration points. The study addresses the dynamics during rendezvous and docking operations with a very large space infrastructure in an EML2 Halo orbit. The model takes into account the coupling effects between the orbital and the attitude motion in a circular restricted three-body problem environment. The flexibility of the system is included, and the interaction between the modes of the structure and those related with the orbital motion is investigated. A lumped parameter technique is used to represents the flexible dynamics. The parameters of the space station are maintained as generic as possible, in a way to delineate a global scenario of the mission. However, the developed model can be tuned and updated according to the information that will be available in the future, when the whole system will be defined with a higher level of precision.

Polynomial expansions of single-mode motions around equilibrium points in the circular restricted three-body problem

NASA Astrophysics Data System (ADS)

Lei, Hanlun; Xu, Bo; Circi, Christian

2018-05-01

In this work, the single-mode motions around the collinear and triangular libration points in the circular restricted three-body problem are studied. To describe these motions, we adopt an invariant manifold approach, which states that a suitable pair of independent variables are taken as modal coordinates and the remaining state variables are expressed as polynomial series of them. Based on the invariant manifold approach, the general procedure on constructing polynomial expansions up to a certain order is outlined. Taking the Earth-Moon system as the example dynamical model, we construct the polynomial expansions up to the tenth order for the single-mode motions around collinear libration points, and up to order eight and six for the planar and vertical-periodic motions around triangular libration point, respectively. The application of the polynomial expansions constructed lies in that they can be used to determine the initial states for the single-mode motions around equilibrium points. To check the validity, the accuracy of initial states determined by the polynomial expansions is evaluated.

On the photo-gravitational restricted four-body problem with variable mass

NASA Astrophysics Data System (ADS)

Mittal, Amit; Agarwal, Rajiv; Suraj, Md Sanam; Arora, Monika

2018-05-01

This paper deals with the photo-gravitational restricted four-body problem (PR4BP) with variable mass. Following the procedure given by Gascheau (C. R. 16:393-394, 1843) and Routh (Proc. Lond. Math. Soc. 6:86-97, 1875), the conditions of linear stability of Lagrange triangle solution in the PR4BP are determined. The three radiating primaries having masses m1, m2 and m3 in an equilateral triangle with m2=m3 will be stable as long as they satisfy the linear stability condition of the Lagrangian triangle solution. We have derived the equations of motion of the mentioned problem and observed that there exist eight libration points for a fixed value of parameters γ (m at time t/m at initial time, 0<γ≤1 ), α (the proportionality constant in Jeans' law (Astronomy and Cosmogony, Cambridge University Press, Cambridge, 1928), 0≤α≤2.2), the mass parameter μ=0.005 and radiation parameters qi, (0< qi≤1, i=1, 2, 3). All the libration points are non-collinear if q2≠ q3. It has been observed that the collinear and out-of-plane libration points also exist for q2=q3. In all the cases, each libration point is found to be unstable. Further, zero velocity curves (ZVCs) and Newton-Raphson basins of attraction are also discussed.

Mapping the stability field of Jupiter Trojans

NASA Technical Reports Server (NTRS)

Levison, H. F.; Shoemaker, E. M.; Wolfe, R. F.

1991-01-01

Jupiter Trojans are a remnant of outer solar system planetesimals captured into stable or quasistable libration about the 1:1 resonance with the mean motion of Jupiter. The observed swarms of Trojans may provide insight into the original mass of condensed solids in the zone from which the Jovian planets accumulated, provided that the mechanisms of capture can be understood. As the first step toward this understanding, the stability field of Trojans were mapped in the coordinate proper eccentricity, e(sub p), and libration amplitude, D. To accomplish this mapping, the orbits of 100 particles with e(sub p) in the range of 0 to 0.8 and D in the range 0 to 140 deg were numerically integrated. Orbits of the Sun, the four Jovian planets, and the massless particles were integrated as a full N-body system, in a barycentric frame using fourth order symplectic scheme.

Topographic-driven instabilities in terrestrial bodies

NASA Astrophysics Data System (ADS)

Vantieghem, S.; Cebron, D.; Herreman, W.; Lacaze, L.

2013-12-01

Models of internal planetary fluid layers (core flows, subsurface oceans) commonly assume that these fluid envelopes have a spherical shape. This approximation however entails a serious restriction from the fluid dynamics point of view. Indeed, in the presence of mechanical forcings (precession, libration, nutation or tides) due to gravitational interaction with orbiting partners, boundary topography (e.g. of the core-mantle boundary) may excite flow instabilities and space-filling turbulence. These phenomena may affect heat transport and dissipation at the main order. Here, we focus on instabilities driven by longitudinal libration. Using a suite of theoretical tools and numerical simulations, we are able to discern a parameter range for which instability may be excited. We thereby consider deformations of different azimuthal order. This study gives the first numerical evidence of the tripolar instability. Furthermore, we explore the non-linear regime and investigate the amplitude as well as the dissipation of the saturated instability. Indeed, these two quantities control the torques on the solid layers and the thermal transport. Furthermore, based on this results, we address the issue of magnetic field generation associated with these flows (by induction or by dynamo process). This instability mechanism applies to both synchronized as non-synchronized bodies. As such, our results show that a tripolar instability might be present in various terrestrial bodies (Early Moon, Gallilean moons, asteroids, etc.), where it could participate in dynamo action. Simulation of a libration-driven tripolar instability in a deformed spherical fluid layer: snapshot of the velocity magnitude, where a complex 3D flow pattern is established.

Dynamics of the retrograde 1/1 mean motion resonance

NASA Astrophysics Data System (ADS)

Huang, Yukun; Li, Miao; Li, Junfeng; Gong, Shengping

2018-04-01

Mean motion resonances are very common in the solar system. Asteroids in mean motion resonances with giant planets have been studied for centuries. But it was not until recently that asteroids in retrograde mean motion resonances with Jupiter and Saturn were discovered. The newly discovered asteroid, 2015 BZ509 is confirmed to be the first asteroid in retrograde 1:1 mean motion resonance (or retrograde co-orbital resonance) with Jupiter, which gives rise to our interests in its unique resonant dynamics. In this study, we thoroughly investigate the phase-space structure of the retrograde 1:1 resonance within the framework of the circular restricted three-body problem. We begin by constructing a simple integrable approximation for the planar retrograde resonance with the Hamiltonian approach and show that the variables definition of the retrograde resonance is very different to the prograde one. When it comes to the disturbing function, we abandon the classical series expansion approach, whereas numerically carry out the averaging process on the disturbing function in closed form. The phase portrait of the retrograde 1:1 resonance is depicted with the level curves of the averaged Hamiltonian. We find that the topological structure of phase space for the retrograde 1:1 resonance is very different to other resonances, due to the consistent existence of the collision separatrix. And the surprising bifurcation of equilibrium point around 180° (i.e., the apocentric libration center) has never been found in any other mean motion resonances before. We thoroughly analyze the novel apocentric librations and find that close encounter with the planet does not always lead to the disruption of a stable apocentric libration. Afterwards, we examine the Kozai dynamics inside the mean motion resonance with the similar Hamiltonian approach and explain why the exact resonant point does not exist in the 3D retrograde 1:1 resonance model.

The effect of the Earth's oblateness on the Moon's physical libration in latitude

NASA Astrophysics Data System (ADS)

Kondratyev, B. P.

2013-05-01

The Moon's physical libration in latitude generated by gravitational forces caused by the Earth's oblateness has been examined by a vector analytical method. Libration oscillations are described by a close set of five linear inhomogeneous differential equations, the dispersion equation has five roots, one of which is zero. A complete solution is obtained. It is revealed that the Earth's oblateness: a) has little effect on the instantaneous axis of Moon's rotation, but causes an oscillatory rotation of the body of the Moon with an amplitude of 0.072″ and pulsation period of 16.88 Julian years; b) causes small nutations of poles of the orbit and of the ecliptic along tight spirals, which occupy a disk with a cut in a center and with radius of 0.072″. Perturbations caused by the spherical Earth generate: a) physical librations in latitude with an amplitude of 34.275″; b) nutational motion for centers of small spiral nutations of orbit (ecliptic) pole over ellipses with semi-major axes of 113.850″ (85.158″) and the first pole rotates round the second one along a circle with radius of 28.691″; c) nutation of the Moon's celestial pole over an ellipse with a semi-major axis of 45.04″ and with an axes ratio of about 0.004 with a period of T = 27.212 days. The principal ellipse's axis is directed tangentially with respect to the precession circumference, along which the celestial pole moves nonuniformly nearly in one dimension. In contrast to the accepted concept, the latitude does not change while the Moon's poles of rotation move. The dynamical reason for the inclination of the Moon's mean equator with respect to the ecliptic is oblateness of the body of the Moon.

Systems Engineering Challenges for GSFC Space Science Mission Operations

NASA Technical Reports Server (NTRS)

Thienel, Julie; Harman, Richard R.

2017-01-01

The NASA Goddard Space Flight Center Space Science Mission Operations (SSMO) project currently manages19 missions for the NASA Science Mission Directorate, within the Planetary, Astrophysics, and Heliophysics Divisions. The mission lifespans range from just a few months to more than20 years. The WIND spacecraft, the oldest SSMO mission, was launched in 1994. SSMO spacecraft reside in low earth, geosynchronous,highly elliptical, libration point, lunar, heliocentric,and Martian orbits. SSMO spacecraft range in size from 125kg (Aeronomy of Ice in the Mesosphere (AIM)) to over 4000kg (Fermi Gamma-Ray Space Telescope (Fermi)). The attitude modes include both spin and three-axis stabilized, with varying requirements on pointing accuracy. The spacecraft are operated from control centers at Goddard and off-site control centers;the Lunar Reconnaissance Orbiter (LRO), the Solar Dynamics Observatory (SDO) and Magnetospheric MultiScale (MMS)mission were built at Goddard. The Advanced Composition Explorer (ACE) and Wind are operated out of a multi-mission operations center, which will also host several SSMO-managed cubesats in 2017. This paper focuses on the systems engineeringchallenges for such a large and varied fleet of spacecraft.

Unique Non-Keplerian Orbit Vantage Locations for Sun-Earth Connection and Earth Science Vision Roadmaps

NASA Technical Reports Server (NTRS)

Folta, David; Young, Corissa; Ross, Adam

2001-01-01

The purpose of this investigation is to determine the feasibility of attaining and maintaining unique non-Keplerian orbit vantage locations in the Earth/Moon environment in order to obtain continuous scientific measurements. The principal difficulty associated with obtaining continuous measurements is the temporal nature of astrodynamics, i.e., classical orbits. This investigation demonstrates advanced trajectory designs to meet demanding science requirements which cannot be met following traditional orbital mechanic logic. Examples of continuous observer missions addressed include Earth pole-sitters and unique vertical libration orbits that address Sun-Earth Connection and Earth Science Vision roadmaps.

Orbital evolution and escape of Martian Trojans due to the Yarkovsky effect

NASA Astrophysics Data System (ADS)

Christou, Apostolos

2017-06-01

Recently it was shown that the Yarkovsky effect can lead to significant orbit change for Trojans of Mars [1,2] and that the orbital distribution of observed Trojans is consistent with a negative along-track acceleration of the same functional form as seasonal yarkovsky; this feature was used to constrain the age of the Eureka family of Mars Trojan asteroids [2]. In contrast, the Yarkovsky effect appears to have a negligible role in shaping observed families of Jupiter Trojans [3].To explore the evolution and end states of Trojans evolved by the Yarkosky effect, I have numerically integrated test particles under a model of the diurnal variant and for different values of the acceleration strength up to 10-2 AU/Myr for da/dt outside the resonance. I use as a starting point the orbits of the three largest Martian Trojans: 5261 Eureka, (101429) 1998 VF31 and (121514) 1999 UJ7.I find, as in [2], that the evolution of the inclination I and the libration amplitude L depends on the sign of the acceleration and is essentially deterministic. Considering the rate of change of the Tisserand constant [5,6] leads to a simple analytical expression that reproduces well the inclination evolution of the Trojans. The evolution of e is somewhat more stochastic, probably due to chaotic diffusion [4] and/or the influence of Mars’ eccentricity [2].Trojans escape upon reaching the boundaries of stability domains mapped out in [4], demarcated by resonances with principal secular modes and the Kozai resonance. The mechanism of escape is by increasing e and/or the libration amplitude to the point of allowing close encounters with Mars.During the presentation I will describe the ensemble evolution of Trojans under Yarkovsky, how it is related to the lifetime in the 1:1 resonance and discuss the implications for Trojan stability at Earth and Jupiter.[1] Christou, A.A., 2013, Icarus, 224, 144.[2] Ćuk, M., Christou, A.A., Hamilton, D.P., 2015, Icarus, 252, 339.[3] Milani, A., Knezević, Z., Spoto, F., Cellino, A., Novaković, B., Tsirvoulis, G., 2017, Icarus, 288, 240.[4] Scholl, H., Marzari, F., Tricarico, P., 2005, Icarus, 175, 397.[5] Hamilton, D.P., 1994, Icarus, 109, 221[6] Liou, J. C., Zook, H. A., 1997, Icarus, 128, 354.

Regular Motions of Resonant Asteroids

NASA Astrophysics Data System (ADS)

Ferraz-Mello, S.

1990-11-01

RESUMEN. Se revisan resultados analiticos relativos a soluciones regulares del problema asteroidal eliptico promediados en la vecindad de una resonancia con jupiten Mencionamos Ia ley de estructura para libradores de alta excentricidad, la estabilidad de los centros de liberaci6n, las perturbaciones forzadas por la excentricidad de jupiter y las 6rbitas de corotaci6n. ABSTRAC This paper reviews analytical results concerning the regular solutions of the elliptic asteroidal problem averaged in the neighbourhood of a resonance with jupiter. We mention the law of structure for high-eccentricity librators, the stability of the libration centers, the perturbations forced by the eccentricity ofjupiter and the corotation orbits. Key words: ASThROIDS

The Detection Of Planets In The 1:1 Resonance

NASA Astrophysics Data System (ADS)

Dvorak, R.; Schneider, J.; Schwarz, R.; Lhotka, C.; Sandor, Z.

Orbits in the mean motion resonance are of special interest for asteroids in our Solar System. It is due to the fact that in a region 60° before Jupiter and 60° behind the largest planet a large number of asteroids are there. Many analytical and numerical work has been devoted to the stability of these two `clouds` of asteroids, which are named after the warriors of the Trojan war. The Trojans librate about these two stable equilibrium points in the so-called tadpole orbits having two well distinct periods. The 'exchange orbits' in the general three body problem can be described as follows: Two small but massive bodies are moving on nearly circular orbits with almost the same semimajor axes around a much more massive host. Because of the 3rd Keplerian law the one with the inner orbit is faster and approaches the outer body from behind. Before they meet, the inner body is shifted to the orbit of the outer and vice-versa the former outer body moves to an orbit with a smaller semimajor axis: they have changed their orbits and their semimajor axis! In the satellite system of Saturn the two moons Janus and Epimetheus (the orbits of these two moons differ only by 50 km; the respective semimajor axes are 151472 km and 151422 km and have themselves diameters of more than 100 km) have exactly these kinds of orbits. We postulate that this kind of orbits may also exist in extrasolar planetary systems.

Constraints on Titan's rotation from Cassini mission radar data

NASA Astrophysics Data System (ADS)

Bills, Bruce; Stiles, Bryan W.; Hayes, Alexander

2015-05-01

We present results of a new analysis of the rotational kinematics of Titan, as constrained by Cassini radar data, extending over the entire currently available set of flyby encounters. Our analysis provides a good constraint on the current orientation of the spin pole, but does not have sufficient accuracy and duration to clearly see the expected spin pole precession. In contrast, we do clearly see temporal variations in the spin rate, which are driven by gravitational torques which attempt to keep the prime meridian oriented toward Saturn.Titan is a synchronous rotator. At lowest order, that means that the rotational and orbital motions are synchronized. At the level of accuracy required to fit the Cassini radar data, we can see that synchronous rotation and uniform rotation are not quite the same thing. Our best fitting model has a fixed pole, and a rotation rate which varies with time, so as to keep Titan's prime meridian oriented towards Saturn, as the orbit varies.A gravitational torque on the tri-axial figure of Titan attempts to keep the axis of least inertia oriented toward Saturn. The main effect is to synchronize the orbit and rotation periods, as seen in inertial space. The response of the rotation angle, to periodic changes in orbital mean longitude, is modeled as a damped, forced harmonic oscillator. This acts as a low-pass filter. The rotation angle accurately tracks orbital variations at periods longer than the free libration period, but is unable to follow higher frequency variations.The mean longitude of Titan's orbit varies on a wide range of time scales. The largest variations are at Saturn's orbital period (29.46 years), and are due to solar torques. There are also variations at periods of 640 and 5800 days, due to resonant interaction with Hyperion.For a rigid body, with moments of inertia estimated from observed gravity, the free libration period for Titan would be 850 days. The best fit to the radar data is obtained with a libration period of 645 days, and a damping time of 1000 years.The principal deviation of Titan's rotation from uniform angular rate, as seen in the Cassini radar data, is a periodic signal resonantly forced by Hyperion.

Waste Management Options for Long-Duration Space Missions: When to Reject, Reuse, or Recycle

NASA Technical Reports Server (NTRS)

Linne, Diane L.; Palaszewski, Bryan A.; Gokoglu, Suleyman; Gallo, Christopher A.; Balasubramaniam, Ramaswamy; Hegde, Uday G.

2014-01-01

The amount of waste generated on long-duration space missions away from Earth orbit creates the daunting challenge of how to manage the waste through reuse, rejection, or recycle. The option to merely dispose of the solid waste through an airlock to space was studied for both Earth-moon libration point missions and crewed Mars missions. Although the unique dynamic characteristics of an orbit around L2 might allow some discarded waste to intersect the lunar surface before re-impacting the spacecraft, the large amount of waste needed to be managed and potential hazards associated with volatiles recondensing on the spacecraft surfaces make this option problematic. A second option evaluated is to process the waste into useful gases to be either vented to space or used in various propulsion systems. These propellants could then be used to provide the yearly station-keeping needs at an L2 orbit, or if processed into oxygen and methane propellants, could be used to augment science exploration by enabling lunar mini landers to the far side of the moon.

The Solar and Heliospheric Observatory (SOHO) Mission: An Overview of Flight Dynamics Support of the Early Mission Phase

NASA Technical Reports Server (NTRS)

Short, R.; Behuncik, J.

1996-01-01

The SOHO spacecraft was successfully launched by an Atlas 2AS from the Eastern Range on December 2, 1995. After a short time in a nearly circular parking orbit, the spacecraft was placed by the Centaur upper stage on a transfer trajectory to the L1 libration point where it was inserted into a class 1 Halo orbit. The nominal mission lifetime is two years which will be spent collecting data from the Sun using a complement of twelve instruments. An overview of the early phases of Flight Dynamics Facility support of the mission is given. Maneuvers required for the mission are discussed, and an evaluation of these maneuvers is given with the attendent effects on the resultant orbit. Thruster performance is presented as well as real time monitoring of thruster activity during maneuvers. Attitude areas presented are the star identification process and role angle determination, momentum management, operating constraints on the star tracker, and guide star switching. A brief description of the two Heads Up displays is given.

The rotation of Titan and Ganymede

NASA Astrophysics Data System (ADS)

Van Hoolst, Tim; Coyette, Alexis; Baland, Rose-Marie; Trinh, Antony

2016-10-01

The rotation rates of Titan and Ganymede, the largest satellites of Saturn and Jupiter, are on average equal to their orbital mean motion. Here we discuss small deviations from the average rotation for both satellites and evaluate the polar motion of Titan induced by its surface fluid layers. We examine different causes at various time scales and assess possible consequences and the potential of using librations and polar motion as probes of the interior structure of the satellites.The rotation rate of Titan and Ganymede cannot be constant on the orbital time scale as a result of the gravitational torque of the central planet acting on the satellites. Titan is moreover expected to show significant polar motion and additional variations in the rotation rate due to angular momentum exchange with the atmosphere, mainly at seasonal periods. Observational evidence for deviations from the synchronous state has been reported several times for Titan but is unfortunately inconclusive. The measurements of the rotation variations are based on determinations of the shift in position of Cassini radar images taken during different flybys. The ESA JUICE (JUpiter ICy moons Explorer) mission will measure the rotation variations of Ganymede during its orbital phase around the satellite starting in 2032.We report on different theoretical aspects of the librations and polar motion. We consider the influence of the rheology of the ice shell and take into account Cassini measurements of the external gravitational field and of the topography of Titan and similar Galileo data about Ganymede. We also evaluate the librations and polar motion induced by Titan's hydrocarbon seas and use the most recent results of Titan's atmosphere dynamics. We finally evaluate the potential of rotation variations to constrain the satellite's interior structure, in particular its ice shell and ocean.

Evidence for a Past High-Eccentricity Lunar Orbit

NASA Technical Reports Server (NTRS)

Garrick-Betthell, Ian; Wisdom, Jack; Zuber, Maria T.

2007-01-01

The large differences between the Moon's three principal moments of inertia have been mystery since Laplace considered them in 1799. Here we present calculations that show how past high eccentricity orbits can account for the moment differences, represented by the low-order lunar gravity field and libration parameters. One of our solutions is that the Moon may have once been in a 3:2 resonance of the orbit period to spin-period, similar to Mercury's present state. The possibility of past high-eccentricity orbits suggests a rich dynamical history and may influence our understanding of the early thermal evolution of the Moon.

Analytical investigation of the dynamics of tethered constellations in Earth orbit, phase 2

NASA Astrophysics Data System (ADS)

Lorenzini, E. C.; Arnold, D. A.; Cosmo, M.; Grossi, M. D.

1986-10-01

The following topics related to the dynamics of the 4-mass tethered system are addressed: (1) the development of damping algorithms for damping the out-of-plane libration of the system and the interaction of the out-of-plane control with the other degrees of freedom; and (2) the development of environmental models to be added to the dynamics simulation computer code. The environmental models are specifically a new drag routine based on the Jacchia's 1977 model, a J(2) model and an accurate thermal model of the wire. Regarding topic (1) a survey of various out-of-plane libration control laws was carried out. Consequently a yo-yo control law with amplitude of the tether length variation proportional to the amplitude of the out-of-game libration has been selected. This control law provides good damping when applied to a (theoretical) two-dimensional system. In the actual 3-dimensional 4-mass tethered system, however, energy is transferred to the least damped degrees of freedom (the out-of-plane lateral deflections are still undamped in the present simulations) in such a way as to decrease the effectiveness of the algorithm for out-of-plane libration control. The addition of damping algorithms for the out-of-plane lateral deflections is therefore necessary.

Analytical investigation of the dynamics of tethered constellations in Earth orbit, phase 2

NASA Technical Reports Server (NTRS)

Lorenzini, E. C.; Arnold, D. A.; Cosmo, M.; Grossi, M. D.

1986-01-01

The following topics related to the dynamics of the 4-mass tethered system are addressed: (1) the development of damping algorithms for damping the out-of-plane libration of the system and the interaction of the out-of-plane control with the other degrees of freedom; and (2) the development of environmental models to be added to the dynamics simulation computer code. The environmental models are specifically a new drag routine based on the Jacchia's 1977 model, a J(2) model and an accurate thermal model of the wire. Regarding topic (1) a survey of various out-of-plane libration control laws was carried out. Consequently a yo-yo control law with amplitude of the tether length variation proportional to the amplitude of the out-of-game libration has been selected. This control law provides good damping when applied to a (theoretical) two-dimensional system. In the actual 3-dimensional 4-mass tethered system, however, energy is transferred to the least damped degrees of freedom (the out-of-plane lateral deflections are still undamped in the present simulations) in such a way as to decrease the effectiveness of the algorithm for out-of-plane libration control. The addition of damping algorithms for the out-of-plane lateral deflections is therefore necessary.

Near-Earth asteroid satellite spins under spin-orbit coupling

DOE Office of Scientific and Technical Information (OSTI.GOV)

Naidu, Shantanu P.; Margot, Jean-Luc

We develop a fourth-order numerical integrator to simulate the coupled spin and orbital motions of two rigid bodies having arbitrary mass distributions under the influence of their mutual gravitational potential. We simulate the dynamics of components in well-characterized binary and triple near-Earth asteroid systems and use surface of section plots to map the possible spin configurations of the satellites. For asynchronous satellites, the analysis reveals large regions of phase space where the spin state of the satellite is chaotic. For synchronous satellites, we show that libration amplitudes can reach detectable values even for moderately elongated shapes. The presence of chaoticmore » regions in the phase space has important consequences for the evolution of binary asteroids. It may substantially increase spin synchronization timescales, explain the observed fraction of asychronous binaries, delay BYORP-type evolution, and extend the lifetime of binaries. The variations in spin rate due to large librations also affect the analysis and interpretation of light curve and radar observations.« less

Diagrammatic theory of transition of pendulum like systems. [orbit-orbit and spin-orbit gravitational resonance interactions

NASA Technical Reports Server (NTRS)

Yoder, C. F.

1979-01-01

Orbit-orbit and spin-orbit gravitational resonances are analyzed using the model of a rigid pendulum subject to both a time-dependent periodic torque and a constant applied torque. First, a descriptive model of passage through resonance is developed from an examination of the polynomial equation that determines the extremes of the momentum variable. From this study, a probability estimate for capture into libration is derived. Second, a lowest order solution is constructed and compared with the solution obtained from numerical integration. The steps necessary to systematically improve this solution are also discussed. Finally, the effect of a dissipative term in the pendulum equation is analyzed.

Dynamics and Origin of the 2:1 Orbital Resonances of the GJ 876 Planets

NASA Astrophysics Data System (ADS)

Lee, Man Hoi; Peale, S. J.

2002-03-01

The discovery by Marcy and coworkers of two planets in 2:1 orbital resonance about the star GJ 876 has been supplemented by a dynamical fit to the data by Laughlin & Chambers, which places the planets in coplanar orbits deep in three resonances at the 2:1 mean-motion commensurability. The selection of this almost singular state by the dynamical fit means that the resonances are almost certainly real, and with the small amplitudes of libration of the resonance variables, indefinitely stable. Several unusual properties of the 2:1 resonances are revealed by the GJ 876 system. The libration of both lowest order mean-motion resonance variables and the secular resonance variable, θ1=λ1- 2λ2+ϖ1, θ2=λ1- 2λ2+ϖ2, and θ3=ϖ1-ϖ2, about 0° (where λ1,2 are the mean longitudes of the inner and outer planet and ϖ1,2 are the longitudes of periapse) differs from the familiar geometry of the Io-Europa pair, where θ2 and θ3 librate about 180°. By considering the condition that ϖ1=ϖ2 for stable simultaneous librations of θ1 and θ2, we show that the GJ 876 geometry results from the large orbital eccentricities ei, whereas the very small eccentricities in the Io-Europa system lead to the latter's geometry. Surprisingly, the GJ 876 configuration, with θ1, θ2, and θ3 all librating, remains stable for e1 up to 0.86 and for amplitude of libration of θ1 approaching 45° with the current eccentricities-further supporting the indefinite stability of the existing system. Any process that drives originally widely separated orbits toward each other could result in capture into the observed resonances at the 2:1 commensurability. We find that forced inward migration of the outer planet of the GJ 876 system results in certain capture into the observed resonances if initially e1<~0.06 and e2<~0.03 and the migration rate |a2/a2|<~3×10- 2(a2/AU)-3/2yr-1. Larger eccentricities lead to likely capture into higher order resonances before the 2:1 commensurability is reached. The planets are sufficiently massive to open gaps in the nebular disk surrounding the young GJ 876 and to clear the disk material between them, and the resulting planet-nebular interaction typically forces the outer planet to migrate inward on the disk viscous timescale, whose inverse is about 3 orders of magnitude less than the above upper bound on |a2/a2| for certain capture. If there is no eccentricity damping, eccentricity growth is rapid with continued migration within the resonance, with ei exceeding the observed values after a further reduction in the semimajor axes ai of only 7%. With eccentricity damping ei/ei=-K|ai/ai|, the eccentricities reach equilibrium values that remain constant for arbitrarily long migration within the resonances. The equilibrium eccentricities are close to the observed eccentricities for K~100 if there is migration and damping of the outer planet only, but for K~10 if there is also migration and damping of the inner planet. This result is independent of the magnitude or functional form of the migration rate ai as long as ei/ei=-K|ai/ai|. Although existing analytic estimates of the effects of planet-nebula interaction are consistent with this form of eccentricity damping for certain disk parameter values, it is as yet unclear that such interaction can produce the large value of K required to obtain the observed eccentricities. The alternative eccentricity damping by tidal dissipation within the star or the planets is completely negligible, so the observed dynamical properties of the GJ 876 system may require an unlikely fine-tuning of the time of resonance capture to be near the end of the nebula lifetime.

The Evolution of Mission Architectures for Human Lunar Exploration

NASA Technical Reports Server (NTRS)

Everett, S. F.

1995-01-01

Defining transportation architectures for the human exploration of the Moon is a complex task due to the multitude of mission scenarios available. The mission transportation architecture recently proposed for the First Lunar Outpost (FLO) was not designed from carefully predetermined mission requirements and goals, but evolved from an initial set of requirements, which were continually modified as studies revealed that some early assumptions were not optimal. This paper focuses on the mission architectures proposed for FLO and investigates how these transportation architectures evolved. A comparison of the strengths and weaknesses of the three distinct mission architectures are discussed, namely (1) Lunar Orbit Rendezvous, (2) staging from the Cislunar Libration Point, and (3) direct to the lunar surface. In addition, several new and revolutionary architectures are discussed.

Low-energy near Earth asteroid capture using Earth flybys and aerobraking

NASA Astrophysics Data System (ADS)

Tan, Minghu; McInnes, Colin; Ceriotti, Matteo

2018-04-01

Since the Sun-Earth libration points L1 and L2 are regarded as ideal locations for space science missions and candidate gateways for future crewed interplanetary missions, capturing near-Earth asteroids (NEAs) around the Sun-Earth L1/L2 points has generated significant interest. Therefore, this paper proposes the concept of coupling together a flyby of the Earth and then capturing small NEAs onto Sun-Earth L1/L2 periodic orbits. In this capture strategy, the Sun-Earth circular restricted three-body problem (CRTBP) is used to calculate target Lypaunov orbits and their invariant manifolds. A periapsis map is then employed to determine the required perigee of the Earth flyby. Moreover, depending on the perigee distance of the flyby, Earth flybys with and without aerobraking are investigated to design a transfer trajectory capturing a small NEA from its initial orbit to the stable manifolds associated with Sun-Earth L1/L2 periodic orbits. Finally, a global optimization is carried out, based on a detailed design procedure for NEA capture using an Earth flyby. Results show that the NEA capture strategies using an Earth flyby with and without aerobraking both have the potential to be of lower cost in terms of energy requirements than a direct NEA capture strategy without the Earth flyby. Moreover, NEA capture with an Earth flyby also has the potential for a shorter flight time compared to the NEA capture strategy without the Earth flyby.

Atlas IIAS ascent trajectory design for the SOHO mission

NASA Technical Reports Server (NTRS)

Willen, Robert E.; Rude, Bradley J.

1993-01-01

In 1995, an Atlas IIAS launch vehicle will loft the Solar and Heliospheric Observatory (SOHO) as part of the International Solar and Terrestrial Physics program. The operational phase of the SOHO mission will be conducted from a `halo orbit' about the Sun-Earth interior libration point. Depending on the time of the year of launch, the optimal transfer requires a parking orbit of variable duration to satisfy widely varying inertial targets. A simulation capability has been developed that optimizes the launch vehicle ascent and spacecraft transfer phases of flight together, subject to both launch vehicle and spacecraft constraints. It will be shown that this `ground-up' simulation removes the need for an intermediate target vector at Centaur upper stage/spacecraft separation. Although providing only a modest gain in deliverable satellite mass, this capability substantially improves the mission integration process by removing the strict reliance on near-Earth target vectors. Trajectory data from several cases are presented and future applications of this capability are also discussed.

James Webb Space Telescope Initial Mid-Course Correction Monte Carlo Implementation using Task Parallelism

NASA Technical Reports Server (NTRS)

Petersen, Jeremy; Tichy, Jason; Wawrzyniak, Geoffrey; Richon, Karen

2014-01-01

The James Webb Space Telescope will be launched into a highly elliptical orbit that does not possess sufficient energy to achieve a proper Sun-Earth L2 libration point orbit. Three mid-course correction (MCC) maneuvers are planned to rectify the energy deficit: MCC-1a, MCC-1b, and MCC-2. To validate the propellant budget and trajectory design methods, a set of Monte Carlo analyses that incorporate MCC maneuver modeling and execution are employed. The first analysis focuses on the effects of launch vehicle injection errors on the magnitude of MCC-1a. The second on the spread of potential V based on the performance of the propulsion system as applied to all three MCC maneuvers. The final highlights the slight, but notable, contribution of the attitude thrusters during each MCC maneuver. Given the possible variations in these three scenarios, the trajectory design methods are determined to be robust to errors in the modeling of the flight system.

James Webb Space Telescope Initial Mid-Course Correction Monte Carlo Implementation using Task Parallelism

NASA Technical Reports Server (NTRS)

Petersen, Jeremy; Tichy, Jason; Wawrzyniak, Geoffrey; Richon, Karen

2014-01-01

The James Webb Space Telescope will be launched into a highly elliptical orbit that does not possess sufficient energy to achieve a proper Sun-Earth/Moon L2 libration point orbit. Three mid-course correction (MCC) maneuvers are planned to rectify the energy deficit: MCC-1a, MCC-1b, and MCC-2. To validate the propellant budget and trajectory design methods, a set of Monte Carlo analyses that incorporate MCC maneuver modeling and execution are employed. The first analysis focuses on the effects of launch vehicle injection errors on the magnitude of MCC-1a. The second on the spread of potential V based on the performance of the propulsion system as applied to all three MCC maneuvers. The final highlights the slight, but notable, contribution of the attitude thrusters during each MCC maneuver. Given the possible variations in these three scenarios, the trajectory design methods are determined to be robust to errors in the modeling of the flight system.

Libration and obliquity of Mercury from the BepiColombo radio science and camera experiments

NASA Astrophysics Data System (ADS)

Pfyffer, G.; van Hoolst, T.; Dehant, V.

2008-12-01

Mercury is the most enigmatic among the terrestrial planets, but the space missions MESSENGER and BepiColombo are expected to advance largely our knowledge of the structure, formation, and evolution of Mercury. In particular, insight into Mercury's deep interior will be obtained from observations of the 88-day forced libration, the obliquity and the degree-two coefficients of the gravity field of Mercury. Of those quantities, the libration is the most difficult to measure and will hence be a limiting factor We report here on aspects of the observational strategy to determine the libration amplitude and obliquity, taking into account the space and ground segment of the experiment. Repeated photographic measurements of selected target positions on the surface of Mercury are central to the strategy to determine the obliquity and libration in the frame of the BepiColombo mission. We simulated these measurements in order to estimate the accuracy of the reconstruction of the orientation and rotational motion of the planet, as a function of the amount of measurements made, the number of different targets considered and their locations on the surface of the planet. From this study, we determine criteria for the distribution and number of target positions to maximize the accuracy on the orientation and rotation determination, from which the obliquity and libration are extracted. We take into account the errors arising from the relative positions of the spacecraft, Mercury and the Earth. We consider various error sources such as the solar thermal influence on the spacecraft bus and the Earth based tracking constraint near solar conjunctions of Mercury. The accuracy on the retrieved parameters is then interpreted in terms of accuracy on the constraints on the interior structure of the planet. Our simulations show that the achievable level of accuracy on the libration amplitude and obliquity will be sufficient to constrain Mercury interior structure models, if the orbiter follows the ESA baseline mission scenario and at least 50 landmarks are imaged at least twice over the mission duration, the libration amplitude can be determined in two Mercury years (176 days) with an accuracy of 3 arcsec or better, which is sufficient to constrain the size and physical state of the planetary core.

Earth-Moon system: Dynamics and parameter estimation

NASA Technical Reports Server (NTRS)

Breedlove, W. J., Jr.

1979-01-01

The following topics are discussed: (1) the Unified Model of Lunar Translation/Rotation (UMLTR); (2) the effect of figure-figure interactions on lunar physical librations; (3) the effect of translational-rotational coupling on the lunar orbit; and(4) an error analysis for estimating lunar inertias from LURE (Lunar Laser Ranging Experiment) data.

Tether fundamentals

NASA Technical Reports Server (NTRS)

Carroll, J. A.

1986-01-01

Some fundamental aspects of tethers are presented and briefly discussed. The effects of gravity gradients, dumbbell libration in circular orbits, tether control strategies and impact hazards for tethers are among those fundamentals. Also considered are aerodynamic drag, constraints in momentum transfer applications and constraints with permanently deployed tethers. The theoretical feasibility of these concepts are reviewed.

Distant magnetic field effects associated with Birkeland currents /made possible by the evaluation of TRIAD's attitude oscillations/

NASA Astrophysics Data System (ADS)

Gustafsson, G.; Potemra, T. A.; Favin, S.; Saflekos, N. A.

1981-10-01

Principal oscillations of the TRIAD satellite are studied in 150 passes and are identified as the librations of a gravity-stabilized satellite. The libration periods are T(O)/2 and T(O)/(3) exp 1/2, where T(O) is the orbit period of about 100 min. The amplitude and phase change over periods of a few days, sometimes vanishing altogether, and these attitude changes are numerically evaluated and removed. Data from three consecutive passes spanning over three hours show a magnetic profile which extends as far as 10 deg in latitude from a single region 1 Birkeland current sheet, confirming the permanent and global nature of large-scale Birkeland currents.

Orbital evolution of small binary asteroids

NASA Astrophysics Data System (ADS)

Ćuk, Matija; Nesvorný, David

2010-06-01

About 15% of both near-Earth and main-belt asteroids with diameters below 10 km are now known to be binary. These small asteroid binaries are relatively uniform and typically contain a fast-spinning, flattened primary and a synchronously rotating, elongated secondary that is 20-40% as large (in diameter) as the primary. The principal formation mechanism for these binaries is now thought to be YORP (Yarkovsky-O'Keefe-Radzievskii-Paddack) effect induced spin-up of the primary followed by mass loss and accretion of the secondary from the released material. It has previously been suggested (Ćuk, M. [2007]. Astrophys. J. 659, L57-L60) that the present population of small binary asteroids is in a steady state between production through YORP and destruction through binary YORP (BYORP), which should increase or decrease secondary's orbit, depending on the satellite's shape. However, BYORP-driven evolution has not been directly modeled until now. Here we construct a simple numerical model of the binary's orbital as well the secondary's rotational dynamics which includes BYORP and selected terms representing main solar perturbations. We find that many secondaries should be vulnerable to chaotic rotation even for relatively low-eccentricity mutual orbits. We also find that the precession of the mutual orbit for typical small binary asteroids might be dominated by the perturbations from the prolate and librating secondary, rather than the oblate primary. When we evolve the mutual orbit by BYORP we find that the indirect effects on the binary's eccentricity (through the coupling between the orbit and the secondary's spin) dominate over direct ones caused by the BYORP acceleration. In particular, outward evolution causes eccentricity to increase and eventually triggers chaotic rotation of the secondary. We conclude that the most likely outcome will be reestablishing of the synchronous lock with a "flipped" secondary which would then evolve back in. For inward evolution we find an initial decrease of eccentricity and secondary's librations, to be followed by later increase. We think that it is likely that various forms of dissipation we did not model may damp the secondary's librations close to the primary, allowing for further inward evolution and a possible merger. We conclude that a merger or a tidal disruption of the secondary are the most likely outcomes of the BYORP evolution. Dissociation into heliocentric pairs by BYORP alone should be very difficult, and satellite loss might be restricted to the minority of systems containing more than one satellite at the time.

Cassini's motions and resonant librations of synchronous satellites of big planets

NASA Astrophysics Data System (ADS)

Barkin, Yu. V.

2008-09-01

Introduction. In the paper the rotations of synchronous satellites of the Jupiter, Saturn, Uran and Neptune are studied. On the base theory of resonant rotation of the rigid satellite on precessing elliptical orbit [1], [2] parameters of Cassini's motions and periods of free resonant librations have been determined for big grope of satellites of planets considered as rigid non-spherical bodies. Here I use observed values of coefficients of second harmonics of gravitational potensials ( 2 J and 22 C ) and of dimension less moment of inertia I = C / ?mr 2 ? of Io, Europa, Ganimede, Callisto and also Rhea and Titan, obtained on the base of data of space missions to these bodies [3]. Here C is the polar moment of inertia, m and r is the mass and the mean radius of satellite. Mentioned parameters 2 J , 22 C and I also have been evaluated for a wide set of another's satellites of big planets for their models as homogeneous ellipsoids of known forms and sizes (www.nasa.gov). These models also have been obtained here effective applications. For corresponding models the notation (e) is used here. For another from considered satellites (without indexes) we use also ellipsoidal models of hydrostatic equilibrium state of synchronous satellite [4]. The full list of discussed parameters for satellites of planets is presented in the paper [5]. Perturbed orbital motions of considered satellites we discribe by mean orbital elements reffered to local Laplacian planes of corresponding satellites ( http://ssd.jpl.nasa. gov/sat_elem. html). From them: the eccentricity ( e ), the inclination of orbit plane ( i ), the mean orbital motion and its period ( n and n T ), the angular velocity and period of preseccion of orbit plane of satellite on local Laplacian plane ( n? and T? ). In our approach all mentioned parameters are considered as constants and more fine effects in orbital motions of satellites do not take into account in this paper. The purpose of paper is to study syncronous motions of satellites in Solar system and for each of them to determine the values of the basic Cassini's parameter 0 ? (it is the average angle of inclination of the axis of rotation relatively to normal of the precessing orbit plane) and the periods of resonant librations in the longitude ( g T ), in the pole wobble ( l T ) and period of space precession ( h T ) (and their errors). Here we use the analytical formulas for mentioned parameters which were developed by study of the Moon Cassini's motion in my early papers [1], [2]. Specially for the case of small eccentricities and inclinations of orbits of synchronous satellites we have obtained the simple reduced formulas for all four considered parameters.

Numerical investigation of the dynamical environment of 65803 Didymos

NASA Astrophysics Data System (ADS)

Dell'Elce, L.; Baresi, N.; Naidu, S. P.; Benner, L. A. M.; Scheeres, D. J.

2017-03-01

The Asteroid Impact & Deflection Assessment (AIDA) mission is planning to visit the Didymos binary system in 2022 in order to perform the first demonstration ever of the kinetic impact technique. Binary asteroids are an ideal target for this since the deflection of the secondary body can be accurately measured by a satellite orbiting in the system. However, these binaries offer an extremely rich dynamical environment whose accurate investigation through analytical approaches is challenging at best and requires a significant number of restrictive assumptions. For this reason, a numerical investigation of the dynamical environment in the vicinity of the Didymos system is offered in this paper. After computing various families of periodic orbits, their robustness is assessed in a high-fidelity environment consisting of the perturbed restricted full three-body problem. The results of this study suggest that several nominally stable trajectories, including the triangular libration points, should not be considered as safe as a state vector perturbation may cause the spacecraft to drift from the nominal orbit and possibly impact one of the primary bodies within a few days. Nonetheless, there exist two safe solutions, namely terminator and interior retrograde orbits. The first one is adequate for observation purposes of the entire system and for communications. The second one is more suitable to perform close investigations of the primary body.

Four-body trajectory optimization

NASA Technical Reports Server (NTRS)

Pu, C. L.; Edelbaum, T. N.

1973-01-01

A collection of typical three-body trajectories from the L1 libration point on the sun-earth line to the earth is presented. These trajectories in the sun-earth system are grouped into four distinct families which differ in transfer time and delta V requirements. Curves showing the variations of delta V with respect to transfer time, and typical two and three-impulse primer vector histories, are included. The development of a four-body trajectory optimization program to compute fuel optimal trajectories between the earth and a point in the sun-earth-moon system are also discussed. Methods for generating fuel optimal two-impulse trajectories which originate at the earth or a point in space, and fuel optimal three-impulse trajectories between two points in space, are presented. A brief qualitative comparison of these methods is given. An example of a four-body two-impulse transfer from the Li libration point to the earth is included.

Bodily tides near the 1:1 spin-orbit resonance: correction to Goldreich's dynamical model

NASA Astrophysics Data System (ADS)

Williams, James G.; Efroimsky, Michael

2012-12-01

Spin-orbit coupling is often described in an approach known as " the MacDonald torque", which has long become the textbook standard due to its apparent simplicity. Within this method, a concise expression for the additional tidal potential, derived by MacDonald (Rev Geophys 2:467-541, 1994), is combined with a convenient assumption that the quality factor Q is frequency-independent (or, equivalently, that the geometric lag angle is constant in time). This makes the treatment unphysical because MacDonald's derivation of the said formula was, very implicitly, based on keeping the time lag frequency-independent, which is equivalent to setting Q scale as the inverse tidal frequency. This contradiction requires the entire MacDonald treatment of both non-resonant and resonant rotation to be rewritten. The non-resonant case was reconsidered by Efroimsky and Williams (Cel Mech Dyn Astron 104:257-289, 2009), in application to spin modes distant from the major commensurabilities. In the current paper, we continue this work by introducing the necessary alterations into the MacDonald-torque-based model of falling into a 1-to-1 resonance. (The original version of this model was offered by Goldreich (Astron J 71:1-7, 1996). Although the MacDonald torque, both in its original formulation and in its corrected version, is incompatible with realistic rheologies of minerals and mantles, it remains a useful toy model, which enables one to obtain, in some situations, qualitatively meaningful results without resorting to the more rigorous (and complicated) theory of Darwin and Kaula. We first address this simplified model in application to an oblate primary body, with tides raised on it by an orbiting zero-inclination secondary. (Here the role of the tidally-perturbed primary can be played by a satellite, the perturbing secondary being its host planet. A planet may as well be the perturbed primary, its host star acting as the tide-raising secondary). We then extend the model to a triaxial primary body experiencing both a tidal and a permanent-figure torque exerted by an orbiting secondary. We consider the effect of the triaxiality on both circulating and librating rotation near the synchronous state. Circulating rotation may evolve toward the libration region or toward a spin faster than synchronous (the so-called pseudosynchronous spin). Which behaviour depends on the orbit eccentricity, the triaxial figure of the primary, and the mass ratio of the secondary and primary bodies. The spin evolution will always stall for the oblate case. For libration with a small amplitude, expressions are derived for the libration frequency, damping rate, and average orientation. Importantly, the stability of pseudosynchronous spin hinges upon the dissipation model. Makarove and Efroimsky (Astrophys J, 2012) have found that a more realistic tidal dissipation model than the corrected MacDonald torque makes pseudosynchronous spin unstable. Besides, for a sufficiently large triaxiality, pseudosynchronism is impossible, no matter what dissipation model is used.

An empirically derived three-dimensional Laplace resonance in the Gliese 876 planetary system

NASA Astrophysics Data System (ADS)

Nelson, Benjamin E.; Robertson, Paul M.; Payne, Matthew J.; Pritchard, Seth M.; Deck, Katherine M.; Ford, Eric B.; Wright, Jason T.; Isaacson, Howard T.

2016-01-01

We report constraints on the three-dimensional orbital architecture for all four planets known to orbit the nearby M dwarf Gliese 876 based solely on Doppler measurements and demanding long-term orbital stability. Our data set incorporates publicly available radial velocities taken with the ELODIE and CORALIE spectrographs, High Accuracy Radial velocity Planet Searcher (HARPS), and Keck HIgh Resolution Echelle Spectrometer (HIRES) as well as previously unpublished HIRES velocities. We first quantitatively assess the validity of the planets thought to orbit GJ 876 by computing the Bayes factors for a variety of different coplanar models using an importance sampling algorithm. We find that a four-planet model is preferred over a three-planet model. Next, we apply a Newtonian Markov chain Monte Carlo algorithm to perform a Bayesian analysis of the planet masses and orbits using an N-body model in three-dimensional space. Based on the radial velocities alone, we find that a 99 per cent credible interval provides upper limits on the mutual inclinations for the three resonant planets (Φcb < 6.20° for the {c} and {b} pair and Φbe < 28.5° for the {b} and {e} pair). Subsequent dynamical integrations of our posterior sample find that the GJ 876 planets must be roughly coplanar (Φcb < 2.60° and Φbe < 7.87°, suggesting that the amount of planet-planet scattering in the system has been low. We investigate the distribution of the respective resonant arguments of each planet pair and find that at least one argument for each planet pair and the Laplace argument librate. The libration amplitudes in our three-dimensional orbital model support the idea of the outer three planets having undergone significant past disc migration.

Orbital Architectures of Dynamically Complex Exoplanet Systems

NASA Astrophysics Data System (ADS)

Nelson, Benjamin E.

2015-01-01

The most powerful constraints on planet formation will come from characterizing the dynamical state of complex multi-planet systems. Unfortunately, with that complexity comes a number of factors that make analyzing these systems a computationally challenging endeavor: the sheer number of model parameters, a wonky shaped posterior distribution, and hundreds to thousands of time series measurements. We develop a differential evolution Markov chain Monte Carlo (RUN DMC) to tackle these difficult aspects of data analysis. We apply RUN DMC to two classic multi-planet systems from radial velocity surveys, 55 Cancri and GJ 876. For 55 Cancri, we find the inner-most planet "e" must be coplanar to within 40 degrees of the outer planets, otherwise Kozai-like perturbations will cause the planet's orbit to cross the stellar surface. We find the orbits of planets "b" and "c" are apsidally aligned and librating with low to median amplitude (50±610 degrees), but they are not orbiting in a mean-motion resonance. For GJ 876, we can meaningfully constrain the three-dimensional orbital architecture of all the planets based on the radial velocity data alone. By demanding orbital stability, we find the resonant planets have low mutual inclinations (Φ) so they must be roughly coplanar (Φcb = 1.41±0.620.57 degrees and Φbe = 3.87±1.991.86 degrees). The three-dimensional Laplace argument librates with an amplitude of 50.5±7.910.0 degrees, indicating significant past disk migration and ensuring long-term stability. These empirically derived models will provide new challenges for planet formation models and motivate the need for more sophisticated algorithms to analyze exoplanet data.

Guidance of a Solar Sail Spacecraft to the Sun - L(2) Point.

NASA Astrophysics Data System (ADS)

Hur, Sun Hae

The guidance of a solar sail spacecraft along a minimum-time path from an Earth orbit to a region near the Sun-Earth L_2 libration point is investigated. Possible missions to this point include a spacecraft "listening" for possible extra-terrestrial electromagnetic signals and a science payload to study the geomagnetic tail. A key advantage of the solar sail is that it requires no fuel. The control variables are the sail angles relative to the Sun-Earth line. The thrust is very small, on the order of 1 mm/s^2, and its magnitude and direction are highly coupled. Despite this limited controllability, the "free" thrust can be used for a wide variety of terminal conditions including halo orbits. If the Moon's mass is lumped with the Earth, there are quasi-equilibrium points near L_2. However, they are unstable so that some form of station keeping is required, and the sail can provide this without any fuel usage. In the two-dimensional case, regulating about a nominal orbit is shown to require less control and result in smaller amplitude error response than regulating about a quasi-equilibrium point. In the three-dimensional halo orbit case, station keeping using periodically varying gains is demonstrated. To compute the minimum-time path, the trajectory is divided into two segments: the spiral segment and the transition segment. The spiral segment is computed using a control law that maximizes the rate of energy increase at each time. The transition segment is computed as the solution of the time-optimal control problem from the endpoint of the spiral to the terminal point. It is shown that the path resulting from this approximate strategy is very close to the exact optimal path. For the guidance problem, the approximate strategy in the spiral segment already gives a nonlinear full-state feedback law. However, for large perturbations, follower guidance using an auxiliary propulsion is used for part of the spiral. In the transition segment, neighboring extremal feedback guidance using the solar sail, with feedforward control only near the terminal point, is used to correct perturbations in the initial conditions.

Stationkeeping Monte Carlo Simulation for the James Webb Space Telescope

NASA Technical Reports Server (NTRS)

Dichmann, Donald J.; Alberding, Cassandra M.; Yu, Wayne H.

2014-01-01

The James Webb Space Telescope (JWST) is scheduled to launch in 2018 into a Libration Point Orbit (LPO) around the Sun-Earth/Moon (SEM) L2 point, with a planned mission lifetime of 10.5 years after a six-month transfer to the mission orbit. This paper discusses our approach to Stationkeeping (SK) maneuver planning to determine an adequate SK delta-V budget. The SK maneuver planning for JWST is made challenging by two factors: JWST has a large Sunshield, and JWST will be repointed regularly producing significant changes in Solar Radiation Pressure (SRP). To accurately model SRP we employ the Solar Pressure and Drag (SPAD) tool, which uses ray tracing to accurately compute SRP force as a function of attitude. As an additional challenge, the future JWST observation schedule will not be known at the time of SK maneuver planning. Thus there will be significant variation in SRP between SK maneuvers, and the future variation in SRP is unknown. We have enhanced an earlier SK simulation to create a Monte Carlo simulation that incorporates random draws for uncertainties that affect the budget, including random draws of the observation schedule. Each SK maneuver is planned to optimize delta-V magnitude, subject to constraints on spacecraft pointing. We report the results of the Monte Carlo simulations and discuss possible improvements during flight operations to reduce the SK delta-V budget.

James Webb Space Telescope Orbit Determination Analysis

NASA Technical Reports Server (NTRS)

Yoon, Sungpil; Rosales, Jose; Richon, Karen

2014-01-01

The James Webb Space Telescope (JWST) is designed to study and answer fundamental astrophysical questions from an orbit about the Sun-Earth/Moon L2 libration point, 1.5 million km away from Earth. This paper describes the results of an orbit determination (OD) analysis of the JWST mission emphasizing the challenges specific to this mission in various mission phases. Three mid-course correction (MCC) maneuvers during launch and early orbit phase and transfer orbit phase are required for the spacecraft to reach L2. These three MCC maneuvers are MCC-1a at Launch+12 hours, MCC-1b at L+2.5 days and MCC-2 at L+30 days. Accurate OD solutions are needed to support MCC maneuver planning. A preliminary analysis shows that OD performance with the given assumptions is adequate to support MCC maneuver planning. During the nominal science operations phase, the mission requires better than 2 cm/sec velocity estimation performance to support stationkeeping maneuver planning. The major challenge to accurate JWST OD during the nominal science phase results from the unusually large solar radiation pressure force acting on the huge sunshield. Other challenges are stationkeeping maneuvers at 21-day intervals to keep JWST in orbit around L2, frequent attitude reorientations to align the JWST telescope with its targets and frequent maneuvers to unload momentum accumulated in the reaction wheels. Monte Carlo analysis shows that the proposed OD approach can produce solutions that meet the mission requirements.

Direct and indirect capture of near-Earth asteroids in the Earth-Moon system

NASA Astrophysics Data System (ADS)

Tan, Minghu; McInnes, Colin; Ceriotti, Matteo

2017-09-01

Near-Earth asteroids have attracted attention for both scientific and commercial mission applications. Due to the fact that the Earth-Moon L1 and L2 points are candidates for gateway stations for lunar exploration, and an ideal location for space science, capturing asteroids and inserting them into periodic orbits around these points is of significant interest for the future. In this paper, we define a new type of lunar asteroid capture, termed direct capture. In this capture strategy, the candidate asteroid leaves its heliocentric orbit after an initial impulse, with its dynamics modeled using the Sun-Earth-Moon restricted four-body problem until its insertion, with a second impulse, onto the L2 stable manifold in the Earth-Moon circular restricted three-body problem. A Lambert arc in the Sun-asteroid two-body problem is used as an initial guess and a differential corrector used to generate the transfer trajectory from the asteroid's initial obit to the stable manifold associated with Earth-Moon L2 point. Results show that the direct asteroid capture strategy needs a shorter flight time compared to an indirect asteroid capture, which couples capture in the Sun-Earth circular restricted three-body problem and subsequent transfer to the Earth-Moon circular restricted three-body problem. Finally, the direct and indirect asteroid capture strategies are also applied to consider capture of asteroids at the triangular libration points in the Earth-Moon system.

Low-Latency Lunar Surface Telerobotics from Earth-Moon Libration Points

NASA Technical Reports Server (NTRS)

Lester, Daniel; Thronson, Harley

2011-01-01

Concepts for a long-duration habitat at Earth-Moon LI or L2 have been advanced for a number of purposes. We propose here that such a facility could also have an important role for low-latency telerobotic control of lunar surface equipment, both for lunar science and development. With distances of about 60,000 km from the lunar surface, such sites offer light-time limited two-way control latencies of order 400 ms, making telerobotic control for those sites close to real time as perceived by a human operator. We point out that even for transcontinental teleoperated surgical procedures, which require operational precision and highly dexterous manipulation, control latencies of this order are considered adequate. Terrestrial telerobots that are used routinely for mining and manufacturing also involve control latencies of order several hundred milliseconds. For this reason, an Earth-Moon LI or L2 control node could build on the technology and experience base of commercially proven terrestrial ventures. A lunar libration-point telerobotic node could demonstrate exploration strategies that would eventually be used on Mars, and many other less hospitable destinations in the solar system. Libration-point telepresence for the Moon contrasts with lunar telerobotic control from the Earth, for which two-way control latencies are at least six times longer. For control latencies that long, telerobotic control efforts are of the "move-and-wait" variety, which is cognitively inferior to near real-time control.

TV observations of Phobos - First results

NASA Technical Reports Server (NTRS)

Avanesov, G. A.; Bonev, B. I.; Boicheva, V.; Kempe, F.; Bazilevskii, A. T.; Duxbury, T.

1990-01-01

From February to March, 1989, Phobos-2 acquired 37 TV images of Phobos at distances from 200 to 1100 km. These images will be used to update the figure model and topographic and geological maps of Phobos, its spectral characteristics and scattering law, the surface composition and texture, and the parameters of the orbital motion and forced libration.

Development of a Two-Wheel Contingency Mode for the MAP Spacecraft

NASA Technical Reports Server (NTRS)

Starin, Scott R.; ODonnell, James R., Jr.; Bauer, Frank H. (Technical Monitor)

2002-01-01

In the event of a failure of one of MAP's three reaction wheel assemblies (RWAs), it is not possible to achieve three-axis, full-state attitude control using the remaining two wheels. Hence, two of the attitude control algorithms implemented on the MAP spacecraft will no longer be usable in their current forms: Inertial Mode, used for slewing to and holding inertial attitudes, and Observing Mode, which implements the nominal dual-spin science mode. This paper describes the effort to create a complete strategy for using software algorithms to cope with a RWA failure. The discussion of the design process will be divided into three main subtopics: performing orbit maneuvers to reach and maintain an orbit about the second Earth-Sun libration point in the event of a RWA failure, completing the mission using a momentum-bias two-wheel science mode, and developing a new thruster-based mode for adjusting the inertially fixed momentum bias. In this summary, the philosophies used in designing these changes is shown; the full paper will supplement these with algorithm descriptions and testing results.

Current Moon - June 15, 2011

NASA Image and Video Library

2017-12-08

Current moon as viewed on Wednesday, June 15, 2011, 19:00 UT (Phase 100%) This marks the first time that accurate shadows at this level of detail are possible in such a computer simulation. The shadows are based on the global elevation map being developed from measurements by the Lunar Orbiter Laser Altimeter (LOLA) aboard the Lunar Reconnaissance Orbiter (LRO). LOLA has already taken more than 10 times as many elevation measurements as all previous missions combined. The Moon always keeps the same face to us, but not exactly the same face. Because of the tilt and shape of its orbit, we see the Moon from slightly different angles over the course of a month. When a month is compressed into 12 seconds, as it is in this animation, our changing view of the Moon makes it look like it's wobbling. This wobble is called libration. The word comes from the Latin for "balance scale" (as does the name of the zodiac constellation Libra) and refers to the way such a scale tips up and down on alternating sides. The sub-Earth point gives the amount of libration in longitude and latitude. The sub-Earth point is also the apparent center of the Moon's disk and the location on the Moon where the Earth is directly overhead. The Moon is subject to other motions as well. It appears to roll back and forth around the sub-Earth point. The roll angle is given by the position angle of the axis, which is the angle of the Moon's north pole relative to celestial north. The Moon also approaches and recedes from us, appearing to grow and shrink. The two extremes, called perigee (near) and apogee (far), differ by more than 10%. The most noticed monthly variation in the Moon's appearance is the cycle of phases, caused by the changing angle of the Sun as the Moon orbits the Earth. The cycle begins with the waxing (growing) crescent Moon visible in the west just after sunset. By first quarter, the Moon is high in the sky at sunset and sets around midnight. The full Moon rises at sunset and is high in the sky at midnight. The third quarter Moon is often surprisingly conspicuous in the daylit western sky long after sunrise. Celestial north is up in these images, corresponding to the view from the northern hemisphere. The descriptions of the print resolution stills also assume a northern hemisphere orientation. To adjust for southern hemisphere views, rotate the images 180 degrees, and substitute "north" for "south" in the descriptions. Credit: NASA/Goddard Space Flight Center Scientific Visualization Studio NASA Goddard Space Flight Center enables NASA’s mission through four scientific endeavors: Earth Science, Heliophysics, Solar System Exploration, and Astrophysics. Goddard plays a leading role in NASA’s accomplishments by contributing compelling scientific knowledge to advance the Agency’s mission. Follow us on Twitter Join us on Facebook Find us on Instagram

First Quarter

NASA Image and Video Library

2017-12-08

First quarter. Visible high in the southern sky in early evening. This marks the first time that accurate shadows at this level of detail are possible in such a computer simulation. The shadows are based on the global elevation map being developed from measurements by the Lunar Orbiter Laser Altimeter (LOLA) aboard the Lunar Reconnaissance Orbiter (LRO). LOLA has already taken more than 10 times as many elevation measurements as all previous missions combined. The Moon always keeps the same face to us, but not exactly the same face. Because of the tilt and shape of its orbit, we see the Moon from slightly different angles over the course of a month. When a month is compressed into 12 seconds, as it is in this animation, our changing view of the Moon makes it look like it's wobbling. This wobble is called libration. The word comes from the Latin for "balance scale" (as does the name of the zodiac constellation Libra) and refers to the way such a scale tips up and down on alternating sides. The sub-Earth point gives the amount of libration in longitude and latitude. The sub-Earth point is also the apparent center of the Moon's disk and the location on the Moon where the Earth is directly overhead. The Moon is subject to other motions as well. It appears to roll back and forth around the sub-Earth point. The roll angle is given by the position angle of the axis, which is the angle of the Moon's north pole relative to celestial north. The Moon also approaches and recedes from us, appearing to grow and shrink. The two extremes, called perigee (near) and apogee (far), differ by more than 10%. The most noticed monthly variation in the Moon's appearance is the cycle of phases, caused by the changing angle of the Sun as the Moon orbits the Earth. The cycle begins with the waxing (growing) crescent Moon visible in the west just after sunset. By first quarter, the Moon is high in the sky at sunset and sets around midnight. The full Moon rises at sunset and is high in the sky at midnight. The third quarter Moon is often surprisingly conspicuous in the daylit western sky long after sunrise. Celestial north is up in these images, corresponding to the view from the northern hemisphere. The descriptions of the print resolution stills also assume a northern hemisphere orientation. To adjust for southern hemisphere views, rotate the images 180 degrees, and substitute "north" for "south" in the descriptions. Credit: NASA/Goddard Space Flight Center Scientific Visualization Studio NASA Goddard Space Flight Center enables NASA’s mission through four scientific endeavors: Earth Science, Heliophysics, Solar System Exploration, and Astrophysics. Goddard plays a leading role in NASA’s accomplishments by contributing compelling scientific knowledge to advance the Agency’s mission. Follow us on Twitter Join us on Facebook Find us on Instagram

Waxing Gibbous

NASA Image and Video Library

2017-12-08

Waxing gibbous. Visible to the southeast in early evening, up for most of the night. This marks the first time that accurate shadows at this level of detail are possible in such a computer simulation. The shadows are based on the global elevation map being developed from measurements by the Lunar Orbiter Laser Altimeter (LOLA) aboard the Lunar Reconnaissance Orbiter (LRO). LOLA has already taken more than 10 times as many elevation measurements as all previous missions combined. The Moon always keeps the same face to us, but not exactly the same face. Because of the tilt and shape of its orbit, we see the Moon from slightly different angles over the course of a month. When a month is compressed into 12 seconds, as it is in this animation, our changing view of the Moon makes it look like it's wobbling. This wobble is called libration. The word comes from the Latin for "balance scale" (as does the name of the zodiac constellation Libra) and refers to the way such a scale tips up and down on alternating sides. The sub-Earth point gives the amount of libration in longitude and latitude. The sub-Earth point is also the apparent center of the Moon's disk and the location on the Moon where the Earth is directly overhead. The Moon is subject to other motions as well. It appears to roll back and forth around the sub-Earth point. The roll angle is given by the position angle of the axis, which is the angle of the Moon's north pole relative to celestial north. The Moon also approaches and recedes from us, appearing to grow and shrink. The two extremes, called perigee (near) and apogee (far), differ by more than 10%. The most noticed monthly variation in the Moon's appearance is the cycle of phases, caused by the changing angle of the Sun as the Moon orbits the Earth. The cycle begins with the waxing (growing) crescent Moon visible in the west just after sunset. By first quarter, the Moon is high in the sky at sunset and sets around midnight. The full Moon rises at sunset and is high in the sky at midnight. The third quarter Moon is often surprisingly conspicuous in the daylit western sky long after sunrise. Celestial north is up in these images, corresponding to the view from the northern hemisphere. The descriptions of the print resolution stills also assume a northern hemisphere orientation. To adjust for southern hemisphere views, rotate the images 180 degrees, and substitute "north" for "south" in the descriptions. Credit: NASA/Goddard Space Flight Center Scientific Visualization Studio NASA Goddard Space Flight Center enables NASA’s mission through four scientific endeavors: Earth Science, Heliophysics, Solar System Exploration, and Astrophysics. Goddard plays a leading role in NASA’s accomplishments by contributing compelling scientific knowledge to advance the Agency’s mission. Follow us on Twitter Join us on Facebook Find us on Instagram

Waning Crescent

NASA Image and Video Library

2017-12-08

Waning crescent. Low to the east before sunrise. This marks the first time that accurate shadows at this level of detail are possible in such a computer simulation. The shadows are based on the global elevation map being developed from measurements by the Lunar Orbiter Laser Altimeter (LOLA) aboard the Lunar Reconnaissance Orbiter (LRO). LOLA has already taken more than 10 times as many elevation measurements as all previous missions combined. The Moon always keeps the same face to us, but not exactly the same face. Because of the tilt and shape of its orbit, we see the Moon from slightly different angles over the course of a month. When a month is compressed into 12 seconds, as it is in this animation, our changing view of the Moon makes it look like it's wobbling. This wobble is called libration. The word comes from the Latin for "balance scale" (as does the name of the zodiac constellation Libra) and refers to the way such a scale tips up and down on alternating sides. The sub-Earth point gives the amount of libration in longitude and latitude. The sub-Earth point is also the apparent center of the Moon's disk and the location on the Moon where the Earth is directly overhead. The Moon is subject to other motions as well. It appears to roll back and forth around the sub-Earth point. The roll angle is given by the position angle of the axis, which is the angle of the Moon's north pole relative to celestial north. The Moon also approaches and recedes from us, appearing to grow and shrink. The two extremes, called perigee (near) and apogee (far), differ by more than 10%. The most noticed monthly variation in the Moon's appearance is the cycle of phases, caused by the changing angle of the Sun as the Moon orbits the Earth. The cycle begins with the waxing (growing) crescent Moon visible in the west just after sunset. By first quarter, the Moon is high in the sky at sunset and sets around midnight. The full Moon rises at sunset and is high in the sky at midnight. The third quarter Moon is often surprisingly conspicuous in the daylit western sky long after sunrise. Celestial north is up in these images, corresponding to the view from the northern hemisphere. The descriptions of the print resolution stills also assume a northern hemisphere orientation. To adjust for southern hemisphere views, rotate the images 180 degrees, and substitute "north" for "south" in the descriptions. Credit: NASA/Goddard Space Flight Center Scientific Visualization Studio NASA Goddard Space Flight Center enables NASA’s mission through four scientific endeavors: Earth Science, Heliophysics, Solar System Exploration, and Astrophysics. Goddard plays a leading role in NASA’s accomplishments by contributing compelling scientific knowledge to advance the Agency’s mission. Follow us on Twitter Join us on Facebook Find us on Instagram

Waning Gibbous

NASA Image and Video Library

2011-06-15

Waning gibbous. Rises after sunset, high in the sky after midnight, visible to the southwest after sunrise. This marks the first time that accurate shadows at this level of detail are possible in such a computer simulation. The shadows are based on the global elevation map being developed from measurements by the Lunar Orbiter Laser Altimeter (LOLA) aboard the Lunar Reconnaissance Orbiter (LRO). LOLA has already taken more than 10 times as many elevation measurements as all previous missions combined. The Moon always keeps the same face to us, but not exactly the same face. Because of the tilt and shape of its orbit, we see the Moon from slightly different angles over the course of a month. When a month is compressed into 12 seconds, as it is in this animation, our changing view of the Moon makes it look like it's wobbling. This wobble is called libration. The word comes from the Latin for "balance scale" (as does the name of the zodiac constellation Libra) and refers to the way such a scale tips up and down on alternating sides. The sub-Earth point gives the amount of libration in longitude and latitude. The sub-Earth point is also the apparent center of the Moon's disk and the location on the Moon where the Earth is directly overhead. The Moon is subject to other motions as well. It appears to roll back and forth around the sub-Earth point. The roll angle is given by the position angle of the axis, which is the angle of the Moon's north pole relative to celestial north. The Moon also approaches and recedes from us, appearing to grow and shrink. The two extremes, called perigee (near) and apogee (far), differ by more than 10%. The most noticed monthly variation in the Moon's appearance is the cycle of phases, caused by the changing angle of the Sun as the Moon orbits the Earth. The cycle begins with the waxing (growing) crescent Moon visible in the west just after sunset. By first quarter, the Moon is high in the sky at sunset and sets around midnight. The full Moon rises at sunset and is high in the sky at midnight. The third quarter Moon is often surprisingly conspicuous in the daylit western sky long after sunrise. Celestial north is up in these images, corresponding to the view from the northern hemisphere. The descriptions of the print resolution stills also assume a northern hemisphere orientation. To adjust for southern hemisphere views, rotate the images 180 degrees, and substitute "north" for "south" in the descriptions. Credit: NASA/Goddard Space Flight Center Scientific Visualization Studio NASA Goddard Space Flight Center enables NASA’s mission through four scientific endeavors: Earth Science, Heliophysics, Solar System Exploration, and Astrophysics. Goddard plays a leading role in NASA’s accomplishments by contributing compelling scientific knowledge to advance the Agency’s mission. Follow us on Twitter Join us on Facebook Find us on Instagram

Third Quarter

NASA Image and Video Library

2017-12-08

Third quarter. Rises around midnight, visible to the south after sunrise. This marks the first time that accurate shadows at this level of detail are possible in such a computer simulation. The shadows are based on the global elevation map being developed from measurements by the Lunar Orbiter Laser Altimeter (LOLA) aboard the Lunar Reconnaissance Orbiter (LRO). LOLA has already taken more than 10 times as many elevation measurements as all previous missions combined. The Moon always keeps the same face to us, but not exactly the same face. Because of the tilt and shape of its orbit, we see the Moon from slightly different angles over the course of a month. When a month is compressed into 12 seconds, as it is in this animation, our changing view of the Moon makes it look like it's wobbling. This wobble is called libration. The word comes from the Latin for "balance scale" (as does the name of the zodiac constellation Libra) and refers to the way such a scale tips up and down on alternating sides. The sub-Earth point gives the amount of libration in longitude and latitude. The sub-Earth point is also the apparent center of the Moon's disk and the location on the Moon where the Earth is directly overhead. The Moon is subject to other motions as well. It appears to roll back and forth around the sub-Earth point. The roll angle is given by the position angle of the axis, which is the angle of the Moon's north pole relative to celestial north. The Moon also approaches and recedes from us, appearing to grow and shrink. The two extremes, called perigee (near) and apogee (far), differ by more than 10%. The most noticed monthly variation in the Moon's appearance is the cycle of phases, caused by the changing angle of the Sun as the Moon orbits the Earth. The cycle begins with the waxing (growing) crescent Moon visible in the west just after sunset. By first quarter, the Moon is high in the sky at sunset and sets around midnight. The full Moon rises at sunset and is high in the sky at midnight. The third quarter Moon is often surprisingly conspicuous in the daylit western sky long after sunrise. Celestial north is up in these images, corresponding to the view from the northern hemisphere. The descriptions of the print resolution stills also assume a northern hemisphere orientation. To adjust for southern hemisphere views, rotate the images 180 degrees, and substitute "north" for "south" in the descriptions. Credit: NASA/Goddard Space Flight Center Scientific Visualization Studio NASA Goddard Space Flight Center enables NASA’s mission through four scientific endeavors: Earth Science, Heliophysics, Solar System Exploration, and Astrophysics. Goddard plays a leading role in NASA’s accomplishments by contributing compelling scientific knowledge to advance the Agency’s mission. Follow us on Twitter Join us on Facebook Find us on Instagram

Waxing crescent

NASA Image and Video Library

2017-12-08

Waxing crescent. Visible toward the southwest in early evening. This marks the first time that accurate shadows at this level of detail are possible in such a computer simulation. The shadows are based on the global elevation map being developed from measurements by the Lunar Orbiter Laser Altimeter (LOLA) aboard the Lunar Reconnaissance Orbiter (LRO). LOLA has already taken more than 10 times as many elevation measurements as all previous missions combined. The Moon always keeps the same face to us, but not exactly the same face. Because of the tilt and shape of its orbit, we see the Moon from slightly different angles over the course of a month. When a month is compressed into 12 seconds, as it is in this animation, our changing view of the Moon makes it look like it's wobbling. This wobble is called libration. The word comes from the Latin for "balance scale" (as does the name of the zodiac constellation Libra) and refers to the way such a scale tips up and down on alternating sides. The sub-Earth point gives the amount of libration in longitude and latitude. The sub-Earth point is also the apparent center of the Moon's disk and the location on the Moon where the Earth is directly overhead. The Moon is subject to other motions as well. It appears to roll back and forth around the sub-Earth point. The roll angle is given by the position angle of the axis, which is the angle of the Moon's north pole relative to celestial north. The Moon also approaches and recedes from us, appearing to grow and shrink. The two extremes, called perigee (near) and apogee (far), differ by more than 10%. The most noticed monthly variation in the Moon's appearance is the cycle of phases, caused by the changing angle of the Sun as the Moon orbits the Earth. The cycle begins with the waxing (growing) crescent Moon visible in the west just after sunset. By first quarter, the Moon is high in the sky at sunset and sets around midnight. The full Moon rises at sunset and is high in the sky at midnight. The third quarter Moon is often surprisingly conspicuous in the daylit western sky long after sunrise. Celestial north is up in these images, corresponding to the view from the northern hemisphere. The descriptions of the print resolution stills also assume a northern hemisphere orientation. To adjust for southern hemisphere views, rotate the images 180 degrees, and substitute "north" for "south" in the descriptions. Credit: NASA/Goddard Space Flight Center Scientific Visualization Studio NASA Goddard Space Flight Center enables NASA’s mission through four scientific endeavors: Earth Science, Heliophysics, Solar System Exploration, and Astrophysics. Goddard plays a leading role in NASA’s accomplishments by contributing compelling scientific knowledge to advance the Agency’s mission. Follow us on Twitter Join us on Facebook Find us on Instagram

Full Moon

NASA Image and Video Library

2017-12-08

Full Moon. Rises at sunset, high in the sky around midnight. Visible all night. This marks the first time that accurate shadows at this level of detail are possible in such a computer simulation. The shadows are based on the global elevation map being developed from measurements by the Lunar Orbiter Laser Altimeter (LOLA) aboard the Lunar Reconnaissance Orbiter (LRO). LOLA has already taken more than 10 times as many elevation measurements as all previous missions combined. The Moon always keeps the same face to us, but not exactly the same face. Because of the tilt and shape of its orbit, we see the Moon from slightly different angles over the course of a month. When a month is compressed into 12 seconds, as it is in this animation, our changing view of the Moon makes it look like it's wobbling. This wobble is called libration. The word comes from the Latin for "balance scale" (as does the name of the zodiac constellation Libra) and refers to the way such a scale tips up and down on alternating sides. The sub-Earth point gives the amount of libration in longitude and latitude. The sub-Earth point is also the apparent center of the Moon's disk and the location on the Moon where the Earth is directly overhead. The Moon is subject to other motions as well. It appears to roll back and forth around the sub-Earth point. The roll angle is given by the position angle of the axis, which is the angle of the Moon's north pole relative to celestial north. The Moon also approaches and recedes from us, appearing to grow and shrink. The two extremes, called perigee (near) and apogee (far), differ by more than 10%. The most noticed monthly variation in the Moon's appearance is the cycle of phases, caused by the changing angle of the Sun as the Moon orbits the Earth. The cycle begins with the waxing (growing) crescent Moon visible in the west just after sunset. By first quarter, the Moon is high in the sky at sunset and sets around midnight. The full Moon rises at sunset and is high in the sky at midnight. The third quarter Moon is often surprisingly conspicuous in the daylit western sky long after sunrise. Celestial north is up in these images, corresponding to the view from the northern hemisphere. The descriptions of the print resolution stills also assume a northern hemisphere orientation. To adjust for southern hemisphere views, rotate the images 180 degrees, and substitute "north" for "south" in the descriptions. Credit: NASA/Goddard Space Flight Center Scientific Visualization Studio NASA Goddard Space Flight Center enables NASA’s mission through four scientific endeavors: Earth Science, Heliophysics, Solar System Exploration, and Astrophysics. Goddard plays a leading role in NASA’s accomplishments by contributing compelling scientific knowledge to advance the Agency’s mission. Follow us on Twitter Join us on Facebook Find us on Instagram

A Secular Resonance Between Iapetus and the Giant Planets

NASA Astrophysics Data System (ADS)

Cuk, Matija; Dones, Henry C. Luke; Nesvorny, David; Walsh, Kevin J.

2017-06-01

Iapetus is the outermost of the regular satellites of Saturn, and its origin and evolution present a number of unsolved problems. From the point of view of orbital dynamics, it is remarkable that Iapetus has a large inclination (8 degrees) and a significantly smaller eccentricity (0.03), contrary to the pattern expected if its orbit was excited by encounters between Saturn and other planets early in the Solar System's history (Nesvorny et al, 2014). Here we report our long-term numerical integrations of Iapetus's orbit that show multi-Myr oscillations of Iapetus's eccentricity with an amplitude on the order of 0.01. We find that the basic argument causing this behavior is the sum of the longitude of pericenter and the longitude of the node of Iapetus, with a 0.3 Myr period. This argument appears to be in resonance with the period of the g5 mode in the eccentricity and perihelion of Saturn. We find that our nominal solution, including Saturn's oblateness, Titan, Iapetus and all four giant planets, shows librations of the argument: ǎrpi_Iapetus - ǎrpi_g5 + \\Omega_Iapetus - \\Omega_SaturnEq, where ǎrpi and \\Omega are the longitudes of pericenters and nodes, respectively, and \\Omega_SaturnEq is Saturn's equinox. While planetary perturbations are crucial in generating the g5 mode and therefore maintaining this resonance, we find that Iapetus is affected by the planets only indirectly, with the Sun being the dominant direct perturber. The libration is stable for tens of Myr for the nominal rate of Saturn's pole precession (French et al, 2017), and appears stable indefinitely if we assume a secular resonance between Saturn's node and the secular mode g18 (Ward and Hamilton, 2004; Hamilton and Ward, 2004). We will present the implication of this resonance for the origin of Iapetus's orbit and the dynamical history of Saturn's system. This research is funded by NASA Outer Planets Research Program award NNX14AO38G. References: French, R. G., McGhee-French, C. A., Lonergan, K., et al. 2017, Icarus, 290, 14; Hamilton, D. P., & Ward, W. R. 2004, AJ, 128, 2510; Nesvorny, D., Vokrouhlicky, D., Deienno, R., & Walsh, K. J. 2014, AJ, 148, 52; Ward, W. R., & Hamilton, D. P. 2004, AJ, 128, 2501.

Binary asteroid population. 3. Secondary rotations and elongations

NASA Astrophysics Data System (ADS)

Pravec, P.; Scheirich, P.; Kušnirák, P.; Hornoch, K.; Galád, A.; Naidu, S. P.; Pray, D. P.; Világi, J.; Gajdoš, Š.; Kornoš, L.; Krugly, Yu. N.; Cooney, W. R.; Gross, J.; Terrell, D.; Gaftonyuk, N.; Pollock, J.; Husárik, M.; Chiorny, V.; Stephens, R. D.; Durkee, R.; Reddy, V.; Dyvig, R.; Vraštil, J.; Žižka, J.; Mottola, S.; Hellmich, S.; Oey, J.; Benishek, V.; Kryszczyńska, A.; Higgins, D.; Ries, J.; Marchis, F.; Baek, M.; Macomber, B.; Inasaridze, R.; Kvaratskhelia, O.; Ayvazian, V.; Rumyantsev, V.; Masi, G.; Colas, F.; Lecacheux, J.; Montaigut, R.; Leroy, A.; Brown, P.; Krzeminski, Z.; Molotov, I.; Reichart, D.; Haislip, J.; LaCluyze, A.

2016-03-01

We collected data on rotations and elongations of 46 secondaries of binary and triple systems among near-Earth, Mars-crossing and small main belt asteroids. 24 were found or are strongly suspected to be synchronous (in 1:1 spin-orbit resonance), and the other 22, generally on more distant and/or eccentric orbits, were found or are suggested to have asynchronous rotations. For 18 of the synchronous secondaries, we constrained their librational angles, finding that their long axes pointed to within 20° of the primary on most epochs. The observed anti-correlation of secondary synchroneity with orbital eccentricity and the limited librational angles agree with the theories by Ćuk and Nesvorný (Ćuk, M., Nesvorný, D. [2010]. Icarus 207, 732-743) and Naidu and Margot (Naidu, S.P., Margot, J.-L. [2015]. Astron. J. 149, 80). A reason for the asynchronous secondaries being on wider orbits than synchronous ones may be longer tidal circularization time scales at larger semi-major axes. The asynchronous secondaries show relatively fast spins; their rotation periods are typically < 10 h. An intriguing observation is a paucity of chaotic secondary rotations; with an exception of (35107) 1991 VH, the secondary rotations are single-periodic with no signs of chaotic rotation and their periods are constant on timescales from weeks to years. The secondary equatorial elongations show an upper limit of a2 /b2 ∼ 1.5 . The lack of synchronous secondaries with greater elongations appears consistent, considering uncertainties of the axis ratio estimates, with the theory by Ćuk and Nesvorný that predicts large regions of chaotic rotation in the phase space for a2 /b2 ≳√{ 2 } . Alternatively, secondaries may not form or stay very elongated in gravitational (tidal) field of the primary. It could be due to the secondary fission mechanism suggested by Jacobson and Scheeres (Jacobson, S.A., Scheeres, D.J. [2011]. Icarus 214, 161-178), as its efficiency is correlated with the secondary elongation. Sharma (Sharma, I. [2014]. Icarus 229, 278-294) found that rubble-pile satellites with a2 /b2 ≲ 1.5 are more stable to finite structural perturbations than more elongated ones. It appears that more elongated secondaries, if they originally formed in spin fission of parent asteroid, are less likely to survive intact and they more frequently fail or fission.

Rotational Properties of Jupiter Trojan 1173 Anchises

NASA Astrophysics Data System (ADS)

Chatelain, Joseph; Henry, Todd; French, Linda; Trilling, David

2015-11-01

Anchises (1173) is a large Trojan asteroid librating about Jupiter’s L5 Lagrange point. Here we examine its rotational and lightcurve properties by way of data collected over a 3.5 year observing campaign. The length of the campaign means that data were gathered for more than a quarter of Anchises' full orbital revolution which allows for accurate determinations of pole orientation and bulk shape properties for the asteroid that can then be compared to results of previous work (i.e. French 1987, Horner et al. 2012). In addition to light curves, photometric data taken during this campaign could potentially detect color differences between hemispheres as the viewing geometry changes over time. Understanding these details about a prominent member of the Jupiter Trojans may help us better understand the history of this fascinating and important group of asteroids.

Trajectory design strategies that incorporate invariant manifolds and swingby

NASA Technical Reports Server (NTRS)

Guzman, J. J.; Cooley, D. S.; Howell, K. C.; Folta, D. C.

1998-01-01

Libration point orbits serve as excellent platforms for scientific investigations involving the Sun as well as planetary environments. Trajectory design in support of such missions is increasingly challenging as more complex missions are envisioned in the next few decades. Software tools for trajectory design in this regime must be further developed to incorporate better understanding of the solution space and, thus, improve the efficiency and expand the capabilities of current approaches. Only recently applied to trajectory design, dynamical systems theory now offers new insights into the natural dynamics associated with the multi-body problem. The goal of this effort is the blending of analysis from dynamical systems theory with the well established NASA Goddard software program SWINGBY to enhance and expand the capabilities for mission design. Basic knowledge concerning the solution space is improved as well.

The Mercury Laser Altimeter Instrument for the MESSENGER Mission

NASA Technical Reports Server (NTRS)

Cavanaugh, John F.; Smith, James C.; Sun, Xiaoli; Bartels, Arlin E.; Ramos-Izquierdo, Luis; Krebs, Danny J.; Novo-Gradac, Anne marie; McGarry, Jan F.; Trunzo, Raymond; Britt, Jamie L.

2006-01-01

The Mercury Laser Altimeter (MLA) is one of the payload science instruments on the MErcury Surface, Space ENvironment, GEochemistry, and Ranging (MESSENGER) mission, which launched on 3 August 2004. The altimeter will measure the round trip time-of-flight of transmitted laser pulses reflected from the surface of the planet that, in combination with the spacecraft orbit position and pointing data, gives a high-precision measurement of surface topography referenced to Mercury's center of mass. The altimeter measurements will be used to determine the planet's forced librations by tracking the motion of large-scale topographic features as a function of time. MLA's laser pulse energy monitor and the echo pulse energy estimate will provide an active measurement of the surface reflectivity at 1064 nm. This paper describes the instrument design, prelaunch testing, calibration, and results of post-launch testing.

An estimation of Envisat's rotational state accounting for the precession of its rotational axis caused by gravity-gradient torque

NASA Astrophysics Data System (ADS)

Lin, Hou-Yuan; Zhao, Chang-Yin

2018-01-01

The rotational state of Envisat is re-estimated using the specular glint times in optical observation data obtained from 2013 to 2015. The model is simplified to a uniaxial symmetric model with the first order variation of its angular momentum subject to a gravity-gradient torque causing precession around the normal of the orbital plane. The sense of Envisat's rotation can be derived from observational data, and is found to be opposite to the sense of its orbital motion. The rotational period is estimated to be (120.674 ± 0.068) · exp((4.5095 ± 0.0096) ×10-4 · t) s , where t is measured in days from the beginning of 2013. The standard deviation is 0.760 s, making this the best fit obtained for Envisat in the literature to date. The results demonstrate that the angle between the angular momentum vector and the negative normal of the orbital plane librates around a mean value of 8.53 ° ± 0.42 ° with an amplitude from about 0.7 ° (in 2013) to 0.5 ° (in 2015), with the libration period equal to the precession period of the angular momentum, from about 4.8 days (in 2013) to 3.4 days (in 2015). The ratio of the minimum to maximum principal moments of inertia is estimated to be 0.0818 ± 0.0011 , and the initial longitude of the angular momentum in the orbital coordinate system is 40.5 ° ± 9.3 ° . The direction of the rotation axis derived from our results at September 23, 2013, UTC 20:57 is similar to the results obtained from satellite laser ranging data but about 20 ° closer to the negative normal of the orbital plane.

An Empirically Derived Three-Dimensional Laplace Resonance in the GJ 876 Planetary System

NASA Astrophysics Data System (ADS)

Nelson, Benjamin Earl; Robertson, Paul; Pritchard, Seth

2015-08-01

We report constraints on the three-dimensional orbital architecture for all four planets known to orbit the nearby M dwarf Gliese 876 (=GJ 876) based solely on Doppler measurements and demanding long-term orbital stability. Our dataset incorporates publicly available radial velocities taken with the ELODIE and CORALIE spectrographs, HARPS, and Keck HIRES as well as previously unpublished HIRES RVs. We first quantitatively assess the validity of the planets thought to orbit GJ 876 by computing the Bayes factors for a variety of different coplanar models using an importance sampling algorithm. We confirm that a four-planet model is indeed preferred over a three-planet model. Next, we apply a Newtonian MCMC algorithm (RUN DMC, B. Nelson et al. 2014) to perform a Bayesian analysis of the planet masses and orbits using an n-body model that allows each planet to take on its own orbit in three-dimensional space. Based on the radial velocities alone, the mutual inclinations for the outer three resonant planets are constrained to Φcb = 2.8±1.71.3 degrees for the "c" and "b" pair and Φbe = 10.3±6.35.1 degrees for the "b" and "e" pair. We integrate the equations of motion of a sample of initial conditions drawn from our posterior for 107 years. We identify dynamically unstable models and find that the GJ 876 planets must be roughly coplanar (Φcb = 1.41±0.620.57 degrees) and (Φbe = 3.9±2.01.9 degrees), indicating the amount of planet-planet scattering in the system has been low. We investigate the distribution of the respective resonant arguments of each planet pair and find that at least one resonant argument for each planet pair and the Laplace argument librate. The libration amplitudes in our three-dimensional orbital model supports the idea of the outer-three planets having undergone significant past disk migration.

Complete tidal evolution of Pluto-Charon

NASA Astrophysics Data System (ADS)

Cheng, W. H.; Lee, Man Hoi; Peale, S. J.

2014-05-01

Both Pluto and its satellite Charon have rotation rates synchronous with their orbital mean motion. This is the theoretical end point of tidal evolution where transfer of angular momentum has ceased. Here we follow Pluto’s tidal evolution from an initial state having the current total angular momentum of the system but with Charon in an eccentric orbit with semimajor axis a≈4RP (where RP is the radius of Pluto), consistent with its impact origin. Two tidal models are used, where the tidal dissipation function Q∝1/frequency and Q = constant, where details of the evolution are strongly model dependent. The inclusion of the gravitational harmonic coefficient C22 of both bodies in the analysis allows smooth, self consistent evolution to the dual synchronous state, whereas its omission frustrates successful evolution in some cases. The zonal harmonic J2 can also be included, but does not cause a significant effect on the overall evolution. The ratio of dissipation in Charon to that in Pluto controls the behavior of the orbital eccentricity, where a judicious choice leads to a nearly constant eccentricity until the final approach to dual synchronous rotation. The tidal models are complete in the sense that every nuance of tidal evolution is realized while conserving total angular momentum-including temporary capture into spin-orbit resonances as Charon’s spin decreases and damped librations about the same.

Exploration of the region near the sun-earth collinear libration points for the control of large formations

NASA Astrophysics Data System (ADS)

Heritier, Aurelie

Spacecraft formations possess many applications in the future of space exploration. During the last decade, due to the detection of a large number of extrasolar planets, new studies on formation flying in multi-body regimes have emerged to support searches for Earth-like planets in other solar systems. The L2 Sun-Earth libration point region has been a popular destination in creating an architecture for astronomical missions. It is a relatively cold environment, far from the disturbances of the Sun and, therefore, ideal for astronomical instruments. However, controlling multiple spacecraft in a multi-body environment is challenging and a good understanding of the natural dynamics in this regime is essential. The current investigation explores the dynamical environment near the L2 Sun-Earth libration point to aid in the control of formations of spacecraft. By exploiting the natural dynamics in the circular restricted three-body model (CR3BP), natural regions are determined that are particularly suitable for maintaining formations of spacecraft. The natural dynamics at small distances from a given reference trajectory are initially investigated for the placement of small formations of spacecraft. Some regions with low relative drift represent suitable locations to maintain small formations and are derived analytically using variational equations. Spacecraft located in such regions avoid large variations in their mutual distances while maintaining the orientation of the formation. These regions represent quadric surfaces, and the type of quadric surfaces, either ellipsoids or elliptic cylinders, depends on the eigenstructure reflecting the phase space along the given reference trajectory. The natural flow at large distances from a given reference trajectory is explored next to characterize regions that are suitable to maintain large formations, i.e., when the mutual distances between the spacecraft reaches tens of thousands of kilometers. Spheres of points at various locations along the reference orbit are constructed to classify the space, and regions of low natural drift on the spheres are numerically identified when the distance between two vehicles is large. These low drift regions are examined in detail, and a correspondance with the quadric surfaces that are derived for small formations is established. In particular, the orientation of these low drift zones along a given reference orbit are investigated as some parameters vary, such as the size of the formation as well as the reference orbit. Using the low natural drift regions, control strategies are then developed for large formations. Traditional controllers, such as impulsive maneuvers and linear quadratic regulators (LQR), are employed to quantify the level of control that is required to maintain large formations along specific directions in the CR3BP. Designs of new controllers are also investigated to produce some set of desired relative motions between two spacecraft placed at large mutual distances. In a potential formation option investigated in this analysis, a deputy vehicle maintains a fixed circular motion in a plane relative to a chief spacecraft moving along its reference trajectory. Finally, the effectiveness of using the low natural drift regions as derived for large formations is tested for the New Worlds Observer mission concept. This scenario involves a large telescope-occulter formation for star observations, to detect and characterize habitable terrestrial exoplanets. The low drift zones are employed to reduce the control effort to maintain a large telescope-occulter formation during the observation of inertially-fixed target stars. In particular, the occulter is maintained via a linear quadratic regulator during star observations. Given a set of inertially-fixed target stars, an automatic star sequence design process is proposed with observation and reconfiguration phases using the low drift regions. This design creates star sequences that lead to relatively small overall maneuver costs for this particular mission concept.

An Anomalous Force on the Map Spacecraft

NASA Technical Reports Server (NTRS)

Starin, Scott R.; ODonnell, James R., Jr.; Ward, David K.; Wollack, Edward J.; Bay, P. Michael; Fink, Dale R.; Bauer, Frank (Technical Monitor)

2002-01-01

The Microwave Anisotropy Probe (MAP) orbits the second Earth-Sun libration point (L2)-about 1.5 million kilometers outside Earth's orbit-mapping cosmic microwave background radiation. To achieve orbit near L2 on a small fuel budget, the MAP spacecraft needed to swing past the Moon for a gravity assist. Timing the lunar swing-by required MAP to travel in three high-eccentricity phasing loops with critical maneuvers at a minimum of two, but nominally all three, of the perigee passes. On the approach to the first perigee maneuver, MAP telemetry showed a considerable change in system angular momentum that threatened to cause on-board Failure Detection and Correction (FDC) to abort the critical maneuver. Fortunately, the system momentum did not reach the FDC limit; however, the MAP team did develop a contingency strategy should a stronger anomaly occur before or during subsequent perigee maneuvers, Simultaneously, members of the MAP team developed and tested various hypotheses for the cause of the anomalous force. The final hypothesis was that water was outgassing from the thermal blanketing and freezing to the cold side of the solar shield. As radiation from Earth warmed the cold side of the spacecraft, the uneven sublimation of frozen water created a torque on the spacecraft.

The role of invariant manifolds in lowthrust trajectory design (part III)

NASA Technical Reports Server (NTRS)

Lo, Martin W.; Anderson, Rodney L.; Lam, Try; Whiffen, Greg

2006-01-01

This paper is the third in a series to explore the role of invariant manifolds in the design of low thrust trajectories. In previous papers, we analyzed an impulsive thrust resonant gravity assist flyby trajectory to capture into Europa orbit using the invariant manifolds of unstable resonant periodic orbits and libration orbits. The energy savings provided by the gravity assist may be interpreted dynamically as the result of a finite number of intersecting invariant manifolds. In this paper we demonstrate that the same dynamics is at work for low thrust trajectories with resonant flybys and low energy capture. However, in this case, the flybys and capture are effected by continuous families of intersecting invariant manifolds.

Lunar Cube Transfer Trajectory Options

NASA Technical Reports Server (NTRS)

Folta, David; Dichmann, Donald James; Clark, Pamela E.; Haapala, Amanda; Howell, Kathleen

2015-01-01

Numerous Earth-Moon trajectory and lunar orbit options are available for Cubesat missions. Given the limited Cubesat injection infrastructure, transfer trajectories are contingent upon the modification of an initial condition of the injected or deployed orbit. Additionally, these transfers can be restricted by the selection or designs of Cubesat subsystems such as propulsion or communication. Nonetheless, many trajectory options can b e considered which have a wide range of transfer duration, fuel requirements, and final destinations. Our investigation of potential trajectories highlights several options including deployment from low Earth orbit (LEO) geostationary transfer orbits (GTO) and higher energy direct lunar transfer and the use of longer duration Earth-Moon dynamical systems. For missions with an intended lunar orbit, much of the design process is spent optimizing a ballistic capture while other science locations such as Sun-Earth libration or heliocentric orbits may simply require a reduced Delta-V imparted at a convenient location along the trajectory.

Lunar Cube Transfer Trajectory Options

NASA Technical Reports Server (NTRS)

Folta, David; Dichmann, Donald J.; Clark, Pamela; Haapala, Amanda; Howell, Kathleen

2015-01-01

Numerous Earth-Moon trajectory and lunar orbit options are available for Cubesat missions. Given the limited Cubesat injection infrastructure, transfer trajectories are contingent upon the modification of an initial condition of the injected or deployed orbit. Additionally, these transfers can be restricted by the selection or designs of Cubesat subsystems such as propulsion or communication. Nonetheless, many trajectory options can be considered which have a wide range of transfer durations, fuel requirements, and final destinations. Our investigation of potential trajectories highlights several options including deployment from low Earth orbit (LEO), geostationary transfer orbits (GTO), and higher energy direct lunar transfers and the use of longer duration Earth-Moon dynamical systems. For missions with an intended lunar orbit, much of the design process is spent optimizing a ballistic capture while other science locations such as Sun-Earth libration or heliocentric orbits may simply require a reduced Delta-V imparted at a convenient location along the trajectory.

Stability of libration points in the restricted four-body problem with variable mass

NASA Astrophysics Data System (ADS)

Mittal, Amit; Aggarwal, Rajiv; Suraj, Md. Sanam; Bisht, Virender Singh

2016-10-01

We have investigated the stability of the Lagrangian solutions for the restricted four-body problem with variable mass. It has been assumed that the three primaries with masses m1, m2 and m3 form an equilateral triangle, wherein m2=m3. According to Jeans' law (Astronomy and Cosmogony, Cambridge University Press, Cambridge, 1928), the infinitesimal body varies its mass m with time. The space-time transformations of Meshcherskii (Studies on the Mechanics of Bodies of Variable Mass, GITTL, Moscow, 1949) are used by taking the values of the parameters q=1/2, k=0, n=1. The equations of motion of the infinitesimal body with variable mass have been determined. The equations of motion of the current problem differ from the ones of the restricted four-body problem with constant mass. There exist eight libration points, out of which two are collinear with the primary m1 and the rest are non-collinear for a fixed value of parameters γ (m {at time} t/m {at initial time}, 0<γ≤1 ), α (the proportionality constant in Jeans' law (Astronomy and Cosmogony, Cambridge University Press, Cambridge, 1928), 0≤α≤2.2) and μ=0.019 (the mass parameter). All the libration points are found to be unstable. The zero velocity surfaces (ZVS) are also drawn and regions of motion are discussed.

Achieving the Earth Science Enterprise Vision for the 21st Century: Platform Challenges

NASA Technical Reports Server (NTRS)

Lemmerman, Loren; Komar, George (Technical Monitor)

2001-01-01

The ESE observational architecture of the future vision is dramatically different from that of today. The vision suggests observations from multiple orbits, collaborating space assets, and even seamless integration of space and other assets. Observations from GEO or from Libration points rather than from LEO suggest spacecraft carrying instruments with large deployable apertures. Minimization of launch costs suggests that these large apertures have long life, be extremely mass and volume efficient, and have low life cycle cost. Another significant challenge associated with high latitude orbits is high precision pointing and control. Finally, networks of spacecraft flying in predetermined constellation will be required either to apply complementary assets to an observation or to extend the virtual aperture beyond that attainable with a single spacecraft. These changes dictate development of new technology on several fronts, which are outlined in this paper. A section on high speed communications will outline requirements and approaches now envisioned. Sensorwebs will be developed from the viewpoint of work already begun for both space and for terrestrial networks. Precision guidance, navigation and control will be addressed from the perspective of precision flying for repeat pass interferometry and extreme pointing stability for advanced altimetry. A separate section will address requirements for distributed systems. Large lightweight deployables will be discussed with an emphasis on inflatable technology and its predicted benefits for large aperture instruments. For each technology area listed, current state-of-the-art, technological approaches for future development, and projected levels of performance are outlined.

Spacecraft Station-Keeping Trajectory and Mission Design Tools

NASA Technical Reports Server (NTRS)

Chung, Min-Kun J.

2009-01-01

Two tools were developed for designing station-keeping trajectories and estimating delta-v requirements for designing missions to a small body such as a comet or asteroid. This innovation uses NPOPT, a non-sparse, general-purpose sequential quadratic programming (SQP) optimizer and the Two-Level Differential Corrector (T-LDC) in LTool (Libration point mission design Tool) to design three kinds of station-keeping scripts: vertical hovering, horizontal hovering, and orbiting. The T-LDC is used to differentially correct several trajectory legs that join hovering points. In a vertical hovering, the maximum and minimum range points must be connected smoothly while maintaining the spacecrafts range from a small body, all within the law of gravity and the solar radiation pressure. The same is true for a horizontal hover. A PatchPoint is an LTool class that denotes a space-time event with some extra information for differential correction, including a set of constraints to be satisfied by T-LDC. Given a set of PatchPoints, each with its own constraint, the T-LDC differentially corrects the entire trajectory by connecting each trajectory leg joined by PatchPoints while satisfying all specified constraints at the same time. Vertical and horizontal hover both are needed to minimize delta-v spent for station keeping. A Python I/F to NPOPT has been written to be used from an LTool script. In vertical hovering, the spacecraft stays along the line joining the Sun and a small body. An instantaneous delta-v toward the anti- Sun direction is applied at the closest approach to the small body for station keeping. For example, the spacecraft hovers between the minimum range (2 km) point and the maximum range (2.5 km) point from the asteroid 1989ML. Horizontal hovering buys more time for a spacecraft to recover if, for any reason, a planned thrust fails, by returning almost to the initial position after some time later via a near elliptical orbit around the small body. The mapping or staging orbit may be similarly generated using T-LDC with a set of constraints. Some delta-v tables are generated for several different asteroid masses.

Multiobjective Optimization of Low-Energy Trajectories Using Optimal Control on Dynamical Channels

NASA Technical Reports Server (NTRS)

Coffee, Thomas M.; Anderson, Rodney L.; Lo, Martin W.

2011-01-01

We introduce a computational method to design efficient low-energy trajectories by extracting initial solutions from dynamical channels formed by invariant manifolds, and improving these solutions through variational optimal control. We consider trajectories connecting two unstable periodic orbits in the circular restricted 3-body problem (CR3BP). Our method leverages dynamical channels to generate a range of solutions, and approximates the areto front for impulse and time of flight through a multiobjective optimization of these solutions based on primer vector theory. We demonstrate the application of our method to a libration orbit transfer in the Earth-Moon system.

Tethered satellite system dynamics and control

NASA Technical Reports Server (NTRS)

Musetti, B.; Cibrario, B.; Bussolino, L.; Bodley, C. S.; Flanders, H. A.; Mowery, D. K.; Tomlin, D. D.

1990-01-01

The first tethered satellite system, scheduled for launch in May 1991, is reviewed. The system dynamics, dynamics control, and dynamics simulations are discussed. Particular attention is given to in-plane and out-of-plane librations; tether oscillation modes; orbiter and sub-satellite dynamics; deployer control system; the sub-satellite attitude measurement and control system; the Aeritalia Dynamics Model; the Martin-Marietta and NASA-MSFC Dynamics Model; and simulation results.

Numerical approach to constructing the lunar physical libration: results of the initial stage

NASA Astrophysics Data System (ADS)

Zagidullin, A.; Petrova, N.; Nefediev, Yu.; Usanin, V.; Glushkov, M.

2015-10-01

So called "main problem" it is taken as a model to develop the numerical approach in the theory of lunar physical libration. For the chosen model, there are both a good methodological basis and results obtained at the Kazan University as an outcome of the analytic theory construction. Results of the first stage in numerical approach are presented in this report. Three main limitation are taken to describe the main problem: -independent consideration of orbital and rotational motion of the Moon; - a rigid body model for the lunar body is taken and its dynamical figure is described by inertia ellipsoid, which gives us the mass distribution inside the Moon. - only gravitational interaction with the Earth and the Sun is considered. Development of selenopotential is limited on this stage by the second harmonic only. Inclusion of the 3-rd and 4-th order harmonics is the nearest task for the next stage.The full solution of libration problem consists of removing the below specified limitations: consideration of the fine effects, caused by planet perturbations, by visco-elastic properties of the lunar body, by the presence of a two-layer lunar core, by the Earth obliquity, by ecliptic rotation, if it is taken as a reference plane.

INPOP:evolution, applications and perspectives

NASA Astrophysics Data System (ADS)

Laskar, Jacques; Fienga, Agnes; Manche, Hervé; Verma, Ashok; Gastineau, Mickael

2012-08-01

The INPOP ephemerides have known several improvement since the last INPOP10a release (Fienga et al. 2011a) . Improvement in the asteroid masse determinations have been implemented in using a priori sigmas and bound values least squares. Estimations of 120 asteroid masses have then been obtained with INPOP10b and presented in (Fieng a et al. 2012a). TDB and TCB versions of this ephemerides have been distributed through the INPOP website as well as spice format versions. Studies about solar corona have also been investigated leading to new electron density modeling presented in (Verma et al. 2012b). Adjustments of the Moon libration and orbits are also continuously operated. Perspectives will also be drawn during this talk, especially related to the analys is of spacecraft data (Messenger) for the planetary orbits and to the combination of spacecraft and LLR data for the Moon orbit and libration. A. Fienga, J. Laskar, P. Kuchynka, H. Manche, G. Desvignes, M. Gastineau, I. Cognard, and G. Theureau, 2011a, “The INPOP10a planetary ephemeris and its applications in fundamental physics,” Celes tial Mechanics and Dynamical Astronomy, vol. 111, pp. 363 - 385. A. Fienga, P. Kuchynka, J. Laskar, H. Manche, and M. Gastineau, 2012a “Asteroid mass determinations with INPOP planetary ephemerides,” in EPSC - DPS Joint Meeting 2011, p. 1879. A. K. Verma and A . Fienga, 2012b “Re - Estimation of Solar Corona Coefficients (a, B, c) by Using MGS Mex Spacecraft Datas,” in EPSC - DPS Joint Meeting 2011, p. 1828.

SECULAR BEHAVIOR OF EXOPLANETS: SELF-CONSISTENCY AND COMPARISONS WITH THE PLANET-PLANET SCATTERING HYPOTHESIS

DOE Office of Scientific and Technical Information (OSTI.GOV)

Timpe, Miles; Barnes, Rory; Kopparapu, Ravikumar

2013-09-15

If mutual gravitational scattering among exoplanets occurs, then it may produce unique orbital properties. For example, two-planet systems that lie near the boundary between circulation and libration of their periapses could result if planet-planet scattering ejected a former third planet quickly, leaving one planet on an eccentric orbit and the other on a circular orbit. We first improve upon previous work that examined the apsidal behavior of known multiplanet systems by doubling the sample size and including observational uncertainties. This analysis recovers previous results that demonstrated that many systems lay on the apsidal boundary between libration and circulation. We thenmore » performed over 12,000 three-dimensional N-body simulations of hypothetical three-body systems that are unstable, but stabilize to two-body systems after an ejection. Using these synthetic two-planet systems, we test the planet-planet scattering hypothesis by comparing their apsidal behavior, over a range of viewing angles, to that of the observed systems and find that they are statistically consistent regardless of the multiplicity of the observed systems. Finally, we combine our results with previous studies to show that, from the sampled cases, the most likely planetary mass function prior to planet-planet scattering follows a power law with index -1.1. We find that this pre-scattering mass function predicts a mutual inclination frequency distribution that follows an exponential function with an index between -0.06 and -0.1.« less

Model Estimated GCR Particle Flux Variation - Assessment with CRIS Data

NASA Astrophysics Data System (ADS)

Saganti, Premkumar

We present model calculated particle flux as a function of time during the current solar cycle along with the comparisons from the ACE/CRIS data and the Mars/MARIE data. In our model calculations we make use of the NASA's HZETRN (High Z and Energy Transport) code along with the nuclear fragmentation cross sections that are described by the quantum multiple scattering (QMSFRG) model. The time dependant variation of the GCR environment is derived making use of the solar modulation potential, phi. For the past ten years, Advanced Composition Explorer (ACE) has been in orbit at the Sun- Earth libration point (L1). Data from the Cosmic Ray Isotope Spectrometer (CRIS) instrument onboard the ACE spacecraft has been available from 1997 through the present time. Our model calculated particle flux showed high degree of correlation during the earlier phase of the current solar cycle (2003) in the lower Z region within 15

Advanced Materials and Component Development for Lithium-ion Cells for NASA Missions

NASA Technical Reports Server (NTRS)

Reid, Concha M.

2012-01-01

Human missions to Near Earth Objects, such as asteroids, planets, moons, libration points, and orbiting structures, will require safe, high specific energy, high energy density batteries to provide new or extended capabilities than are possible with today s state-of-the-art aerospace batteries. The National Aeronautics and Space Administration is developing advanced High Energy and Ultra High Energy lithium-ion cells to address these needs. In order to meet the performance goals, advanced, high-performing materials are required to provide improved performance at the component-level that contributes to performance at the integrated cell level. This paper will provide an update on the performance of experimental materials through the completion of two years of development. The progress of materials development, remaining challenges, and an outlook for the future of these materials in near term cell products will be discussed.

Development of a Two-Wheel Contingency Mode for the MAP Spacecraft

NASA Technical Reports Server (NTRS)

Starin, Scott R.; ODonnell, James R., Jr.; Bauer, Frank (Technical Monitor)

2002-01-01

The Microwave Anisotropy Probe (MAP) is a follow-on mission to the Cosmic Background Explorer (COBE), and is currently collecting data from its orbit near the second Sun-Earth libration point. Due to limited mass, power, and financial resources, a traditional reliability concept including fully redundant components was not feasible for MAP. Instead, the MAP design employs selective hardware redundancy in tandem with contingency software modes and algorithms to improve the odds of mission success. One direction for such improvement has been the development of a two-wheel backup control strategy. This strategy would allow MAP to position itself for maneuvers and collect science data should one of its three reaction wheels fail. Along with operational considerations, the strategy includes three new control algorithms. These algorithms would use the remaining attitude control actuators-thrusters and two reaction wheels-in ways that achieve control goals while minimizing adverse impacts on the functionality of other subsystems and software.

Optical transmission for the James Webb Space Telescope

NASA Astrophysics Data System (ADS)

Lightsey, Paul A.; Gallagher, Benjamin B.; Nickles, Neal; Copp, Tracy

2012-09-01

The fabrication and coating of the mirrors for the James Webb Space Telescope has been completed. The spectral reflectivity of the protected gold coated beryllium mirrors has been measured. The predicted end-of-life transmission through the telescope builds from these values. The additional phenomena that have been analyzed are contamination effects and effects of the environment for the JWST operation about the Earth-Sun L2 Lagrange libration point. The L2 environment analysis has been based on radiation testing of mirror samples and hypervelocity testing to assess the micrometeoroid impact effects. The mirror showed no change in reflectance over the VIS-SWIR wavelengths after exposure to 6-9 Grad (Si) that simulated 6 years orbiting the L2 Lagrange point. The effects of hypervelocity particle impacts on the mirrors from test data has been extrapolated to the to the anticipated flux characteristics for micrometeoroids at the L2 environment. The results show that the micrometeoroid effects are orders of magnitude below the particulate contamination effects. The final end-of-life transmission for the mirrors including all of these phenomena will meet the performance requirements for JWST.

Interior properties of the inner Saturnian moons from space astrometry data

NASA Astrophysics Data System (ADS)

Lainey, Valery; Noyelles, Benoît; Cooper, Nick; Murray, Carl; Park, Ryan; Rambaux, Nicolas

2018-04-01

During thirteen years in orbit around Saturn before its final plunge, the Cassini spacecraft provided more than ten thousand astrometric measurements. Such large amounts of accurate data enable the search for extremely faint signals in the orbital motion of the moons. Among those, the detection of the dynamical feedback of the rotation of the inner moons of Saturn on their respective orbits becomes possible. Using all the currently available astrometric data associated with Atlas, Prometheus, Pandora, Janus and Epimetheus, we provide a detailed analysis of the ISS data, with special emphasis on their statistical behavior and source of biases. Then, we try quantifying the physical librations of Prometheus, Pandora, Epimetheus and Janus from the monitoring of their orbits. Last, we show how introducing measurements directly derived from imaging can provide tighter constraints on these quantities.

Spin-Orbit Evolution of Mercury Revisited

DTIC Science & Technology

2014-06-23

Astronomy and Center for Interdisciplinary Exploration and Research in Astrophysics (CIERA), Northwestern University, Evanston, IL 60208, USA. cUS Naval...numerical simulations. So the principal novelty of our paper is that the 3:2 end-state is more ancient than the same end-state obtained when the constant...longitudinal librations (Margot et al., 2007), which are significantly larger in amplitude than what should be expected from a uniformly solid planet. As a

Analytical model of multi-planetary resonant chains and constraints on migration scenarios

NASA Astrophysics Data System (ADS)

Delisle, J.-B.

2017-09-01

Resonant chains are groups of planets for which each pair is in resonance, with an orbital period ratio locked at a rational value (2/1, 3/2, etc.). Such chains naturally form as a result of convergent migration of the planets in the proto-planetary disk. In this article, I present an analytical model of resonant chains of any number of planets. Using this model, I show that a system captured in a resonant chain can librate around several possible equilibrium configurations. The probability of capture around each equilibrium depends on how the chain formed, and especially on the order in which the planets have been captured in the chain. Therefore, for an observed resonant chain, knowing around which equilibrium the chain is librating allows for constraints to be put on the formation and migration scenario of the system. I apply this reasoning to the four planets orbiting Kepler-223 in a 3:4:6:8 resonant chain. I show that the system is observed around one of the six equilibria predicted by the analytical model. Using N-body integrations, I show that the most favorable scenario to reproduce the observed configuration is to first capture the two intermediate planets, then the outermost, and finally the innermost.

Cooperative motion in liquids: On librational dynamics of chloroform throughout its normal liquid-phase range

NASA Astrophysics Data System (ADS)

Rothschild, Walter G.; Cavagnat, Raymond M.

1994-03-01

We have extended the Raman spectral accumulations of the ν3 mode (A1, 367 cm-1) of liquid CHCl3-Cl-35 and its simulation in terms of an orientational equilibrium renewal process [W. G. Rothschild, R. M. Cavagnat, and P. Maraval, J. Chem. Phys. 99, 8922 (1993)] to a temperature of 338 K, about the normal boiling point of the system (335 K). The values of the best-fit parameters predict that the orientational motion of liquid chloroform, even at such a relatively high kinetic energy, is described predominantly by libratory states; their lifetime (˜1 ps) is four times longer than that of the free-rotational steps. The character of the orientational motion of the system, when traversing the range of 213 to 338 K from just above its melting to near its boiling point at about atmospheric pressure, reflects the softening of the liquid-cage structure in terms of an increasing dispersion and/or a decreasing value of the mean libration frequency, a lowering of the depth of its potential well, but near-invariance of its lifetime. Simultaneously, there is an approximately twofold increase in the lifetime of the much shorter stages of free-rotational motion. In essence, the system dynamics remain that of an assembly of librators.

Locations of stationary/periodic solutions in mean motion resonances according to the properties of dust grains

NASA Astrophysics Data System (ADS)

Pástor, P.

2016-07-01

The equations of secular evolution for dust grains in mean motion resonances with a planet are solved for stationary points. Non-gravitational effects caused by stellar radiation (the Poynting-Robertson effect and the stellar wind) are taken into account. The solutions are stationary in the semimajor axis, eccentricity and resonant angle, but allow the pericentre to advance. The semimajor axis of stationary solutions can be slightly shifted from the exact resonant value. The periodicity of the stationary solutions in a reference frame orbiting with the planet is proved analytically. The existence of periodic solutions in mean motion resonances means that analytical theory enables infinitely long capture times for dust particles. The stationary solutions are periodic motions to which the eccentricity asymptotically approaches and around which the libration occurs. Initial conditions corresponding to the stationary solutions are successfully found by numerically integrating the equation of motion. Numerically and analytically determined shifts of the semimajor axis from the exact resonance for the stationary solutions are in excellent agreement. The stationary solutions can be plotted by the locations of pericentres in the reference frame orbiting with the planet. The pericentres are distributed in space according to the properties of the dust particles.

Formation Flying Satellite Control Around the L2 Sun-Earth Libration Point

NASA Technical Reports Server (NTRS)

Hamilton, Nicholas H.; Folta, David; Carpenter, Russell; Bauer, Frank (Technical Monitor)

2002-01-01

This paper discusses the development of a linear control algorithm for formations in the vicinity of the L2 sun-Earth libration point. The development of a simplified extended Kalman filter is included as well. Simulations are created for the analysis of the stationkeeping and various formation maneuvers of the Stellar Imager mission. The simulations provide tracking error, estimation error, and control effort results. For formation maneuvering, the formation spacecraft track to within 4 meters of their desired position and within 1.5 millimeters per second of their desired zero velocity. The filter, with few exceptions, keeps the estimation errors within their three-sigma values. Without noise, the controller performs extremely well, with the formation spacecraft tracking to within several micrometers. Each spacecraft uses around 1 to 2 grams of propellant per maneuver, depending on the circumstances.

Fractal basins of attraction in the restricted four-body problem when the primaries are triaxial rigid bodies

NASA Astrophysics Data System (ADS)

Suraj, Md Sanam; Asique, Md Chand; Prasad, Umakant; Hassan, M. R.; Shalini, Kumari

2017-11-01

The planar equilateral restricted four-body problem, formulated on the basis of Lagrange's triangular solutions is used to determine the existence and locations of libration points and the Newton-Raphson basins of convergence associated with these libration points. We have supposed that all the three primaries situated on the vertices of an equilateral triangle are triaxial rigid bodies. This paper also deals with the effect of these triaxiality parameters on the regions of motion where the test particle is free to move. Further, the regions on the configuration plane filled by the basins of attraction are determined by using the multivariate version of the Newton-Raphson iterative system. The numerical study reveals that the triaxiality of the primaries is one of the most influential parameters in the four-body problem.

Effect of catalogues coordinate errors of a star onto determination of the physical libration of the Moon from the observations of stars

NASA Astrophysics Data System (ADS)

Petrova, Natalia; Kocoulin, Valerii; Nefediev, Yurii

2016-07-01

In the Kazan University computer simulation is carried out for observation of lunar physical libration in projects planned installation of measuring equipment on the lunar surface. One such project is the project of ILOM (Japan), in which on the lunar pole an optical telescope with CCD will be equipped. As a result, the determining the selenographic coordinates (x and y) of a star with an accuracy of 1 ms of arc will be achieved. On the basis of the analytical theory of physical libration we developed a technique for solving the inverse problem of the libration. And we have already shown, for example, that the error in determining selenographic coordinates about ɛ seconds does not lead to errors in the determination of the libration angles ρ and Iσ larger than the 1.414ɛ. Libration in longitude is not determined from observations of the polar star (Petrova et al., 2012). The accuracy of the libration in the inverse problem depends on accuracy of the coordinates of the stars - α and δ - taken from the star catalogs. Checking this influence is the task of the present study. To do simulation we have developed that allows to choose the stars, falling in the field of view of the lunar telescope on observation period. Equatorial coordinates of stars were chosen by us from several fundamental catalogs: UCAC2-BSS, Hipparcos, Tycho, FK6 (part I, III) and the Astronomical Almanac. An analysis of these catalogues from the point of view accuracy of coordinates of stars represented in them was performed by Nefediev et al., 2013. The largest error, 20-70 ms, found in the catalogues UCAC2 and Tycho, the others have an error about a millisecond of arc. We simulated the observations with mentioned errors and got the following results. 1. The error in the declination Δδ of the star causes the same order error in libration parameters ρ and Iσ , while the sensitivity of libration to errors in Δα is ten time smaller. Fortunately, due to statistics (30 to 70, depending on the time of observation), this error is reduced by an order, i.e. does not exceed the error of observation selenographic coordinates. 2. The worst thing - errors in coordinates of catalogue causes though a small but constant shift in the ρ and Iσ. So, when Δα, Δδ ˜0.01", then the shift reaches 0.0025". Moreover there is a trend, with a slight, but noticeable slope. 3. Effect of error in declination of a stars is substantially strong than the error in right ascension. Perhaps it is characteristic only for polar observations. For the required accuracy in determination of the physical libration these phenomena must be taken into account when processing the planned observations. Referencies. Nefediev et al., 2013. Uchenye zapiski Kazanskogo universiteta, v. 155, 1, p.188-194. Petrova, N., Abdulmyanov T., Hanada H. Some qualitative manifestations of the physical libration of the Moon by observing stars from the lunar surface. //J. Adv. Space Res., 2012a. V. 50, p. 1702-1711

Formation Control of the MAXIM L2 Libration Orbit Mission

NASA Technical Reports Server (NTRS)

Folta, David; Hartman, Kate; Howell, Kathleen; Marchand, Belinda

2004-01-01

The Micro-Arcsecond Imaging Mission (MAXIM), a proposed concept for the Structure and Evolution of the Universe (SEU) Black Hole Imaging mission, is designed to make a ten million-fold improvement in X-ray image clarity of celestial objects by providing better than 0.1 microarcsecond imaging. To achieve mission requirements, MAXIM will have to improve on pointing by orders of magnitude. This pointing requirement impacts the control and design of the formation. Currently the architecture is comprised of 25 spacecraft, which will form the sparse apertures of a grazing incidence X-ray interferometer covering the 0.3-10 keV bandpass. This configuration will deploy 24 spacecraft as optics modules and one as the detector. The formation must allow for long duration continuous science observations and also for reconfiguration that permits re-pointing of the formation. In this paper, we provide analysis and trades of several control efforts that are dependent upon the pointing requirements and the configuration and dimensions of the MAXIM formation. We emphasize the utilization of natural motions in the Lagrangian regions that minimize the control efforts and we address both continuous and discrete control via LQR and feedback linearization. Results provide control cost, configuration options, and capabilities as guidelines for the development of this complex mission.

Design and Implementation of the ARTEMIS Lunar Transfer Using Multi-Body Dynamics

NASA Technical Reports Server (NTRS)

Folta, David; Woodard, Mark; Sweetser, Theodore; Broschart, Stephen B.; Cosgrove, Daniel

2011-01-01

The use of multi-body dynamics to design the transfer of spacecraft from Earth elliptical orbits to the Earth-Moon libration (L(sub 1) and L(sub 2)) orbits has been successfully demonstrated by the Acceleration Reconnection and Turbulence and Electrodynamics of the Moon's Interaction with the Sun (ARTEMIS) mission. Operational support of the two ARTEMIS spacecraft is a final step in the realization of a design process that can be used to transfer spacecraft with restrictive operational constraints and fuel limitations. The focus of this paper is to describe in detail the processes and implementation of this successful approach.

Preparing GMAT for Operational Maneuver Planning of the Advanced Composition Explorer (ACE)

NASA Technical Reports Server (NTRS)

Qureshi, Rizwan Hamid; Hughes, Steven P.

2014-01-01

The General Mission Analysis Tool (GMAT) is an open-source space mission design, analysis and trajectory optimization tool. GMAT is developed by a team of NASA, private industry, public and private contributors. GMAT is designed to model, optimize and estimate spacecraft trajectories in flight regimes ranging from low Earth orbit to lunar applications, interplanetary trajectories and other deep space missions. GMAT has also been flight qualified to support operational maneuver planning for the Advanced Composition Explorer (ACE) mission. ACE was launched in August, 1997 and is orbiting the Sun-Earth L1 libration point. The primary science objective of ACE is to study the composition of both the solar wind and the galactic cosmic rays. Operational orbit determination, maneuver operations and product generation for ACE are conducted by NASA Goddard Space Flight Center (GSFC) Flight Dynamics Facility (FDF). This paper discusses the entire engineering lifecycle and major operational certification milestones that GMAT successfully completed to obtain operational certification for the ACE mission. Operational certification milestones such as gathering of the requirements for ACE operational maneuver planning, gap analysis, test plans and procedures development, system design, pre-shadow operations, training to FDF ACE maneuver planners, shadow operations, Test Readiness Review (TRR) and finally Operational Readiness Review (ORR) are discussed. These efforts have demonstrated that GMAT is flight quality software ready to support ACE mission operations in the FDF.

International Space Station as a Base Camp for Exploration Beyond Low Earth Orbit

NASA Technical Reports Server (NTRS)

Raftery, Michael; Hoffman, Jeffrey

2011-01-01

The idea for using the International Space Station (ISS) as platform for exploration has matured in the past year and the concept continues to gain momentum. ISS provides a robust infrastructure which can be used to test systems and capabilities needed for missions to the Moon, Mars, asteroids and other potential destinations. International cooperation is a critical enabler and ISS has already demonstrated successful management of a large multi-national technical endeavor. Systems and resources needed for expeditions can be aggregated and thoroughly tested at ISS before departure thus providing wide operational flexibility and the best assurance of mission success. A small part of ISS called an Exploration Platform (ISS-EP) can be placed at Earth-Moon Libration point 1 (EML1) providing immediate benefits and flexibility for future exploration missions. We will show how ISS and the ISS-EP can be used to reduce risk and improve the operational flexibility for missions beyond low earth orbit. Life support systems and other technology developed for ISS can be evolved and adapted to the ISS-EP and other exploration spacecraft. New technology, such as electric propulsion and advanced life support systems can be tested and proven at ISS as part of an incremental development program. Commercial companies who are introducing transportation and other services will benefit with opportunities to contribute to the mission since ISS will serve as a focal point for the commercialization of low earth orbit services. Finally, we will show how use of ISS provides immediate benefits to the scientific community because its capabilities are available today and certain critical aspects of exploration missions can be simulated.

Real-time control of optimal low-thrust transfer to the Sun-Earth L 1 halo orbit in the bicircular four-body problem

NASA Astrophysics Data System (ADS)

Salmani, Majid; Büskens, Christof

2011-11-01

In this article, after describing a procedure to construct trajectories for a spacecraft in the four-body model, a method to correct the trajectory violations is presented. To construct the trajectories, periodic orbits as the solutions of the three-body problem are used. On the other hand, the bicircular model based on the Sun-Earth rotating frame governs the dynamics of the spacecraft and other bodies. A periodic orbit around the first libration-point L1 is the destination of the mission which is one of the equilibrium points in the Sun-Earth/Moon three-body problem. In the way to reach such a far destination, there are a lot of disturbances such as solar radiation and winds that make the plans untrustworthy. However, the solar radiation pressure is considered in the system dynamics. To prevail over these difficulties, considering the whole transfer problem as an optimal control problem makes the designer to be able to correct the unavoidable violations from the pre-designed trajectory and strategies. The optimal control problem is solved by a direct method, transcribing it into a nonlinear programming problem. This transcription gives an unperturbed optimal trajectory and its sensitivities with respect perturbations. Modeling these perturbations as parameters embedded in a parametric optimal control problem, one can take advantage of the parametric sensitivity analysis of nonlinear programming problem to recalculate the optimal trajectory with a very smaller amount of computation costs. This is obtained by evaluating a first-order Taylor expansion of the perturbed solution in an iterative process which is aimed to achieve an admissible solution. At the end, the numerical results show the applicability of the presented method.

Improvements on the interior structure of Mercury expected from geodesy measurements

NASA Astrophysics Data System (ADS)

Rivoldini, A.; van Hoolst, T.; Verhoeven, O.

2008-09-01

ABSTRACT We assess the improvements on the interior structure of Mercury provided by expected data from geodesy experiments to be performed with the MESSENGER and BepiColombo orbiters. The observation of obliquity will allow estimating the moment of inertia, whereas measurements of libration will determine the moment of inertia of the silicate shell (mantle and crust). Tidal measurements will constrain the Love numbers that characterize the response of Mercury to the solar tidal forcing. Here, we construct depth-dependent interior structure models of Mercury for several plausible chemical compositions of the core and of the mantle using recent data on core and mantle materials. In particular we study the core structure for different mantle mineralogies and two different temperature profiles. We investigate the influence of the core light element concentration, temperature, and melting law on core state and inner core size. We compute libration amplitude, obliquity, tidal deformation, and tidal changes in the external potential for our models.

Determination of the lunar orbital and rotational parameters and of the ecliptic reference system orientation from LLR measurements and IERS data

NASA Astrophysics Data System (ADS)

Chapront, J.; Chapront-Touzé, M.; Francou, G.

1999-03-01

An analysis of Lunar Laser Ranging (LLR) observations from January 1972 till March 1998 is performed using the lunar theory ELP 2000-96 and the completed Moons' theory of the lunar libration. The LLR station coordinates, polar motion and Universal Time are provided by the International Earth Rotation Service (IERS). In Solution 1 the precession-nutation transformation is given by recent analytical theories, while in Solution 2 it is derived from the IERS daily corrections. Orbital and free libration parameters of the Moon, and coordinates of the reflectors are obtained in both cases. The position of the inertial mean ecliptic of J2000.0 with respect to the equator of the mean Celestial Ephemeris Pole (CEP) of J2000.0 (in Solution 1) and to the International Celestial Reference System (ICRS), the IERS celestial reference system, (in Solution 2) are fit. The position of the mean CEP equator of J2000.0 and of several dynamical reference planes and origins, with respect to ICRS, are derived from these fits (Fig. 1). The leading results are the following: 0farcs057 60+/- 0farcs000 20 (in the equator) for the separation of the origin of right ascensions in ICRS from the ascending node of the inertial mean ecliptic of J2000.0 on the reference plane of ICRS, -0farcs0460 +/- 0farcs0008 (in the ecliptic) for the separation of the latter point from the inertial dynamical mean equinox of J2000.0, -0farcs015 19+/- 0farcs000 35 (in the equator) for the separation of the inertial dynamical mean equinox of J2000.0 from the J2000.0 right ascension origin derived from IERS polar motion and Universal Time and from precise theories of precession-nutation, and 23degr26 arcmin21 farcs405 22+/- 0farcs000 07 for the inertial obliquity of J2000.0. A correction of -0farcs3437 +/- 0farcs0040 /cy to the IAU 1976 value of the precession constant is also obtained (the errors quoted are formal errors).

New Moon

NASA Image and Video Library

2017-12-08

New Moon. By the modern definition, New Moon occurs when the Moon and Sun are at the same geocentric ecliptic longitude. The part of the Moon facing us is completely in shadow then. Pictured here is the traditional New Moon, the earliest visible waxing crescent, which signals the start of a new month in many lunar and lunisolar calendars. This marks the first time that accurate shadows at this level of detail are possible in such a computer simulation. The shadows are based on the global elevation map being developed from measurements by the Lunar Orbiter Laser Altimeter (LOLA) aboard the Lunar Reconnaissance Orbiter (LRO). LOLA has already taken more than 10 times as many elevation measurements as all previous missions combined. The Moon always keeps the same face to us, but not exactly the same face. Because of the tilt and shape of its orbit, we see the Moon from slightly different angles over the course of a month. When a month is compressed into 12 seconds, as it is in this animation, our changing view of the Moon makes it look like it's wobbling. This wobble is called libration. The word comes from the Latin for "balance scale" (as does the name of the zodiac constellation Libra) and refers to the way such a scale tips up and down on alternating sides. The sub-Earth point gives the amount of libration in longitude and latitude. The sub-Earth point is also the apparent center of the Moon's disk and the location on the Moon where the Earth is directly overhead. The Moon is subject to other motions as well. It appears to roll back and forth around the sub-Earth point. The roll angle is given by the position angle of the axis, which is the angle of the Moon's north pole relative to celestial north. The Moon also approaches and recedes from us, appearing to grow and shrink. The two extremes, called perigee (near) and apogee (far), differ by more than 10%. The most noticed monthly variation in the Moon's appearance is the cycle of phases, caused by the changing angle of the Sun as the Moon orbits the Earth. The cycle begins with the waxing (growing) crescent Moon visible in the west just after sunset. By first quarter, the Moon is high in the sky at sunset and sets around midnight. The full Moon rises at sunset and is high in the sky at midnight. The third quarter Moon is often surprisingly conspicuous in the daylit western sky long after sunrise. Celestial north is up in these images, corresponding to the view from the northern hemisphere. The descriptions of the print resolution stills also assume a northern hemisphere orientation. To adjust for southern hemisphere views, rotate the images 180 degrees, and substitute "north" for "south" in the descriptions. Credit: NASA/Goddard Space Flight Center Scientific Visualization Studio NASA Goddard Space Flight Center enables NASA’s mission through four scientific endeavors: Earth Science, Heliophysics, Solar System Exploration, and Astrophysics. Goddard plays a leading role in NASA’s accomplishments by contributing compelling scientific knowledge to advance the Agency’s mission. Follow us on Twitter Join us on Facebook Find us on Instagram

Preliminary Planar Formation: Flight Dynamics Near Sun-Earth L2 Point

NASA Technical Reports Server (NTRS)

Segerman, Alan M.; Zedd, Michael F.

2003-01-01

NASA's Goddard Space Flight Center is planning a series of missions in the vicinity of the Sun-Earth L2 libration point. Some of these projects will involve a distributed space system of telescope spacecraft acting together as a single telescope for high-resolution. The individual telescopes will be configured in a plane, surrounding a hub, where the telescope plane can be aimed toward various astronomical targets of interest. In preparation for these missions, it is necessary to develop an improved understanding of the dynamical behavior of objects in a planar configuration near L2. The classical circular restricted three body problem is taken as the basis for the analysis. At first order, the motion of such a telescope relative to the hub is described by a system of linear second order differential equations. These equations are identical to the circular restricted problem's linear equations describing the hub motion about L2. Therefore, the fundamental frequencies, both parallel to and normal to the ecliptic plane, are the same for the relative telescope motion as for the hub motion. To maintain the telescope plane for the duration necessary for the planned observations, a halo-type orbit of the telescopes about the hub is investigated. By using a halo orbit, the individual telescopes remain in approximately the same plane over the observation duration. For such an orbit, the fundamental periods parallel to and normal to the ecliptic plane are forced to be the same by careful selection of the initial conditions in order to adjust the higher order forces. The relative amplitudes of the resulting oscillations are associated with the orientation of the telescope plane relative to the ecliptic. As in the circular restricted problem, initial conditions for the linearized equations must be selected so as not to excite the convergent or divergent linear modes. In a higher order analysis, the telescope relative motion equations include the effects of the position of the hub relative to L2. In this paper, the differential equations are developed through second order in the distance of the hub from the libration point. A modified Lindstedt-Poincad perturbation method is employed to construct the solution of these differential equations through that same order of magnitude. In the course of the solution process, relationships are determined between the initial conditions of the telescopes, selected in order to avoid resonance excitation. As the differential equations include the hub position, it is necessary to simultaneously develop the solution for the hub. As has been done in past analyses of the circular restricted problem, the hub position is written in a power series formulation in terms of its distance from L2. Then, in order to be included in the telescope equations, the hub solution is cast in terms of the nonlinear frequency of the relative telescope motion. In the course of the analysis, it is determined that the hub should also maintain a halo orbit - about L2. Additionally, relationships are formed between the initial conditions of the telescopes and the hub. These relationships may be used to associate sets of initial conditions with particular orientations of the telescope plane. The accuracy of the analytical solution is verified through various simulations and comparison to numerical integration of the differential equations. The results of the simulations are presented, along with a graphical representation of the relationships between the initial conditions of the telescopes and hub.

New Worlds Observer Formation Control Design Based on the Dynamics of Relative Motion

NASA Technical Reports Server (NTRS)

Luquette, Richard J.

2008-01-01

The New Worlds Observer (NWO) mission is designed for the direct detection and characterization of extrasolar planets. The NWO mission concept employs a two spacecraft leader-follower formation on a trajectory around the Earth/Moon-Sun L(sub 2) Libration Point. The leader spacecraft is baselined as a 4 meter optical telescope. The follower, Starshade spacecraft, is designed to suppress light from a central body star permitting direct detection of a surrounding exoplanetary system. The current design requires a nominal leader-follower separation range of 72 Megameters. NWO poses many challenges including formation control. NWO cycles between three principal control modes during the nominal mission timeline: science (fine pointing), realignment and transition. This paper examines formation control strategies in the context of dynamics of relative motion for two spacecraft operating in the vicinity of the Earth/Moon-Sun L(sub 2)libration point. The paper presents an overview of the equations of relative motion followed by a discussion of each of the control modes. Discussion and analysis characterize control strategies for each of the mission control modes, including requirements, implementation challenges and project fuel budgets.

A Summary on Progress in Materials Development for Advanced Lithium-ion Cells for NASA's Exploration Missions

NASA Technical Reports Server (NTRS)

Reid, Concha M.

2011-01-01

Vehicles and stand-alone power systems that enable the next generation of human missions to the moon will require energy storage systems that are safer, lighter, and more compact than current state-of-the-art (SOA) aerospace quality lithium-ion (Li-ion) batteries. NASA is developing advanced Li-ion cells to enable or enhance future human missions to Near Earth Objects, such as asteroids, planets, moons, libration points, and orbiting structures. Advanced, high-performing materials are required to provide component-level performance that can offer the required gains at the integrated cell level. Although there is still a significant amount of work yet to be done, the present state of development activities has resulted in the synthesis of promising materials that approach the ultimate performance goals. This paper on interim progress of the development efforts will present performance of materials and cell components and will elaborate on the challenges of the development activities and proposed strategies to overcome technical issues.

The development of a cislunar space infrastructure

NASA Technical Reports Server (NTRS)

Buck, C. A.; Johnson, A. S.; Mcglinchey, J. M.; Ryan, K. D.

1989-01-01

The primary objective of this Advanced Mission Design Program is to define the general characteristics and phased evolution of a near-Earth space infrastructure. The envisioned foundation includes a permanently manned, self-sustaining base on the lunar surface, a space station at the Libration Point between earth and the moon (L1), and a transportation system that anchors these elements to the Low Earth Orbit (LEO) station. The implementation of this conceptual design was carried out with the idea that the infrastructure is an important step in a larger plan to expand man's capabilities in space science and technology. Such expansion depends on low cost, reliable, and frequent access to space for those who wish to use the multiple benefits of this environment. The presence of a cislunar space infrastructure would greatly facilitate the staging of future planetary missions, as well as the full exploration of the lunar potential for science and industry. The rationale for, and a proposed detailed scenario in support of, the cislunar space infrastructure are discussed.

On the first ν6 anti-aligned librating asteroid family of Tina

NASA Astrophysics Data System (ADS)

Carruba, V.; Morbidelli, A.

2011-04-01

Asteroid families are groups of bodies identified in the space of proper elements or of frequencies that share a common origin in the collisional break-up of their progenitors. Their dynamical evolution is shaped by the interaction with the local web of mean-motion and secular resonances, and by non-gravitational effects, such as the 'Yarkovsky' and 'Yarkovsky-O'Keefe-Radzievskii-Paddack' (YORP) effects. Thus, obtaining information on their age and original ejection velocity field is generally a difficult task. Recently, two families were found to have a large fraction of members in the non-linear secular resonance z1: the Agnia and Padua families. Conserved quantities of the z1resonance allowed for a more precise determination of their ages and ejection velocity fields. So far, however, no family was known to be in a linear secular resonance, such as the ν6 resonance, although individual asteroids were known to be in ν6 anti-aligned librating states. The ν6 resonance occurs when there is a commensurability between the frequency of precession of the pericentre of an asteroid and that of Saturn. As a consequence, in librating states, the resonant argument oscillates around a stable point. In anti-aligned librating states, the resonant argument oscillates around the stable point at 180°. Here we show that the newly identified Tina family is characterized by having all its members in such a state, making it the only family in the asteroid belt known to be completely embedded in a secular resonance configuration. This rare dynamical configuration limits the maximum eccentricity of Tina members, preventing them from experiencing Martian close encounters and forming a stable island of a new dynamical type. The current dispersion of asteroid resonant elements suggests that the family should be at least 2.5 Myr old, while Monte Carlo simulations including the Yarkovsky and YORP effects suggest that the Tina family should be 170+20-30 Myr old.

Site Selection and Deployment Scenarios for Servicing of Deep-Space Observatories

NASA Technical Reports Server (NTRS)

Willenberg, Harvey J.; Fruhwirth, Michael A.; Potter, Seth D.; Leete, Stephen J.; Moe, Rud V.

2001-01-01

The deep-space environment and relative transportation accessibility of the Weak Stability Boundary (WSB) region connecting the Earth-Moon and Sun-Earth libration points makes the Sun-Earth L2 an attractive operating location for future observatories. A summary is presented of key characteristics of future observatories designed to operate in this region. The ability to service observatories that operate within the region around the Lagrange points may greatly enhance their reliability, lifetime, and scientific return. The range of servicing missions might begin with initial deployment, assembly, test, and checkout. Post-assembly servicing missions might also include maintenance and repair, critical fluids resupply, and instrument upgrades. We define the range of servicing missions that can be performed with extravehicular activity, with teleoperated robots, and with autonomous robots. We then describe deployment scenarios that affect payload design. A trade study is summarized of the benefits and risks of alternative servicing sites, including at the International Space Station, at other low-Earth-orbit locations, at the Earth-Moon L1 location, and on-site at the Sun-Earth L2 location. Required technology trades and development issues for observatory servicing at each site, and with each level of autonomy, are summarized.

Astronomical aspects of cosmic threats: new problems and approaches to asteroid—comet hazard following the chelyabinsk event of February 15, 2013

NASA Astrophysics Data System (ADS)

Shustov, B. M.; Shugarov, A. S.; Naroenkov, S. A.; Prokhorov, M. E.

2015-10-01

A new definition of hazardous celestial bodies (HCBs) is introduced, in which the lower limit of the size of a HCB is reduced to 10 m. A new definition for threatening and collisional orbits of DCBs is introduced. The main astronomical factors that must be taken into account when creating systems for the detection of HCBs are analyzed. The most important of these are the uniformity of the distribution of points (regions) for the appearance of HCBs on the celestial sphere in near-Earth space and the practical limit for the velocity of approach of a HCB of 20 km/s (for 90% of bodies). It is shown that the creation of a system for the nearby detection of asteroids and comets arriving from the daytime sky requires the use of a space-based system. A concept for such a system, in which one or several optical telescopes are placed in the vicinity of the libration point L1 for the Sun—Earth system, is developed. Preliminary plans for such a system, called the System for the Detection of Daytime Asteroids (SDDA), are briefly described.

Formation Control of the MAXIM L2 Libration Orbit Mission

NASA Technical Reports Server (NTRS)

Folta, David; Hartman, Kate; Howell, Kathleen; Marchand, Belinda

2004-01-01

The Micro-Arcsecond X-ray Imaging Mission (MAXIM), a proposed concept for the Structure and Evolution of the Universe (SEU) Black Hole Imager mission, is designed to make a ten million-fold improvement in X-ray image clarity of celestial objects by providing better than 0.1 micro-arcsecond imaging. Currently the mission architecture comprises 25 spacecraft, 24 as optics modules and one as the detector, which will form sparse sub-apertures of a grazing incidence X-ray interferometer covering the 0.3-10 keV bandpass. This formation must allow for long duration continuous science observations and also for reconfiguration that permits re-pointing of the formation. To achieve these mission goals, the formation is required to cooperatively point at desired targets. Once pointed, the individual elements of the MAXIM formation must remain stable, maintaining their relative positions and attitudes below a critical threshold. These pointing and formation stability requirements impact the control and design of the formation. In this paper, we provide analysis of control efforts that are dependent upon the stability and the configuration and dimensions of the MAXIM formation. We emphasize the utilization of natural motions in the Lagrangian regions to minimize the control efforts and we address continuous control via input feedback linearization (IFL). Results provide control cost, configuration options, and capabilities as guidelines for the development of this complex mission.

A Survey Of Earth-Moon Libration Orbits: Stationkeeping Strategies And Intra-Orbit Transfers

NASA Technical Reports Server (NTRS)

Folta, David; Vaughn, Frank

2004-01-01

Cislunar space is a readily accessible region that may well develop into a prime staging area in the effort to colonize space near Earth or to colonize the Moon. While there have been statements made by various NASA programs regarding placement of resources in orbit about the Earth-Moon Lagrangian locations, there is no survey of the total cost associated with attaining and maintaining these unique orbits in an operational fashion. Transfer trajectories between these orbits required for assembly, servicing, and positioning of these resources have not been extensively investigated. These orbits are dynamically similar to those used for the Sun-Earth missions, but differences in governing gravitational ratios and perturbation sources result in unique characteristics. We implement numerical computations using high fidelity models and linear and nonlinear targeting techniques to compute the various maneuver (Delta)V and temporal costs associated with orbits about each of the Earth-Moon Lagrangian locations (L1, L2, L3, L4, and L5). From a dynamical system standpoint, we speak to the nature of these orbits and their stability. We address the cost of transfers between each pair of Lagrangian locations.

Saturnʼs Inner Satellites: Orbits, Masses, and the Chaotic Motion of Atlas from New Cassini Imaging Observations

NASA Astrophysics Data System (ADS)

Cooper, N. J.; Renner, S.; Murray, C. D.; Evans, M. W.

2015-01-01

We present numerically derived orbits and mass estimates for the inner Saturnian satellites, Atlas, Prometheus, Pandora, Janus, and Epimetheus from a fit to 2580 new Cassini Imaging Science Subsystem astrometric observations spanning 2004 February to 2013 August. The observations are provided as machine-readable and Virtual Observatory tables. We estimate G{{M}Atlas} = (0.384 ± 0.001) × 10-3 km3 s-2, a value 13% smaller than the previously published estimate but with an order of magnitude reduction in the uncertainty. We also find G{{M}Prometheus} = (10.677 ± 0.006) × 10-3 km3 s-2, G{{M}Pandora} = (9.133 ± 0.009) × 10-3 km3 s-2, G{{M}Janus} = (126.51 ± 0.03) × 10-3 km3 s-2, and G{{M}Epimetheus} = (35.110 ± 0.009) × 10-3 km3 s-2, consistent with previously published values, but also with significant reductions in uncertainties. We show that Atlas is currently librating in both the 54:53 co-rotation-eccentricity resonance (CER) and the 54:53 inner Lindblad (ILR) resonance with Prometheus, making it the latest example of a coupled CER-ILR system, in common with the Saturnian satellites Anthe, Aegaeon, and Methone, and possibly Neptune's ring arcs. We further demonstrate that Atlas's orbit is chaotic, with a Lyapunov time of ˜10 years, and show that its chaotic behavior is a direct consequence of the coupled resonant interaction with Prometheus, rather than being an indirect effect of the known chaotic interaction between Prometheus and Pandora. We provide an updated analysis of the second-order resonant perturbations involving Prometheus, Pandora, and Epimetheus based on the new observations, showing that these resonant arguments are librating only when Epimetheus is the innermost of the co-orbital pair, Janus and Epimetheus. We also find evidence that the known chaotic changes in the orbits of Prometheus and Pandora are not confined to times of apse anti-alignment.

Two Approaches in the Lunar Libration Theory: Analytical vs. Numerical Methods

NASA Astrophysics Data System (ADS)

Petrova, Natalia; Zagidullin, Arthur; Nefediev, Yurii; Kosulin, Valerii

2016-10-01

Observation of the physical libration of the Moon and the celestial bodies is one of the astronomical methods to remotely evaluate the internal structure of a celestial body without using expensive space experiments. Review of the results obtained due to the physical libration study, is presented in the report.The main emphasis is placed on the description of successful lunar laser ranging for libration determination and on the methods of simulating the physical libration. As a result, estimation of the viscoelastic and dissipative properties of the lunar body, of the lunar core parameters were done. The core's existence was confirmed by the recent reprocessing of seismic data Apollo missions. Attention is paid to the physical interpretation of the phenomenon of free libration and methods of its determination.A significant part of the report is devoted to describing the practical application of the most accurate to date the analytical tables of lunar libration built by comprehensive analytical processing of residual differences obtained when comparing the long-term series of laser observations with numerical ephemeris DE421 [1].In general, the basic outline of the report reflects the effectiveness of two approaches in the libration theory - numerical and analytical solution. It is shown that the two approaches complement each other for the study of the Moon in different aspects: numerical approach provides high accuracy of the theory necessary for adequate treatment of modern high-accurate observations and the analytic approach allows you to see the essence of the various kind manifestations in the lunar rotation, predict and interpret the new effects in observations of physical libration [2].[1] Rambaux, N., J. G. Williams, 2011, The Moon's physical librations and determination of their free modes, Celest. Mech. Dyn. Astron., 109, 85-100.[2] Petrova N., A. Zagidullin, Yu. Nefediev. Analysis of long-periodic variations of lunar libration parameters on the basis of analytical theory / // The Russian-Japanese Workshop, 20-25 October, Tokyo (Mitaka) - Mizusawa, Japan. - 2014.

Determination of the free lunar libration modes from ephemeris DE430

NASA Astrophysics Data System (ADS)

Yang, Yong-Zhang; Li, Jin-Ling; Ping, Jin-Song; Hanada, Hideo

2017-12-01

The Moon’s physical librations have been extensively studied, and elaborate researches have been developed for the purpose of deriving accurate modes of free librations. Our motivation comes from the Planetary and Lunar Ephemeris DE430 by JPL/NASA, which was created in April 2013, and is reported to be the most accurate lunar ephemeris today using the data from Gravity Recovery and Interior Laboratory (GRAIL). Therefore, the residuals after fitting the model have reduced owing to improvement in the libration models, and the free librations embedded in the Euler angles have also improved. We use Fourier analysis to extract the approximate frequencies from DE430 and then a quadratic interpolation method is used to determine higher accuracy frequencies. With the frequencies, the linear least-squares fitting method is employed to fit the lunar physical librations to DE430. From this analysis we identified the three modes of free physical librations, and estimated the amplitudes as {1.471}\\prime\\prime in longitude, {0.025}\\prime\\prime in latitude and {8.19}\\prime\\prime× {3.31}\\prime\\prime for the wobble, with the respective periods of 1056.16, 8806.9 and 27262.99 d. Since the free librations damp with time, they require recent excitation or a continuous stimulating mechanism in order to sustain.

Reduced cost mission design using surrogate models

NASA Astrophysics Data System (ADS)

Feldhacker, Juliana D.; Jones, Brandon A.; Doostan, Alireza; Hampton, Jerrad

2016-01-01

This paper uses surrogate models to reduce the computational cost associated with spacecraft mission design in three-body dynamical systems. Sampling-based least squares regression is used to project the system response onto a set of orthogonal bases, providing a representation of the ΔV required for rendezvous as a reduced-order surrogate model. Models are presented for mid-field rendezvous of spacecraft in orbits in the Earth-Moon circular restricted three-body problem, including a halo orbit about the Earth-Moon L2 libration point (EML-2) and a distant retrograde orbit (DRO) about the Moon. In each case, the initial position of the spacecraft, the time of flight, and the separation between the chaser and the target vehicles are all considered as design inputs. The results show that sample sizes on the order of 102 are sufficient to produce accurate surrogates, with RMS errors reaching 0.2 m/s for the halo orbit and falling below 0.01 m/s for the DRO. A single function call to the resulting surrogate is up to two orders of magnitude faster than computing the same solution using full fidelity propagators. The expansion coefficients solved for in the surrogates are then used to conduct a global sensitivity analysis of the ΔV on each of the input parameters, which identifies the separation between the spacecraft as the primary contributor to the ΔV cost. Finally, the models are demonstrated to be useful for cheap evaluation of the cost function in constrained optimization problems seeking to minimize the ΔV required for rendezvous. These surrogate models show significant advantages for mission design in three-body systems, in terms of both computational cost and capabilities, over traditional Monte Carlo methods.

Stability Analysis of the Planetary System Orbiting Upsilon Andromedae. 2; Simulations Using New Lick Observatory Fits

NASA Technical Reports Server (NTRS)

Lissauer, Jack J.; Rivera, Eugenio J.; DeVincenzi, Donald (Technical Monitor)

2001-01-01

We present results of long-term numerical orbital integrations designed to test the stability of the three-planet system orbiting upsilon Andromedae and short-term integrations to test whether mutual perturbations among the planets can be used to determine planetary masses. Our initial conditions are based on recent fits to the radial velocity data obtained by the planet search group at Lick Observatory. The new fits result in significantly more stable systems than did the initially announced planetary parameters. Our integrations using the 2000 February parameters show that if the system is nearly planar, then it is stable for at least 100 Myr for m(sub f) = 1/sin i less than or = 4. In some stable systems, the eccentricity of the inner planet experiences large oscillations. The relative periastra of the outer two planets' orbits librate about 0 deg. in most of the stable systems; if future observations imply that the periastron longitudes of these planets are very closely aligned at the present epoch, dynamical simulations may provide precise estimates for the masses and orbital inclinations of these two planets.

Identification of new orbits to enable future mission opportunities for the human exploration of the Martian moon Phobos

NASA Astrophysics Data System (ADS)

Zamaro, Mattia; Biggs, James D.

2016-02-01

One of the paramount stepping stones towards NASA's long-term goal of undertaking human missions to Mars is the exploration of the Martian moons. Since a precursor mission to Phobos would be easier than landing on Mars itself, NASA is targeting this moon for future exploration, and ESA has also announced Phootprint as a candidate Phobos sample-and-return mission. Orbital dynamics around small planetary satellites are particularly complex because many strong perturbations are involved, and the classical circular restricted three-body problem (R3BP) does not provide an accurate approximation to describe the system's dynamics. Phobos is a special case, since the combination of a small mass-ratio and length-scale means that the sphere-of-influence of the moon moves very close to its surface. Thus, an accurate nonlinear model of a spacecraft's motion in the vicinity of this moon must consider the additional perturbations due to the orbital eccentricity and the complete gravity field of Phobos, which is far from a spherical-shaped body, and it is incorporated into an elliptic R3BP using the gravity harmonics series-expansion (ER3BP-GH). In this paper, a showcase of various classes of non-keplerian orbits is identified and a number of potential mission applications in the Mars-Phobos system are proposed: these results could be exploited in upcoming unmanned missions targeting the exploration of this Martian moon. These applications include: low-thrust hovering and orbits around Phobos for close-range observations; the dynamical substitutes of periodic and quasi-periodic Libration Point Orbits in the ER3BP-GH to enable unique low-cost operations for space missions in the proximity of Phobos; their manifold structure for high-performance landing/take-off maneuvers to and from Phobos' surface and for transfers from and to Martian orbits; Quasi-Satellite Orbits for long-period station-keeping and maintenance. In particular, these orbits could exploit Phobos' occulting bulk and shadowing wake as a passive radiation shield during future manned flights to Mars to reduce human exposure to radiation, and the latter orbits can be used as an orbital garage, requiring no orbital maintenance, where a spacecraft could make planned pit-stops during a round-trip mission to Mars.

Mercury's capture into the 3/2 spin-orbit resonance as a result of its chaotic dynamics.

PubMed

Correia, Alexandre C M; Laskar, Jacques

2004-06-24

Mercury is locked into a 3/2 spin-orbit resonance where it rotates three times on its axis for every two orbits around the sun. The stability of this equilibrium state is well established, but our understanding of how this state initially arose remains unsatisfactory. Unless one uses an unrealistic tidal model with constant torques (which cannot account for the observed damping of the libration of the planet) the computed probability of capture into 3/2 resonance is very low (about 7 per cent). This led to the proposal that core-mantle friction may have increased the capture probability, but such a process requires very specific values of the core viscosity. Here we show that the chaotic evolution of Mercury's orbit can drive its eccentricity beyond 0.325 during the planet's history, which very efficiently leads to its capture into the 3/2 resonance. In our numerical integrations of 1,000 orbits of Mercury over 4 Gyr, capture into the 3/2 spin-orbit resonant state was the most probable final outcome of the planet's evolution, occurring 55.4 per cent of the time.

The 2014 Earth return of the ISEE-3/ICE spacecraft

NASA Astrophysics Data System (ADS)

Dunham, David W.; Farquhar, Robert W.; Loucks, Michel; Roberts, Craig E.; Wingo, Dennis; Cowing, Keith L.; Garcia, Leonard N.; Craychee, Tim; Nickel, Craig; Ford, Anthony; Colleluori, Marco; Folta, David C.; Giorgini, Jon D.; Nace, Edward; Spohr, John E.; Dove, William; Mogk, Nathan; Furfaro, Roberto; Martin, Warren L.

2015-05-01

In 1978, the 3rd International Sun-Earth Explorer (ISEE-3) became the first libration-point mission, about the Sun-Earth L1 point. Four years later, a complex series of lunar swingbys and small propulsive maneuvers ejected ISEE-3 from the Earth-Moon system, to fly by a comet (Giacobini-Zinner) for the first time in 1985, as the rechristened International Cometary Explorer (ICE). In its heliocentric orbit, ISEE-3/ICE slowly drifted around the Sun to return to the Earth's vicinity in 2014. Maneuvers in 1986 targeted a 2014 August 10th lunar swingby to recapture ISEE-3 into Earth orbit. In 1999, ISEE-3/ICE passed behind the Sun; after that, tracking of the spacecraft ceased and its control center at Goddard was shut down. In 2013, meetings were held to assess the viability of "re-awakening" ISEE-3. The goal was to target the 2014 lunar swingby, to recapture the spacecraft back into a halo-like Sun-Earth L1 orbit. However, special hardware for communicating with the spacecraft via NASA's Deep Space Network stations was discarded after 1999, and NASA had no funds to reconstruct the lost equipment. After ISEE-3's carrier signal was detected on March 1st with the 20 m antenna at Bochum, Germany, Skycorp, Inc. decided to initiate the ISEE-3 Reboot Project, to use software-defined radio with a less costly S-band transmitter that was purchased with a successful RocketHub crowdsourcing effort. NASA granted Skycorp permission to command the spacecraft. Commanding was successfully accomplished using the 300 m radio telescope at Arecibo. New capture trajectories were computed, including trajectories that would target the August lunar swingby and use a second ΔV (velocity change) that could target later lunar swingbys that would allow capture into almost any desired final orbit, including orbits about either the Sun-Earth L1 or L2 points, a lunar distant retrograde orbit, or targeting a flyby of the Earth-approaching active Comet Wirtanen in 2018. A tiny spinup maneuver was performed on July 2nd, the first since 1987. A 7 m/s ΔV maneuver was attempted on July 8th, to target the August lunar swingby. But the maneuver failed; telemetry showed that only about 0.15 m/s of ΔV was accomplished, then the thrust quickly decayed. The telemetry indicated that the nitrogen pressurant was gone so hydrazine could not be forced to the thrusters. The experience showed how a spacecraft can survive 30 years of space weather. The spacecraft flew 18 thousand km from the Moon, resulting in a heliocentric orbit that will return near the Earth in 2029.

Gaseous Vortices in Barred Spiral Galaxies

NASA Technical Reports Server (NTRS)

England, Martin N.; Hunter, James H., Jr.

1995-01-01

During the course of examining many two-dimensional, as well as a smaller sample of three-dimensional, models of gas flows in barred spiral galaxies, we have been impressed by the ubiquitous presence fo vortex pairs, oriented roughly perpendicular to their bars, with one vortex on each side. The vortices are obvious only when viewed in the bar frame, and the centers of their velocity fields usually are near Lagrangian points L(sub 4,5). In all models that we have studied, the vortices form on essentially the same time scale as that for the development of gaseous spiral arms, typically two bar rotations. Usually the corotation radius, r(sub c), lies slightly beyond the end of the bar. Depending upon the mass distributions of the various components, gas spirals either into, or out of, the vortices: In the former case, the vortices become regions of high density, whereas the opposite is true if the gas spirals out of a vortex. The models described in this paper have low-density vortices, as do most of the models we have studied. Moreover, usually the vortex centers lie approximately within +/- 15 deg of L(sub 4,5). In the stellar dynamic limit, when pressure and viscous forces are absent, short-period orbits exist, centered on L(sub 4,5). These orbits need not cross and therefore their morphology is that of gas streamlines, that is, vortices. We believe that the gas vortices in our models are hydrodynamic analogues of closed, short-period, libration orbits centered on L(sub 4,5).

Laser Prevention of Earth Impact Disasters

NASA Technical Reports Server (NTRS)

Campbell, J.; Smalley, L.; Boccio, D.; Howell, Joe T. (Technical Monitor)

2002-01-01

We now believe that while there are about 2000 earth orbit crossing rocks greater than 1 kilometer in diameter, there may be as many as 100,000 or more objects in the 100m size range. Can anything be done about this fundamental existence question facing us? The answer is a resounding yes! We have the technology to prevent collisions. By using an intelligent combination of Earth and space based sensors coupled with an infrastructure of high-energy laser stations and other secondary mitigation options, we can deflect inbound asteroids, meteoroids, and comets and prevent them from striking the Earth. This can be accomplished by irradiating the surface of an inbound rock with sufficiently intense pulses so that ablation occurs. This ablation acts as a small rocket incrementally changing the shape of the rock's orbit around the Sun. One-kilometer size rocks can be moved sufficiently in a month while smaller rocks may be moved in a shorter time span.We recommend that the World's space objectives be immediately reprioritized to start us moving quickly towards a multiple option defense capability. While lasers should be the primary approach, all mitigation options depend on robust early warning, detection, and tracking resources to find objects sufficiently prior to Earth orbit passage in time to allow mitigation. Infrastructure options should include ground, LEO, GEO, Lunar, and libration point laser and sensor stations for providing early warning, tracking, and deflection. Other options should include space interceptors that will carry both laser and nuclear ablators for close range work. Response options must be developed to deal with the consequences of an impact should we move too slowly.

Genealogy and stability of periodic orbit families around uniformly rotating asteroids

NASA Astrophysics Data System (ADS)

Hou, Xiyun; Xin, Xiaosheng; Feng, Jinglang

2018-03-01

Resonance orbits around a uniformly rotating asteroid are studied from the approach of periodic orbits in this work. Three periodic families (denoted as I, II, and III in the paper) are fundamental in organizing the resonance families. For the planar case: (1) Genealogy and stability of Families I, II and the prograde resonance families are studied. For extremely irregular asteroids, family genealogy close to the asteroid is greatly distorted from that of the two body-problem (2BP), indicating that it is inappropriate to treat the orbital motions as perturbed Keplerian orbits. (2) Genealogy and stability of Family III are also studied. Stability of this family may be destroyed by the secular resonance between the orbital ascending node's precession and the asteroid's rotation. For the spatial case: (1) Genealogy of the near circular three-dimensional periodic families are studied. The genealogy may be broken apart by families of eccentric frozen orbits whose argument of perigee is ;frozen; in space. (2) The joint effects between the secular resonance and the orbital resonances may cause instability to three-dimensional orbital motion with orbit inclinations close to the critical values. Applying the general methodology to a case study - the asteroid Eros and also considering higher order non-spherical terms, some extraordinary orbits are found, such as the ones with orbital plane co-rotating with the asteroid, and the stable frozen orbits with argument of perigee librating around values different from 0°, 90°, 180°, 270°.

Infrequent visitors of the Kozai kind: the dynamical lives of 2012 FC71, 2014 EK24, 2014 QD364, and 2014 UR

NASA Astrophysics Data System (ADS)

de la Fuente Marcos, C.; de la Fuente Marcos, R.

2015-08-01

Context. Asteroids with semi-major axes very close to that of a host planet can avoid node crossings when their nodal points are at perihelion and at aphelion. This layout protects the asteroids from close encounters, and eventual collisions, with the host planet. Aims: Here, we study the short-term dynamical evolution of four recently discovered near-Earth asteroids (NEAs) - 2012 FC71, 2014 EK24, 2014 QD364, and 2014 UR - that follow very Earth-like orbits. Methods: Our analysis is based on results of direct N-body calculations that use the most updated ephemerides and include perturbations from the eight major planets, the Moon, the barycentre of the Pluto-Charon system, and the three largest asteroids. Results: These four NEAs exhibit an orbital evolution unlike any other known near-Earth object (NEO). Beyond horseshoe, tadpole, or quasi-satellite trajectories, they follow co-orbital passing orbits relative to the Earth within the Kozai domain. Our calculations show that secular interactions induce librations of their relative argument of perihelion with respect to our planet but also to Venus, Mars, and Jupiter. Secular chaos is also present. The size of this transient population is probably large. Conclusions: Although some of these NEAs can remain orbitally stable for many thousands of years, their secular dynamics are substantially more complicated than commonly thought and cannot be properly described within the framework of the three-body problem alone owing to the overlapping of multiple secular resonances. Objects in this group are amongst the most atypical NEOs regarding favourable visibility windows because these are separated in time by many decades or even several centuries. Figures 2, 3, 5, 7, 9, 11, 13, 15, 17, 18, Table 2, and Appendix A are available in electronic form at http://www.aanda.org

On the dynamical structure of the Trojan group of asteroids

NASA Technical Reports Server (NTRS)

Zagretdinov, R. V.; Williams, I. P.; Yoshikawa, M.

1992-01-01

Using a semi-analytical approach, domains of possible motion for Trojan asteroids were established. It is shown that stable librating motion is possible for both high inclination and high eccentricity. Frequency distributions were also produced for real Trojan asteroids, against differing libration amplitudes and libration periods.

Capture of near-Earth objects with low-thrust propulsion and invariant manifolds

NASA Astrophysics Data System (ADS)

Tang, Gao; Jiang, Fanghua

2016-01-01

In this paper, a mission incorporating low-thrust propulsion and invariant manifolds to capture near-Earth objects (NEOs) is investigated. The initial condition has the spacecraft rendezvousing with the NEO. The mission terminates once it is inserted into a libration point orbit (LPO). The spacecraft takes advantage of stable invariant manifolds for low-energy ballistic capture. Low-thrust propulsion is employed to retrieve the joint spacecraft-asteroid system. Global optimization methods are proposed for the preliminary design. Local direct and indirect methods are applied to optimize the two-impulse transfers. Indirect methods are implemented to optimize the low-thrust trajectory and estimate the largest retrievable mass. To overcome the difficulty that arises from bang-bang control, a homotopic approach is applied to find an approximate solution. By detecting the switching moments of the bang-bang control the efficiency and accuracy of numerical integration are guaranteed. By using the homotopic approach as the initial guess the shooting function is easy to solve. The relationship between the maximum thrust and the retrieval mass is investigated. We find that both numerically and theoretically a larger thrust is preferred.

Geodesy at Mercury with MESSENGER

NASA Technical Reports Server (NTRS)

Smith, David E.; Zuber, Maria t.; Peale, Stanley J.; Phillips, Roger J.; Solomon, Sean C.

2006-01-01

In 2011 the MESSENGER (MErcury Surface, Space ENvironment, GEochemistry, and Ranging) spacecraft will enter Mercury orbit and begin the mapping phase of the mission. As part of its science objectives the MESSENGER mission will determine the shape and gravity field of Mercury. These observations will enable the topography and the crustal thickness to be derived for the planet and will determine the small libration of the planet about its axis, the latter critical to constraining the state of the core. These measurements require very precise positioning of the MESSENGER spacecraft in its eccentric orbit, which has a periapsis altitude as low as 200 km, an apoapsis altitude near 15,000 km, and a closest approach to the surface varying from latitude 60 to about 70 N. The X-band tracking of MESSENGER and the laser altimetry are the primary data that will be used to measure the planetary shape and gravity field. The laser altimeter, which has an expected range of 1000 to 1200 km, is expected to provide significant data only over the northern hemisphere because of MESSENGER's eccentric orbit. For the southern hemisphere, radio occultation measurements obtained as the spacecraft passes behind the planet as seen from Earth and images obtained with the imaging system will be used to provide the long-wavelength shape of the planet. Gravity, derived from the tracking data, will also have greater resolution in the northern hemisphere, but full global models for both topography and gravity will be obtained at low harmonic order and degree. The limiting factor for both gravity and topography is expected to be knowledge of the spacecraft location. Present estimations are that in a combined tracking, altimetry, and occultation solution the spacecraft position uncertainty is likely to be of order 10 m. This accuracy should be adequate for establishing an initial geodetic coordinate system for Mercury that will enable positioning of imaged features on the surface, determination of the planet's obliquity, and detection of the librational motion of the planet about its axis.

The Spin-Orbit Resonant Rotation of Mercury: A Two Degree of Freedom Hamiltonian Model

NASA Astrophysics Data System (ADS)

D'Hoedt, Sandrine; Lemaitre, Anne

2004-04-01

The paper develops a hamiltonian formulation describing the coupled orbital and spin motions of a rigid Mercury rotation about its axis of maximum moment of inertia in the frame of a 3:2 spin orbit resonance; the (ecliptic) obliquity is not constant, the gravitational potential of mercury is developed up to the second degree terms (the only ones for which an approximate numerical value can be given) and is reduced to a two degree of freedom model in the absence of planetary perturbations. Four equilibria can be calculated, corresponding to four different values of the (ecliptic) obliquity. The present situation of Mercury corresponds to one of them, which is proved to be stable. We introduce action-angle variables in the neighborhood of this stable equilibrium, by several successive canonical transformations, so to get two constant frequencies, the first one for the free spin-orbit libration, the other one for the 1:1 resonant precession of both nodes (orbital and rotational) on the ecliptic plane. The numerical values obtained by this simplified model are in perfect agreement with those obtained by Rambaux and Bois [Astron. Astrophys. 413, 381 393].

Chaotic dynamics outside Saturn’s main rings: The case of Atlas

NASA Astrophysics Data System (ADS)

Renner, Stéfan; Cooper, Nicholas J.; El Moutamid, Maryame; Evans, Mike W.; Murray, Carl D.; Sicardy, Bruno

2014-11-01

We revisit in detail the dynamics of Atlas. From a fit to new Cassini ISS astrometric observations spanning February 2004 to August 2013, we estimate GM_Atlas=0.384+/-0.001 x 10^(-3)km^3s^(-2), a value 13% smaller than the previously published estimate but with an order of magnitude reduction in the uncertainty. Our numerically-derived orbit shows that Atlas is currently librating in both a 54:53 corotation eccentricity resonance (CER) and a 54:53 Lindblad eccentricity resonance (LER) with Prometheus. We demonstrate that the orbit of Atlas is chaotic, with a Lyapunov time of order 10 years, as a direct consequence of the coupled resonant interaction (CER/LER) with Prometheus. The interactions between the two resonances is investigated using the CoraLin analytical model (El Moutamid et al., 2014), showing that the chaotic zone fills almost all the corotation site occupied by the satellite’s orbit. Four 70 :67 apse-type mean motion resonances with Pandora are also overlapping, but these resonances have a much weaker effect on Atlas.We estimate the capture probabilities of Atlas into resonances with Prometheus as the orbits expand through tidal effects, and discuss the implications for the orbital evolution.

Titan gravity investigation with the Oceanus mission

NASA Astrophysics Data System (ADS)

Tortora, Paolo; Zannoni, Marco; Nimmo, Francis; Mazarico, Erwan; Iess, Luciano; Sotin, Christophe; Hayes, Alexander; Malaska, Michael

2017-04-01

Oceanus is a proposed mission for NASA's New Frontiers 4 Announcement of Opportunity to study Saturn's largest moon Titan. One of the main goals of Oceanus is to examine crustal properties and determine the potential interaction of organics with the subsurface ocean, with implications for potential habitability of Titan. To this end, Oceanus could potentially characterize the thickness of the external icy shell and determine the extent of convection in the shell. The product (average ice rigidity) x (ice shell thickness) can be retrieved from the Love numbers k2 and h2, which describe Titan's gravity and shape response to Saturn's tidal field during its orbital motion around the planet, using a combined analysis of gravity and topography but also measuring Titan's physical librations from gravity data and the on-board camera surface landmarks. The gravity science experiment is crucial to accomplish the mission goals, because precise orbit determination of the spacecraft provides a direct measure of Titan's static gravitational field, the real and imaginary parts of the Love number k2, and its rotational state (obliquity and amplitude of physical librations in longitude). Moreover, a precise spacecraft orbit reconstruction throughout the entire mission is necessary to process radar altimetry data and accurately measure Titan's h2 through crossover analysis. We present the expected accuracy in the estimation of the scientific parameters of interest, obtained through numerical simulations of the orbit determination of the Oceanus spacecraft during its 2-year mission around Titan. The main observable quantities used in the analysis are two-way Doppler data obtained from the frequency shift of a highly stable microwave carrier between the spacecraft and the stations of NASA's Deep Space Network. White Gaussian noise was added to the simulated data, with a realistic standard deviation obtained from an accurate noise budget derived from the experience with Cassini Ka-band Doppler data. A covariance analysis was carried out using a multi-arc approach, comparing different observational and modeling strategies, in particular for the non-gravitational perturbations. Our results show that Oceanus will allow estimating the real and imaginary parts of Titan's k2 to an accuracy of 0.0001, the gravity field to at least degree 12 with SNR of 10, and also provide spacecraft orbit reconstruction with a radial uncertainty better than 0.5 meter during the mission.

A Dwarf Planet Class Object in the 21:5 Resonance with Neptune

NASA Astrophysics Data System (ADS)

Holman, Matthew J.; Payne, Matthew J.; Fraser, Wesley; Lacerda, Pedro; Bannister, Michele T.; Lackner, Michael; Chen, Ying-Tung; Lin, Hsing Wen; Smith, Kenneth W.; Kokotanekova, Rosita; Young, David; Chambers, K.; Chastel, S.; Denneau, L.; Fitzsimmons, A.; Flewelling, H.; Grav, Tommy; Huber, M.; Induni, Nick; Kudritzki, Rolf-Peter; Krolewski, Alex; Jedicke, R.; Kaiser, N.; Lilly, E.; Magnier, E.; Mark, Zachary; Meech, K. J.; Micheli, M.; Murray, Daniel; Parker, Alex; Protopapas, Pavlos; Ragozzine, Darin; Veres, Peter; Wainscoat, R.; Waters, C.; Weryk, R.

2018-03-01

We report the discovery of an H r = 3.4 ± 0.1 dwarf planet candidate by the Pan-STARRS Outer Solar System Survey. 2010 JO179 is red with (g ‑ r) = 0.88 ± 0.21, roughly round, and slowly rotating, with a period of 30.6 hr. Estimates of its albedo imply a diameter of 600–900 km. Observations sampling the span between 2005 and 2016 provide an exceptionally well determined orbit for 2010 JO179, with a semimajor axis of 78.307 ± 0.009 au; distant orbits known to this precision are rare. We find that 2010 JO179 librates securely within the 21:5 mean-motion resonance with Neptune on 100 Myr timescales, joining the small but growing set of known distant dwarf planets on metastable resonant orbits. These imply a substantial trans-Neptunian population that shifts between stability in high-order resonances, the detached population, and the eroding population of the scattering disk.

Symbolic computation of the Birkhoff normal form in the problem of stability of the triangular libration points

NASA Astrophysics Data System (ADS)

Shevchenko, I. I.

2008-05-01

The problem of stability of the triangular libration points in the planar circular restricted three-body problem is considered. A software package, intended for normalization of autonomous Hamiltonian systems by means of computer algebra, is designed so that normalization problems of high analytical complexity could be solved. It is used to obtain the Birkhoff normal form of the Hamiltonian in the given problem. The normalization is carried out up to the 6th order of expansion of the Hamiltonian in the coordinates and momenta. Analytical expressions for the coefficients of the normal form of the 6th order are derived. Though intermediary expressions occupy gigabytes of the computer memory, the obtained coefficients of the normal form are compact enough for presentation in typographic format. The analogue of the Deprit formula for the stability criterion is derived in the 6th order of normalization. The obtained floating-point numerical values for the normal form coefficients and the stability criterion confirm the results by Markeev (1969) and Coppola and Rand (1989), while the obtained analytical and exact numeric expressions confirm the results by Meyer and Schmidt (1986) and Schmidt (1989). The given computational problem is solved without constructing a specialized algebraic processor, i.e., the designed computer algebra package has a broad field of applicability.

Research in the Restricted Problems of Three and Four Bodies Final Scientific Report

NASA Technical Reports Server (NTRS)

Richards, Paul B.; Bernstein, Irwin S.; Chai, Winchung A.; Cronin, Jane; Ellis, Jordan; Fine, William E.; Kass, Sheldon; Musa, Samuel A.; Russell, Lawrence H.

1968-01-01

Seven studies have been conducted on research in the existence and nature of solutions of the restricted problems of three and four bodies. The details and results of five of these research investigations have already been published, and the latest two studies will be published shortly. A complete bibliography of publications is included in this report. This research has been primarily qualitative and has yielded new information on the behavior of trajectories near the libration points in the Earth-Moon-Sun and Sun-Jupiter-Saturn systems, and on the existence of periodic trajectories about the libration points of the circular and elliptical restricted four-body models. We have also implemented Birkhoff's normalization process for conservative and nonconservative Hamiltonian systems with equilibrium points. This makes available a technique for analyzing stability properties of certain nonlinear dynamical systems, and we have applied this technique to the circular and elliptical restricted three-body models. A related study was also conducted to determine the feasibility of using cislunar periodic trajectories for various space missions. Preliminary results suggest that this concept is attractive for space flight safety operations in cislunar space. Results of this research will be of interest to mathematicians, particularly those working in ordinary differential equations, dynamical systems and celestial mechanics; to astronomers; and to space guidance and mission analysts.

Variations in rotation rate and polar motion of a non-hydrostatic Titan

NASA Astrophysics Data System (ADS)

Coyette, Alexis; Baland, Rose-Marie; Van Hoolst, Tim

2018-06-01

Observation of the rotation of synchronously rotating satellites can help to probe their interior. Previous studies mostly assume that these large icy satellites are in hydrostatic equilibrium, although several measurements indicate that they deviate from such a state. Here we investigate the effect of non-hydrostatic equilibrium and of flow in the subsurface ocean on the rotation of Titan. We consider the variations in rotation rate and the polar motion due to (1) the gravitational force exerted by Saturn at orbital period and (2) exchanges of angular momentum between the seasonally varying atmosphere and the solid surface. The deviation of the mass distribution from hydrostaticity can significantly increase the diurnal libration and decrease the amplitude of the seasonal libration. The effect of the non-hydrostatic mass distribution is less important for polar motion, which is more sensitive to flow in the subsurface ocean. By including a large spectrum of atmospheric perturbations, the smaller than synchronous rotation rate measured by Cassini in the 2004-2009 period (Meriggiola et al., 2016) could be explained by the atmospheric forcing. If our interpretation is correct, we predict a larger than synchronous rotation rate in the 2009-2014 period.

Enceladus: three-act play and current state

NASA Astrophysics Data System (ADS)

Luan, J.; Goldreich, P.

2017-12-01

Eccentricity (e) growth as Enceladus migrates deeper into mean motion resonance with Dione results in increased tidal heating. As the bottom of the ice shell melts, the rate of tidal heating jumps and runaway melting ensues. At the end of run-away melting, the shell's thickness has fallen below the value at which the frequency of free libration equals the orbital mean motion and e has damped to well below its current value. Subsequently, both the shell thickness and e partake in a limit cycle. As e damps toward its minimum value, the shell's thickness asymptotically approaches its resonant value from below. After minimum e, the shell thickens quickly and e grows even faster. This cycle is likely to have been repeated multiple times in the past. Currently, e is much smaller than its equilibrium value corresponding to the shell thickness. Physical libration resonance resolves this mystery, it ensures that the low-e and medium-thickness state is present for most of the time between consecutive limit cycles. It is a robust scenario that avoids fine tuning or extreme parameter choice, and naturally produces episodic stages of high heating, consistent with softening of topographical features on Enceladus.

Interpreting the librations of a synchronous satellite - How their phase assesses Mimas' global ocean

NASA Astrophysics Data System (ADS)

Noyelles, Benoît

2017-01-01

Most of the main planetary satellites of our Solar System are expected to be in synchronous rotation, the departures from the strict synchronicity being a signature of the interior. Librations have been measured for the Moon, Phobos, and some satellites of Saturn. I here revisit the theory of the longitudinal librations in considering that part of the interior is not hydrostatic, i.e. has not been shaped by the rotational and tidal deformations, but is fossil. This consideration affects the rotational behavior. For that, I derive the tensor of inertia of the satellite in splitting these two parts, before proposing an analytical solution that I validate with numerical simulations. I apply this new theory on Mimas and Epimetheus, for which librations have been measured from Cassini data. I show that the large measured libration amplitude of these bodies can be explained by an excess of triaxiality that would not result from the hydrostatic theory. This theory cannot explain the phase shift which has been measured in the diurnal librations of Mimas. This speaks against a solid structure for Mimas, i.e. Mimas could have a global internal ocean.

Modern studies of the Lunar Physical libration at the Kazan University

NASA Astrophysics Data System (ADS)

Petrova, Natalia; Hanada, Hideo; Nefedyev, Yuri; Gusev, Alexander

Main results in investigation of the lunar physical libration in the Kazan University are presented in the report. Modern problems in the lunar spin-dynamics are considered. The accent is done on the fine phenomena of the lunar libration caused by complicated interior structure. Parameters of a free libration are discussed; geometrical interpretation of the chandler-like and free core nutation is given. Over the past 10 years a creative cooperation has been formed between scientists of the Kazan University and the National Astronomical Observatory of Japan (Mizusava). The project ILOM (In situ Lunar Orientation Measurement), planned in the frame of SELENE-2 or -3 missions is aimed at monitoring the physical libration of the Moon. The Russian side has taken over some of the theoretical tasks to ensure the planned observations. One of the important elements of the project is placing of a small optical telescope on the lunar surface with the purpose to detect the lunar physical libration with millisecond accuracy. Computer simulation of the future observations is being done with the purpose of their optimization: effective placement of measuring system on the lunar surface, testing of sensitivity of new observations to various features of the lunar interior structure. The results of the first stage of the simulation are presented in the paper. At this stage the software for the selection of stars and reduction of their coordinates onto the period of observations is developed, the tracks for the selected stars are constructed and analyzed, their sensitivity to the internal characteristics of the lunar body, in the first place, to the selenopotential coefficients, is tested. Inverse problem of lunar physical libration is formulated and solved. It is shown that selenographic coordinates of polar stars are insensitive to longitudinal librations tau(t). Comparing coordinates calculated for two models of a rigid and deformable Moon is carried out and components sensitive to Love number k _{2} are revealed. Analytical theory of physical libration was very convenient tool for modeling the upcoming observations. The main outcome of this collaboration was the understanding of the strategy and tactics of building an improved analytical theory of physical libration. This work was supported by RFBR grant No. 13-02-00792.

Design of a Lunar Farside Observatory

NASA Technical Reports Server (NTRS)

1989-01-01

The design of a mantendable lunar farside observatory and science base is presented. A farside observatory will allow high accuracy astronomical observations, as well as the opportunity to perform geological and low gravity studies on the Moon. The requirements of the observatory and its support facilities are determined, and a preliminary timeline for the project development is presented. The primary areas of investigation include observatory equipment, communications, habitation, and surface operations. Each area was investigated to determine the available options, and each option was evaluated to determine the advantages and disadvantages. The options selected for incorporation into the design of the farside base are presented. The observatory equipment deemed most suitable for placement on the lunar farside consist of large optical and radio arrays and seismic equipment. A communications system consisting of a temporary satellite about the L sub 2 libration point and followed by a satellite at the stable L sub 5 libration point was selected. A space station common module was found to be the most practical option for housing the astronauts at the base. Finally, a support system based upon robotic construction vehicles and the use of lunar materials was determined to be a necessary component of the base.

Far-infrared VRT spectroscopy of the water dimer: Characterization of the 20 μm out-of-plane librational vibration.

PubMed

Cole, William T S; Fellers, Ray S; Viant, Mark R; Leforestier, Claude; Saykally, Richard J

2015-10-21

We report the first high-resolution spectra for the out-of-plane librational vibration in the water dimer. Three vibrational subbands comprising a total of 188 transitions have been measured by diode laser spectroscopy near 500 cm(-1) and assigned to (H2O)2 libration-rotation-tunneling eigenstates. The band origin for the Ka = 1 subband is ~524 cm(-1). Librational excitation increases the interchange and bifurcation hydrogen bond rearrangement tunneling splittings by factors of 3-5 and 4-40, respectively. Analysis of the rotational constants obtained from a nonlinear least squares fit indicates that additional external perturbations to the energy levels are likely.

Far-infrared VRT spectroscopy of the water dimer: Characterization of the 20 μm out-of-plane librational vibration

NASA Astrophysics Data System (ADS)

Cole, William T. S.; Fellers, Ray S.; Viant, Mark R.; Leforestier, Claude; Saykally, Richard J.

2015-10-01

We report the first high-resolution spectra for the out-of-plane librational vibration in the water dimer. Three vibrational subbands comprising a total of 188 transitions have been measured by diode laser spectroscopy near 500 cm-1 and assigned to (H2O)2 libration-rotation-tunneling eigenstates. The band origin for the Ka = 1 subband is ˜524 cm-1. Librational excitation increases the interchange and bifurcation hydrogen bond rearrangement tunneling splittings by factors of 3-5 and 4-40, respectively. Analysis of the rotational constants obtained from a nonlinear least squares fit indicates that additional external perturbations to the energy levels are likely.

Librations and tides of icy satellites: model comparison for Enceladus

NASA Astrophysics Data System (ADS)

Trinh, A.; Van Hoolst, T.; Baland, R. M.; Beuthe, M.; Rivoldini, A.; Dehant, V. M. A.

2015-12-01

The latest measurements of the librations of Enceladus suggest that it could have a global subsurface ocean or a non-hydrostatic core (Thomas et al. 2014). Further observations should constrain the properties of the ice shell, and similar insights are expected from future investigation of Europa and Ganymede.Detailed models of the librations and tides are therefore required to properly interpret these measurements in terms of interior structure. Here we compare the `classical', separate tide and libration models (where spherical symmetry is assumed to compute the tides, Van Hoolst et al. 2013) with our combined tide+libration model (Trinh et al. 2013), both extended to account for non-hydrostatic structure.Even with a global ocean, different mechanisms act to prevent Enceladus's shell from moving independently from the rest. Among those, pressure coupling across the flattened boundaries of the ocean requires special care if the shape is not fully relaxed. We discuss how it should be modelled in the classical approach to be consistent with the combined model.

Simulating parameters of lunar physical libration on the basis of its analytical theory

NASA Astrophysics Data System (ADS)

Petrova, N.; Zagidullin, A.; Nefediev, Yu.

2014-04-01

Results of simulating behavior of lunar physical libration parameters are presented. Some features in the speed change of impulse variables are revealed: fast periodic changes in р2 and long periodic changes in р3. A problem of searching for a dynamic explanation of this phenomenon is put. The simulation was performed on the basis of the analytical libration theory [1] in the programming environment VBA.

Experimental study of inertial waves in a spherical shell induced by librations of the inner sphere

NASA Astrophysics Data System (ADS)

Hoff, Michael; Harlander, Uwe; Jahangir, Saad; Egbers, Christoph

2015-04-01

Many planetary bodies do not rotate with a constant velocity but undergo rotations with superposed oscillations called longitudinal librations. This is the case e.g. for the Earth's moon, Mars' moon, Mercury and many other moons of Jupiter and Saturn and some of them have a solid inner core and a molten outer core. It is worth to know the interaction between the libration of the core and the interior of the fluid to understand tidal heating, fluid mixing, and the generation of magnetic fields. Here we present an experimental investigation of inertial waves in a spherical shell. The shell rotates with a mean angular velocity Ω around its vertical axis overlaid by a time periodic oscillation of the inner sphere in the range 0 < ω < 2Ω, in order to excite inertial waves with a known frequency. We want to show the influence of the libration amplitude ɛ on different libration frequencies ω and how efficient libration is, to excite inertial waves in the given frequency range. For low ω and high ɛ instability starts to grow and, beside the excited inertial waves, several low frequency structures can be found. Quantitative PIV analyses of the horizontal plane in the co-rotation frame show clear spiral structures with different wave numbers for high libration amplitudes due to strong shear, similar to differential rotation. Another question, we like to address, is whether high libration amplitudes can also excite very low frequency Rossby wave structures? If the frequency increases, it can be seen from Poincaré plots that large attractor windows for inertial waves appear. We want to show PIV analyses for such flows dominated by wave attractors. It is known that for large excitation frequencies subharmonic parametric instability starts to grow and triads will be excited. Our experimental data show hints for the existence of triads and preliminary results will be discussed.

Far-infrared VRT spectroscopy of the water dimer: Characterization of the 20 μm out-of-plane librational vibration

DOE Office of Scientific and Technical Information (OSTI.GOV)

Cole, William T. S.; Fellers, Ray S.; Viant, Mark R.

We report the first high-resolution spectra for the out-of-plane librational vibration in the water dimer. Three vibrational subbands comprising a total of 188 transitions have been measured by diode laser spectroscopy near 500 cm{sup −1} and assigned to (H{sub 2}O){sub 2} libration-rotation-tunneling eigenstates. The band origin for the K{sub a} = 1 subband is ~524 cm{sup −1}. Librational excitation increases the interchange and bifurcation hydrogen bond rearrangement tunneling splittings by factors of 3-5 and 4-40, respectively. Analysis of the rotational constants obtained from a nonlinear least squares fit indicates that additional external perturbations to the energy levels are likely.

Dynamical Analysis of the Circumprimary Planet in the Eccentric Binary System HD 59686

NASA Astrophysics Data System (ADS)

Trifonov, Trifon; Lee, Man Hoi; Reffert, Sabine; Quirrenbach, Andreas

2018-04-01

We present a detailed orbital and stability analysis of the HD 59686 binary-star planet system. HD 59686 is a single-lined, moderately close (a B = 13.6 au) eccentric (e B = 0.73) binary, where the primary is an evolved K giant with mass M = 1.9 M ⊙ and the secondary is a star with a minimum mass of m B = 0.53 M ⊙. Additionally, on the basis of precise radial velocity (RV) data, a Jovian planet with a minimum mass of m p = 7 M Jup, orbiting the primary on a nearly circular S-type orbit with e p = 0.05 and a p = 1.09 au, has recently been announced. We investigate large sets of orbital fits consistent with HD 59686's RV data by applying bootstrap and systematic grid search techniques coupled with self-consistent dynamical fitting. We perform long-term dynamical integrations of these fits to constrain the permitted orbital configurations. We find that if the binary and the planet in this system have prograde and aligned coplanar orbits, there are narrow regions of stable orbital solutions locked in a secular apsidal alignment with the angle between the periapses, Δω, librating about 0°. We also test a large number of mutually inclined dynamical models in an attempt to constrain the three-dimensional orbital architecture. We find that for nearly coplanar and retrograde orbits with mutual inclination 145° ≲ Δi ≤ 180°, the system is fully stable for a large range of orbital solutions.

Resolving Nonadiabatic Dynamics of Hydrated Electrons Using Ultrafast Photoemission Anisotropy.

PubMed

Karashima, Shutaro; Yamamoto, Yo-Ichi; Suzuki, Toshinori

2016-04-01

We have studied ultrafast nonadiabatic dynamics of excess electrons trapped in the band gap of liquid water using time- and angle-resolved photoemission spectroscopy. Anisotropic photoemission from the first excited state was discovered, which enabled unambiguous identification of nonadiabatic transition to the ground state in 60 fs in H_{2}O and 100 fs in D_{2}O. The photoelectron kinetic energy distribution exhibited a rapid spectral shift in ca. 20 fs, which is ascribed to the librational response of a hydration shell to electronic excitation. Photoemission anisotropy indicates that the electron orbital in the excited state is depolarized in less than 40 fs.

Climates of Oblique Exoplanets

NASA Astrophysics Data System (ADS)

Dobrovolskis, A. R.

2008-12-01

A previous paper (Dobrovolskis 2007; Icarus 192, 1-23) showed that eccentricity can have profound effects on the climate, habitability, and detectability of extrasolar planets. This complementary study shows that obliquity can have comparable effects. The known exoplanets exhibit a wide range of orbital eccentricities, but those within several million km of their suns are generally in near-circular orbits. This fact is widely attributed to the dissipation of tides in the planets, which is particularly effective for solid/liquid bodies like "Super-Earths". Along with friction between a solid mantle and a liquid core, tides also are expected to despin a planet until it is captured in the synchronous resonance, so that its rotation period is identical to its orbital period. The canonical example of synchronous spin is the way that our Moon always keeps nearly the same hemisphere facing the Earth. Tides also tend to reduce the planet's obliquity (the angle between its spin and orbital angular velocities). However, orbit precession can cause the rotation to become locked in a "Cassini state", where it retains a nearly constant non-zero obliquity. For example, our Moon maintains an obliquity of about 6.7° with respect to its orbit about the Earth. For comparison, stable Cassini states can exist for practically any obliquity up to 180° for planets of binary stars, or in multi-planet systems with high mutual inclinations, such as are produced by scattering or by the Kozai mechanism. This work considers planets in synchronous rotation with circular orbits. For obliquities greater than 90°, the ground track of the sub-solar point wraps around all longitudes on the surface of such a planet. For smaller obliquities, the sub-solar track takes the figure-8 shape of an analemma. This can be visualized as the intersection of the planet's spherical surface with a right circular cylinder, parallel to the spin axis and tangent to the equator from the inside. The excursion of the sub-solar point in latitude is equal to the obliquity β, while the corresponding libration in longitude is smaller (±arcsin(tan2(β/2))). Obliquity thus affects the distribution of insolation over the planet's surface, particularly near its poles. For β = 0, one hemisphere bakes in permanent sunshine, while the opposite hemisphere experiences eternal darkness. As β increases, the region of permanent daylight and the antipodal realm of endless night both shrink, while a more temperate area of alternating day and night spreads in longitude, and especially in latitude. The regions of permanent day or night disappear at β = 90°. The insolation regime passes through several more transitions as β continues to increase toward 180°, but the surface distribution of insolation remains non-uniform in both latitude and longitude.

Tidal deformation, Orbital Dynamics and JIMO

NASA Astrophysics Data System (ADS)

Ratcliff, J. T.; Wu, X.; Williams, J. G.

2003-12-01

Observations of Europa, Ganymede and Callisto obtained from encounters by the Galileo spacecraft strongly suggest the possibility of liquid oceans under the icy shells of these Jovian satellites. The strong tidal environments in which these moons are found and the fact that a planetary body with internal fluid undergoes greater deformation than an otherwise solid body make a compelling case for using tidal observations as a method for ocean detection. Given the high degree of uncertainty in our knowledge of the interiors of these moons, a comprehensive geodetic program measuring different physical signatures related to tidal deformation and interior structure is preferred to using separate and various interior parameters that may not be as closely tied to actual measurable quantities. Potential and displacement tidal Love numbers, libration amplitudes of the surface ice shell and rocky mantle, static topography and gravity fields and other quantities should all be included in the measurement objectives. Many geodetic techniques rely heavily upon orbital positions of the spacecraft. Their accurate determination depend on factors such as the orbital configuration, the gravity fields of the icy moons, as well as the duration and geometry of tracking. Given the competing science, engineering and planetary protection demands, orbital accuracy subject to constraints has become a critical mission design issue. Orbit determination simulations and covariance analyses will be used to investigate the achievable accuracies of spacecraft position and geodetic signatures under different orbital and tracking scenarios.

Infrastructure for large space telescopes

NASA Astrophysics Data System (ADS)

MacEwen, Howard A.; Lillie, Charles F.

2016-10-01

It is generally recognized (e.g., in the National Aeronautics and Space Administration response to recent congressional appropriations) that future space observatories must be serviceable, even if they are orbiting in deep space (e.g., around the Sun-Earth libration point, SEL2). On the basis of this legislation, we believe that budgetary considerations throughout the foreseeable future will require that large, long-lived astrophysics missions must be designed as evolvable semipermanent observatories that will be serviced using an operational, in-space infrastructure. We believe that the development of this infrastructure will include the design and development of a small to mid-sized servicing vehicle (MiniServ) as a key element of an affordable infrastructure for in-space assembly and servicing of future space vehicles. This can be accomplished by the adaptation of technology developed over the past half-century into a vehicle approximately the size of the ascent stage of the Apollo Lunar Module to provide some of the servicing capabilities that will be needed by very large telescopes located in deep space in the near future (2020s and 2030s). We specifically address the need for a detailed study of these servicing requirements and the current proposals for using presently available technologies to provide the appropriate infrastructure.

Navigation Concepts for the James Webb Space Telescope

NASA Technical Reports Server (NTRS)

Long, Anne; Leung, Dominic; Kelbel, David; Beckman, Mark; Grambling, Cheryl

2003-01-01

This paper evaluates the performance that can be achieved using candidate ground and onboard navigation approaches for operation of the James Webb Space Telescope, which will be in an orbit about the Sun-Earth L2 libration point. The ground navigation approach processes standard range and Doppler measurements from the Deep Space Network The onboard navigation approach processes celestial object measurements and/or ground-to- spacecraft Doppler measurements to autonomously estimate the spacecraft s position and velocity and Doppler reference frequency. Particular attention is given to assessing the absolute position and velocity accuracy that can be achieved in the presence of the frequent spacecraft reorientations and momentum unloads planned for this mission. The ground navigation approach provides stable navigation solutions using a tracking schedule of one 30-minute contact per day. The onboard navigation approach that uses only optical quality celestial object measurements provides stable autonomous navigation solutions. This study indicates that unmodeled changes in the solar radiation pressure cross-sectional area and modeled momentum unload velocity changes are the major error sources. These errors can be mitigated by modeling these changes, by estimating corrections to compensate for the changes, or by including acceleration measurements.

The lunar libration: comparisons between various models - a model fitted to LLR observations

NASA Astrophysics Data System (ADS)

Chapront, J.; Francou, G.

2005-09-01

We consider 4 libration models: 3 numerical models built by JPL (ephemerides for the libration in DE245, DE403 and DE405) and an analytical model improved with numerical complements fitted to recent LLR observations. The analytical solution uses 3 angular variables (ρ1, ρ2, τ) which represent the deviations with respect to Cassini's laws. After having referred the models to a unique reference frame, we study the differences between the models which depend on gravitational and tidal parameters of the Moon, as well as amplitudes and frequencies of the free librations. It appears that the differences vary widely depending of the above quantities. They correspond to a few meters displacement on the lunar surface, reminding that LLR distances are precise to the centimeter level. Taking advantage of the lunar libration theory built by Moons (1984) and improved by Chapront et al. (1999) we are able to establish 4 solutions and to represent their differences by Fourier series after a numerical substitution of the gravitational constants and free libration parameters. The results are confirmed by frequency analyses performed separately. Using DE245 as a basic reference ephemeris, we approximate the differences between the analytical and numerical models with Poisson series. The analytical solution - improved with numerical complements under the form of Poisson series - is valid over several centuries with an internal precision better than 5 centimeters.

Inertial Waves and Steady Flows in a Liquid Filled Librating Cylinder

NASA Astrophysics Data System (ADS)

Subbotin, Stanislav; Dyakova, Veronika

2018-05-01

The fluid flow in a non-uniformly rotating (librating) cylinder about a horizontal axis is experimentally studied. In the absence of librations the fluid performs a solid-body rotation together with the cavity. Librations lead to the appearance of steady zonal flow in the whole cylinder and the intensive steady toroidal flows near the cavity corners. If the frequency of librations is twice lower than the mean rotation rate the inertial waves are excited. The oscillating motion associated with the propagation of inertial wave in the fluid bulk leads to the appearance of an additional steady flow in the Stokes boundary layers on the cavity side wall. In this case the heavy particles of the visualizer are assembled on the side wall into ring structures. The patterns are determined by the structure of steady flow, which in turn depends on the number of reflections of inertial wave beams from the cavity side wall. For some frequencies, inertial waves experience spatial resonance, resulting in inertial modes, which are eigenmodes of the cavity geometry. The resonance of the inertial modes modifies the steady flow structure close to the boundary layer that is manifested in the direct rebuilding of patterns. It is shown that the intensity of zonal flow, as well as the intensity of steady flows excited by inertial waves, is proportional to the square of the amplitude of librations.

Low-temperature matrix effects on orientational motion of Methyl radical trapped in gas solids: Angular tunneling vs. libration

NASA Astrophysics Data System (ADS)

Dmitriev, Yurij A.; Zelenetckii, Ilia A.; Benetis, Nikolas P.

2018-05-01

EPR investigation of the lineshape of matrix -isolated methyl radical, CH3, spectra recorded in solid N2O and CO2 was carried out. Reversible temperature-dependent line width anisotropy was observed in both matrices. This effect is a fingerprint of the extra-slow radical rotation about the in-plane C2 axes. The rotation was found to be anisotropic and closely correlated to the orientational dynamics of the matrix molecules. It was suggested that a recently discovered "hoping precession" effect of matrix molecules in solid CO2 is a common feature of matrices of the linear molecules CO, N2O, and CO2. A new low-temperature matrix effect, referred to as "libration trap", was proposed which accounts for the changing CH3 reorientational motion about the radical C3-axis from rotation to libration. Temperature dependence of the intensity of the EPR satellites produced by these nonrotating-but librating methyls was presented. This allowed for a rough estimation of the rotation hindering potential due to correlation mismatch between the radical and the nearest matrix molecules' librations.

FSD- FLEXIBLE SPACECRAFT DYNAMICS

NASA Technical Reports Server (NTRS)

Fedor, J. V.

1994-01-01

The Flexible Spacecraft Dynamics and Control program (FSD) was developed to aid in the simulation of a large class of flexible and rigid spacecraft. FSD is extremely versatile and can be used in attitude dynamics and control analysis as well as in-orbit support of deployment and control of spacecraft. FSD has been used to analyze the in-orbit attitude performance and antenna deployment of the RAE and IMP class satellites, and the HAWKEYE, SCATHA, EXOS-B, and Dynamics Explorer flight programs. FSD is applicable to inertially-oriented spinning, earth oriented, or gravity gradient stabilized spacecraft. The spacecraft flexibility is treated in a continuous manner (instead of finite element) by employing a series of shape functions for the flexible elements. Torsion, bending, and three flexible modes can be simulated for every flexible element. FSD can handle up to ten tubular elements in an arbitrary orientation. FSD is appropriate for studies involving the active control of pointed instruments, with options for digital PID (proportional, integral, derivative) error feedback controllers and control actuators such as thrusters and momentum wheels. The input to FSD is in four parts: 1) Orbit Construction FSD calculates a Keplerian orbit with environmental effects such as drag, magnetic torque, solar pressure, thermal effects, and thruster adjustments; or the user can supply a GTDS format orbit tape for a particular satellite/time-span; 2) Control words - for options such as gravity gradient effects, control torques, and integration ranges; 3) Mathematical descriptions of spacecraft, appendages, and control systems- including element geometry, properties, attitudes, libration damping, tip mass inertia, thermal expansion, magnetic tracking, and gimbal simulation options; and 4) Desired state variables to output, i.e., geometries, bending moments, fast Fourier transform plots, gimbal rotation, filter vectors, etc. All FSD input is of free format, namelist construction. FSD is written in FORTRAN 77, PASCAL, and MACRO assembler for batch execution and has been implemented on a DEC VAX series computer operating under VMS. The PASCAL and MACRO routines (in addition to the FORTRAN program) are supplied as both source and object code, so the PASCAL compiler is not required for implementation. This program was last updated in 1985.

Strike-Slip Fault Patterns on Europa: Obliquity or Polar Wander?

NASA Technical Reports Server (NTRS)

Rhoden, Alyssa Rose; Hurford, Terry A.; Manga, Michael

2011-01-01

Variations in diurnal tidal stress due to Europa's eccentric orbit have been considered as the driver of strike-slip motion along pre-existing faults, but obliquity and physical libration have not been taken into account. The first objective of this work is to examine the effects of obliquity on the predicted global pattern of fault slip directions based on a tidal-tectonic formation model. Our second objective is to test the hypothesis that incorporating obliquity can reconcile theory and observations without requiring polar wander, which was previously invoked to explain the mismatch found between the slip directions of 192 faults on Europa and the global pattern predicted using the eccentricity-only model. We compute predictions for individual, observed faults at their current latitude, longitude, and azimuth with four different tidal models: eccentricity only, eccentricity plus obliquity, eccentricity plus physical libration, and a combination of all three effects. We then determine whether longitude migration, presumably due to non-synchronous rotation, is indicated in observed faults by repeating the comparisons with and without obliquity, this time also allowing longitude translation. We find that a tidal model including an obliquity of 1.2?, along with longitude migration, can predict the slip directions of all observed features in the survey. However, all but four faults can be fit with only 1? of obliquity so the value we find may represent the maximum departure from a lower time-averaged obliquity value. Adding physical libration to the obliquity model improves the accuracy of predictions at the current locations of the faults, but fails to predict the slip directions of six faults and requires additional degrees of freedom. The obliquity model with longitude migration is therefore our preferred model. Although the polar wander interpretation cannot be ruled out from these results alone, the obliquity model accounts for all observations with a value consistent with theoretical expectations and cycloid modeling.

Applying Strategic Visualization(Registered Trademark) to Lunar and Planetary Mission Design

NASA Technical Reports Server (NTRS)

Frassanito, John R.; Cooke, D. R.

2002-01-01

NASA teams, such as the NASA Exploration Team (NEXT), utilize advanced computational visualization processes to develop mission designs and architectures for lunar and planetary missions. One such process, Strategic Visualization (trademark), is a tool used extensively to help mission designers visualize various design alternatives and present them to other participants of their team. The participants, which may include NASA, industry, and the academic community, are distributed within a virtual network. Consequently, computer animation and other digital techniques provide an efficient means to communicate top-level technical information among team members. Today,Strategic Visualization(trademark) is used extensively both in the mission design process within the technical community, and to communicate the value of space exploration to the general public. Movies and digital images have been generated and shown on nationally broadcast television and the Internet, as well as in magazines and digital media. In our presentation will show excerpts of a computer-generated animation depicting the reference Earth/Moon L1 Libration Point Gateway architecture. The Gateway serves as a staging corridor for human expeditions to the lunar poles and other surface locations. Also shown are crew transfer systems and current reference lunar excursion vehicles as well as the Human and robotic construction of an inflatable telescope array for deployment to the Sun/Earth Libration Point.

The Euclid AOCS science mode design

NASA Astrophysics Data System (ADS)

Bacchetta, A.; Saponara, M.; Torasso, A.; Saavedra Criado, G.; Girouart, B.

2015-06-01

Euclid is a Medium-Class mission of the ESA Cosmic Vision 2015-2025 plan. Thales Alenia Space Italy has been selected as prime contractor for the Euclid design and implementation. The spacecraft will be launched in 2020 on a Soyuz launch vehicle from Kourou, to a large-amplitude orbit around the sun-earth libration point L2. The objective of Euclid is to understand the origin of the Universe's accelerating expansion, by mapping large-scale structure over a cosmic time covering the last 10 billion years. The mission requires the ability to survey a large fraction of the extragalactic sky (i.e. portion of sky with latitude higher than 30 deg with respect to galactic plane) over its lifetime, with very high system stability (telescope, focal plane, spacecraft pointing) to minimize systematic effects. The AOCS is a key element to meet the scientific requirements. The AOCS design drivers are pointing performance and image quality (Relative Pointing Error over 700 s less than 25 m as, 68 % confidence level), and minimization of slew time between observation fields to meet the goal of completing the Wide Extragalactic Survey in 6 years. The first driver demands a Fine Guidance Sensor in the telescope focal plane for accurate attitude measurement and actuators with low noise and fine command resolution. The second driver requires high-torque actuators and an extended attitude control bandwidth. In the design, reaction wheels (RWL) and cold-gas micro-propulsion (MPS) are used in a synergetic and complementary way during different operational phases of the science mode. The RWL are used for performing the field slews, whereas during scientific observation they are stopped not to perturb the pointing by additional mechanical noise. The MPS is used for maintaining the reference attitude with high pointing accuracy during the scientific observation. This unconventional concept achieves the pointing performance with the shortest maneuver times, with significant mass savings with respect to the MPS-only solution.

Hydrogen bond breaking dynamics in the water pentamer: Terahertz VRT spectroscopy of a 20 μm libration

NASA Astrophysics Data System (ADS)

Cole, William T. S.; Fellers, Raymond S.; Viant, Mark R.; Saykally, Richard J.

2017-01-01

Hydrogen bonds in solid and liquid water are formed and broken via librational vibrations, hence characterizing the details of these motions is vital to understanding these important dynamics. Here we report the measurement and assignment of 875 transitions comprising 6 subbands originating from out-of-plane librational transitions of the water pentamer-d10 near 512 cm-1. The precisely measured (ca. 1 ppm) transitions reveal bifurcation splittings of ˜1884 MHz, a ˜4000× enhancement over ground state splittings and 100× greater than predicted by theory. The pentamer is thus the third water cluster to display greatly enhanced bifurcation tunneling upon single quantum excitation of librational vibrations. From the intensity pattern of the observed transitions, the mechanism of bifurcation is established by comparison with theoretical predictions.

Hydrogen bond breaking dynamics in the water pentamer: Terahertz VRT spectroscopy of a 20 μm libration.

PubMed

Cole, William T S; Fellers, Raymond S; Viant, Mark R; Saykally, Richard J

2017-01-07

Hydrogen bonds in solid and liquid water are formed and broken via librational vibrations, hence characterizing the details of these motions is vital to understanding these important dynamics. Here we report the measurement and assignment of 875 transitions comprising 6 subbands originating from out-of-plane librational transitions of the water pentamer-d 10 near 512 cm -1 . The precisely measured (ca. 1 ppm) transitions reveal bifurcation splittings of ∼1884 MHz, a ∼4000× enhancement over ground state splittings and 100× greater than predicted by theory. The pentamer is thus the third water cluster to display greatly enhanced bifurcation tunneling upon single quantum excitation of librational vibrations. From the intensity pattern of the observed transitions, the mechanism of bifurcation is established by comparison with theoretical predictions.

On the intermolecular vibrational coupling, hydrogen bonding, and librational freedom of water in the hydration shell of mono- and bivalent anions.

PubMed

Ahmed, Mohammed; Namboodiri, V; Singh, Ajay K; Mondal, Jahur A

2014-10-28

The hydration energy of an ion largely resides within the first few layers of water molecules in its hydration shell. Hence, it is important to understand the transformation of water properties, such as hydrogen-bonding, intermolecular vibrational coupling, and librational freedom in the hydration shell of ions. We investigated these properties in the hydration shell of mono- (Cl(-) and I(-)) and bivalent (SO4(2-) and CO3(2-)) anions by using Raman multivariate curve resolution (Raman-MCR) spectroscopy in the OH stretch, HOH bend, and [bend+librational] combination bands of water. Raman-MCR of aqueous Na-salt (NaCl, NaI, Na2SO4, and Na2CO3) solutions provides ion-correlated spectra (IC-spectrum) which predominantly bear the vibrational characteristics of water in the hydration shell of respective anions. Comparison of these IC-spectra with the Raman spectrum of bulk water in different spectral regions reveals that the water is vibrationally decoupled with its neighbors in the hydration shell. Hydrogen-bond strength and librational freedom also vary with the nature of anion: hydrogen-bond strength, for example, decreases as CO3(2-) > SO4(2-) > bulk water ≈ Cl(-) > I(-); and the librational freedom increases as CO3(2-) ≈ SO4(2-) < bulk water < Cl(-) < I(-). It is believed that these structural perturbations influence the dynamics of coherent energy transfer and librational reorientation of water in the hydration shell of anions.

Libration-driven flows in ellipsoidal shells

NASA Astrophysics Data System (ADS)

Lemasquerier, D.; Grannan, A. M.; Vidal, J.; Cébron, D.; Favier, B.; Le Bars, M.; Aurnou, J. M.

2017-09-01

Planets and satellites can undergo physical librations, which consist of forced periodic variations in their rotation rate induced by gravitational interactions with nearby bodies. This mechanical forcing may drive turbulence in interior fluid layers such as subsurface oceans and metallic liquid cores through a libration-driven elliptical instability (LDEI) that refers to the resonance of two inertial modes with the libration-induced base flow. LDEI has been studied in the case of a full ellipsoid. Here we address for the first time the question of the persistence of LDEI in the more geophysically relevant ellipsoidal shell geometries. In the experimental setup, an ellipsoidal container with spherical inner cores of different sizes is filled with water. Direct side view flow visualizations are made in the librating frame using Kalliroscope particles. A Fourier analysis of the light intensity fluctuations extracted from recorded movies shows that the presence of an inner core leads to spatial heterogeneities but does not prevent LDEI. Particle image velocimetry and direct numerical simulations are performed on selected cases to confirm our results. Additionally, our survey at a fixed forcing frequency and variable rotation period (i.e., variable Ekman number, E) shows that the libration amplitude at the instability threshold varies as ˜E0.65. This scaling is explained by a competition between surface and bulk dissipation. When extrapolating to planetary interior conditions, this leads to the E1/2 scaling commonly considered. We argue that Enceladus' subsurface ocean and the core of the exoplanet 55 CnC e should both be unstable to LDEI.

Statistical and dynamical remastering of classic exoplanet systems

NASA Astrophysics Data System (ADS)

Nelson, Benjamin Earl

The most powerful constraints on planet formation will come from characterizing the dynamical state of complex multi-planet systems. Unfortunately, with that complexity comes a number of factors that make analyzing these systems a computationally challenging endeavor: the sheer number of model parameters, a wonky shaped posterior distribution, and hundreds to thousands of time series measurements. In this dissertation, I will review our efforts to improve the statistical analyses of radial velocity (RV) data and their applications to some renown, dynamically complex exoplanet system. In the first project (Chapters 2 and 4), we develop a differential evolution Markov chain Monte Carlo (RUN DMC) algorithm to tackle the aforementioned difficult aspects of data analysis. We test the robustness of the algorithm in regards to the number of modeled planets (model dimensionality) and increasing dynamical strength. We apply RUN DMC to a couple classic multi-planet systems and one highly debated system from radial velocity surveys. In the second project (Chapter 5), we analyze RV data of 55 Cancri, a wide binary system known to harbor five planetary orbiting the primary. We find the inner-most planet "e" must be coplanar to within 40 degrees of the outer planets, otherwise Kozai-like perturbations will cause the planet to enter the stellar photosphere through its periastron passage. We find the orbits of planets "b" and "c" are apsidally aligned and librating with low to median amplitude (50+/-6 10 degrees), but they are not orbiting in a mean-motion resonance. In the third project (Chapters 3, 4, 6), we analyze RV data of Gliese 876, a four planet system with three participating in a multi-body resonance, i.e. a Laplace resonance. From a combined observational and statistical analysis computing Bayes factors, we find a four-planet model is favored over one with three-planets. Conditioned on this preferred model, we meaningfully constrain the three-dimensional orbital architecture of all the planets orbiting Gliese 876 based on the radial velocity data alone. By demanding orbital stability, we find the resonant planets have low mutual inclinations phi so they must be roughly coplanar (phicb = 1.41(+/-0.62/0.57) degrees and phibe = 3.87(+/-1.99/1.86 degrees). The three-dimensional Laplace argument librates chaotically with an amplitude of 50.5(+/-7.9/10.0) degrees, indicating significant past disk migration and ensuring long-term stability. In the final project (Chapter 7), we analyze the RV data for nu Octantis, a closely separated binary with an alleged planet orbiting interior and retrograde to the binary. Preliminary results place very tight constraints on the planet-binary mutual inclination but no model is dynamically stable beyond 105 years. These empirically derived models motivate the need for more sophisticated algorithms to analyze exoplanet data and will provide new challenges for planet formation models.

High-Power Krypton Hall Thruster Technology Being Developed for Nuclear-Powered Applications

NASA Technical Reports Server (NTRS)

Jacobson, David T.; Manzella, David H.

2004-01-01

The NASA Glenn Research Center has been performing research and development of moderate specific impulse, xenon-fueled, high-power Hall thrusters for potential solar electric propulsion applications. These applications include Mars missions, reusable tugs for low-Earth-orbit to geosynchronous-Earth-orbit transportation, and missions that require transportation to libration points. This research and development effort resulted in the design and fabrication of the NASA-457M Hall thruster that has been tested at input powers up to 95 kW. During project year 2003, NASA established Project Prometheus to develop technology in the areas of nuclear power and propulsion, which are enabling for deep-space science missions. One of the Project-Prometheus-sponsored Nuclear Propulsion Research tasks is to investigate alternate propellants for high-power Hall thruster electric propulsion. The motivation for alternate propellants includes the disadvantageous cost and availability of xenon propellant for extremely large scale, xenon-fueled propulsion systems and the potential system performance benefits of using alternate propellants. The alternate propellant krypton was investigated because of its low cost relative to xenon. Krypton propellant also has potential performance benefits for deep-space missions because the theoretical specific impulse for a given voltage is 20 percent higher than for xenon because of krypton's lower molecular weight. During project year 2003, the performance of the high-power NASA-457M Hall thruster was measured using krypton as the propellant at power levels ranging from 6.4 to 72.5 kW. The thrust produced ranged from 0.3 to 2.5 N at a discharge specific impulse up to 4500 sec.

Prospects For Earth-Based Measurements Of Europa's Librations

NASA Astrophysics Data System (ADS)

Margot, Jean-Luc; Campbell, D. B.; Peale, S. J.

2010-10-01

The exploration of Europa is of great interest because it may be hospitable to certain life forms [1]. Several lines of evidence suggest that a subsurface ocean exists beneath an icy shell [2,3], but there is debate about the thickness of the shell [4], which impacts Europa's astrobiological potential. As in the case of Mercury, it may be possible to determine whether an outer shell is decoupled from the interior and to evaluate the shell thickness by measuring the amplitude of forced longitude librations [5,6]. In the simplest configuration of a rigid shell decoupled from a spherically symmetric interior, the libration amplitude is amplified from the nominal value of 18" by C/Cs, where C is the polar moment of inertia of the body and Cs is that of the outer shell that participates in the librations. For a 100-km thick shell, the libration amplitude would reach 200", an estimate that remains valid even in the presence of gravitational coupling between asymmetrical layers [7]. If there are significant departures from rigid behavior, the shell may deform with the ocean underneath and exhibit a libration amplitude of 52" [8]. Europa reaches closest approach in October 2011, offering a once-in-a-decade opportunity to measure spin rate variations by tracking radar speckles, as advocated by Holin [9,10]. Librations of a rigid shell thinner than 100 km would be detectable. We will describe the experimental design and expected sensitivity. References: [1] NRC, Europa Science Strategy, 1999. [2,3] Kivelson et al, Greeley et al, in Jupiter, CUP, 2004. [4] Greenberg, Unmasking Europa, Praxis, 2008. [5] Peale, Nature 262, 1976. [6] Margot et al, Science 316, 2007. [7] van Hoolst et al, Icarus 195, 2008. [8] Goldreich and Mitchell, Icarus, in press. [9] Green, in Radar Astronomy, McGraw-Hill, 1968. [10] Holin, Radiophys. Quant. Elec. 31, 1988.

Far-infrared laser vibration-rotation-tunneling spectroscopy of water clusters in the librational band region of liquid water

NASA Astrophysics Data System (ADS)

Keutsch, Frank N.; Fellers, Ray S.; Viant, Mark R.; Saykally, Richard J.

2001-03-01

We report the first high resolution spectrum of a librational vibration for a water cluster. Four parallel bands of (H2O)3 were measured between 510 and 525 cm-1 using diode laser vibration-rotation-tunneling (VRT) spectroscopy. The bands lie in the "librational band" region of liquid water and are assigned to the nondegenerate out of plane librational vibration. The observation of at least three distinct bands within 8 cm-1 originating in the vibrational ground state is explained by a dramatically increased splitting of the rovibrational levels relative to the ground state by bifurcation tunneling and is indicative of a greatly reduced barrier height in the excited state. This tunneling motion is of special significance, as it is the lowest energy pathway for breaking and reforming of hydrogen bonds, a salient aspect of liquid water dynamics.

LONG-LIVED CHAOTIC ORBITAL EVOLUTION OF EXOPLANETS IN MEAN MOTION RESONANCES WITH MUTUAL INCLINATIONS

DOE Office of Scientific and Technical Information (OSTI.GOV)

Barnes, Rory; Deitrick, Russell; Quinn, Thomas R.

2015-03-10

We present N-body simulations of resonant planets with inclined orbits that show chaotically evolving eccentricities and inclinations that can persist for at least 10 Gyr. A wide range of behavior is possible, from fast, low amplitude variations to systems in which eccentricities reach 0.9999 and inclinations 179.°9. While the orbital elements evolve chaotically, at least one resonant argument always librates. We show that the HD 73526, HD 45364, and HD 60532 systems may be in chaotically evolving resonances. Chaotic evolution is apparent in the 2:1, 3:1, and 3:2 resonances, and for planetary masses from lunar- to Jupiter-mass. In some cases, orbital disruption occurs aftermore » several gigayears, implying the mechanism is not rigorously stable, just long-lived relative to the main sequence lifetimes of solar-type stars. Planet-planet scattering appears to yield planets in inclined resonances that evolve chaotically in about 0.5% of cases. These results suggest that (1) approximate methods for identifying unstable orbital architectures may have limited applicability, (2) the observed close-in exoplanets may be produced during epochs of high eccentricit induced by inclined resonances, (3) those exoplanets' orbital planes may be misaligned with the host star's spin axis, (4) systems with resonances may be systematically younger than those without, (5) the distribution of period ratios of adjacent planets detected via transit may be skewed due to inclined resonances, and (6) potentially habitable planets may have dramatically different climatic evolution than Earth. The Gaia spacecraft is capable of discovering giant planets in these types of orbits.« less

Asteroid 2014 OL339: yet another Earth quasi-satellite

NASA Astrophysics Data System (ADS)

de la Fuente Marcos, C.; de la Fuente Marcos, R.

2014-12-01

Our planet has one permanently bound satellite - the Moon - a likely large number of mini-moons or transient irregular natural satellites, and three temporary natural retrograde satellites or quasi-satellites. These quasi-moons - (164207) 2004 GU9, (277810) 2006 FV35 and 2013 LX28 - are unbound companions to the Earth. The orbital evolution of quasi-satellites may transform them into temporarily bound satellites of our planet. Here, we study the dynamical evolution of the recently discovered Aten asteroid 2014 OL339 to show that it is currently following a quasi-satellite orbit with respect to the Earth. This episode started at least about 775 yr ago and it will end 165 yr from now. The orbit of this object is quite chaotic and together with 164207 are the most unstable of the known Earth quasi-satellites. This group of minor bodies is, dynamically speaking, very heterogeneous but three of them exhibit Kozai-like dynamics: the argument of perihelion of 164207 oscillates around -90°, the one of 277810 librates around 180° and that of 2013 LX28 remains around 0°. Asteroid 2014 OL339 is not currently engaged in any Kozai-like dynamics.

The dynamics of the outer edge of Saturn's A ring disturbed by Janus-Epimetheus

NASA Astrophysics Data System (ADS)

Renner, Stéfan; Santos Araujo, Nilton Carlos; Cooper, Nicholas; El Moutamid, Maryame; Murray, Carl; Sicardy, Bruno

2016-10-01

We developed an analytical model to study the dynamics of the outer edge of Saturn's A ring. The latter is influenced by 7:6 mean motion resonances with Janus and Epimetheus. Because of the horseshoe motion of the two co-orbital moons, the location of the resonances shift inwards or outwards every four years, making the ring edge particles alternately trapped in a corotation eccentricity resonance (CER) or a Lindblad eccentricity resonance (LER). However, the oscillation periods of the resonances are longer than the four-year interval between the switches in the orbits of Janus and Epimetheus.Averaged equations of motion are used, and our model is numerically integrated to describe the effects of the periodic sweeping of the 7:6 CER and LER over the ring edge region.We show that four radial zones (ranges 136715-136723, 136738-136749, 136756-136768, 136783-136791 km) are chaotic on decadal timescales, within which particle semimajor axes have periodic changes due to partial libration motions around the CER fixed points. After a few decades, the maximum variation of semimajor axis is about eleven (resp. three) kilometers in the case of the CER with Janus (resp. Epimetheus).Similarly, particle eccentricities have partial oscillations forced by the LERs every four years, and are in good agreement with the observed eccentricities (Spitale and Porco 2009, El Moutamid et al. 2015). For initially circular orbits, the maximum eccentricity reached (~0.001) corresponds to the value obtained from the classical theory of resonance (proportional to the cube root of the satellite-to-planet mass ratio).We notice that the fitted semimajor axes for the object recently discovered at the ring edge (Murray et al. 2014) are just outside the chaotic zone of radial range 136756-136768 km.We compare our results to Cassini observations, and discuss how the periodic LER/CER perturbations by Janus/Epimetheus may help to aggregate ring edge particles into clumps, as seen in high-resolution images.

Skylab

NASA Image and Video Library

1973-01-01

This chart describes the Skylab student experiment Libration Clouds, proposed by Alison Hopfield of Princeton, New Jersey. This experiment utilized Skylab's astronomical telescopes to observe the two zero-force regions (Lagrangian points) within the Earth-Moon System in which small space particles were expected to accumulate. In March 1972, NASA and the National Science Teachers Association selected 25 experiment proposals for flight on Skylab. Science advisors from the Marshall Space Flight Center aided and assisted the students in developing the proposals for flight on Skylab.

Relative Navigation of Formation Flying Satellites

NASA Technical Reports Server (NTRS)

Long, Anne; Kelbel, David; Lee, Taesul; Leung, Dominic; Carpenter, Russell; Gramling, Cheryl; Bauer, Frank (Technical Monitor)

2002-01-01

The Guidance, Navigation, and Control Center (GNCC) at Goddard Space Flight Center (GSFC) has successfully developed high-accuracy autonomous satellite navigation systems using the National Aeronautics and Space Administration's (NASA's) space and ground communications systems and the Global Positioning System (GPS). In addition, an autonomous navigation system that uses celestial object sensor measurements is currently under development and has been successfully tested using real Sun and Earth horizon measurements.The GNCC has developed advanced spacecraft systems that provide autonomous navigation and control of formation flyers in near-Earth, high-Earth, and libration point orbits. To support this effort, the GNCC is assessing the relative navigation accuracy achievable for proposed formations using GPS, intersatellite crosslink, ground-to-satellite Doppler, and celestial object sensor measurements. This paper evaluates the performance of these relative navigation approaches for three proposed missions with two or more vehicles maintaining relatively tight formations. High-fidelity simulations were performed to quantify the absolute and relative navigation accuracy as a function of navigation algorithm and measurement type. Realistically-simulated measurements were processed using the extended Kalman filter implemented in the GPS Enhanced Inboard Navigation System (GEONS) flight software developed by GSFC GNCC. Solutions obtained by simultaneously estimating all satellites in the formation were compared with the results obtained using a simpler approach based on differencing independently estimated state vectors.

Dynamics and control of orbiting flexible systems: A formulation with applications

NASA Astrophysics Data System (ADS)

Ng, Chun-Ki Alfred

1992-06-01

A relatively general formulation for studying the nonlinear dynamics and control of spacecraft with interconnected flexible members in a tree-type topology is developed. The distinctive features of the formulation include the following: (1) It is applicable to a large class of present and future spacecraft with flexible beam and plate type appendages, arbitrary in number and orientation. (2) The members are free to undergo predefined slewing maneuvers to facilitate modelling of sun tracking solar panels and large angle maneuvers of space based robots. (3) Solar radiation induced thermal deformations of flexible members are incorporated in the study. (4) The governing equations of motion are highly nonlinear, nonautonomous and coupled. They are programmed in a modular fashion to help isolate the effects of flexibility, librational motion, thermal deformations, slewing maneuvers, shifting center of mass, higher modes, initial conditions, etc. The first chapter of the thesis presents a general background to the subject and a brief review of the relevant literature on multibody dynamics. This is followed by the kinematics and kinetics of the problem leading to the Lagrangian equations of motion. The third chapter focuses on methodology and development of the computer code suitable for parametric dynamical study and control. Next versatility of the general formulation is illustrated through the analysis of five spacecraft configurations of contemporary interest the next generation of multi-purpose communications spacecraft represented by the INdian SATellite II (IN-SAT II): the First Element Launch (FEL) and the Permanently Manned Configuration (PMC) of the proposed Space Station Freedom; the Mobile Servicing System (MSS) to be developed by Canada for operation on the Space Station; and the Space Flyer Unit (SFU) to be launched by Japan in mid-nineties. In the FEL study, the attention is directed towards interactions between the librational and vibrational dynamics. During the PMC investigation, effects of the thermal deformation and orbital eccentricity are introduced and the microgravity environment around the station center of mass explored. The MSS study assesses pointing errors arising from inplane and out-of-plane maneuvers of the robotic arms. The SFU represents a challenging configuration to assess deployment and retrieval dynamics associated with a solar array. Parameters considered here include symmetry, orientation, and duration of the deployment/retrieval maneuvers. Results of the dynamical study clearly shows that, under critical combinations of parameters, the systems can become unstable. Obviously, the next logical step is to explore control strategies to restore equilibrium. To that end, feasibility of the nonlinear control based on the Feedback Linearization Technique (FLT) is explored with reference to the INSAT II and the MSS. Results show the procedure to be quite promising in controlling the INSAT II over a range of disturbances, including the thermal effects. Application of the control to the MSS reduced the pointing error induced by robotic arm maneuvers significantly. The amount of information obtained through a planned parametric analysis of the system dynamics and control is indeed enormous.

Dynamical and Physical Properties of 65803 Didymos, the Proposed AIDA Mission Target

NASA Astrophysics Data System (ADS)

Richardson, Derek C.; Barnouin, Olivier S.; Benner, Lance A. M.; Bottke, William; Campo Bagatin, Adriano; Cheng, Andrew F.; Eggl, Siegfried; Hamilton, Douglas P.; Hestroffer, Daniel; Hirabayashi, Masatoshi; Maurel, Clara; McMahon, Jay W.; Michel, Patrick; Murdoch, Naomi; Naidu, Shantanu P.; Pravec, Petr; Rivkin, Andrew S.; Rosenblatt, Pascal; Sarid, Gal; Scheeres, Daniel J.; Scheirich, Peter; Tsiganis, Kleomenis; Zhang, Yun; AIDA Dynamical and Physical Properties of Didymos Working Group

2016-10-01

Binary near-Earth asteroid (NEA) 65803 Didymos is the proposed Asteroid Impact & Deflection Assessment (AIDA) mission target, combining an orbiter [1] and a kinetic impactor for a planned encounter in fall 2022 [2]. The Dynamical and Physical Properties of Didymos Working Group supports this mission by addressing questions related to understanding the dynamical state of the system and inferring physical properties. Didymos is an Apollo-class NEA that likely reached its current orbit by exiting the inner main belt near or within the nu-6 resonance (> 82% chance) [3]. Remote observations [4] show Didymos is spectroscopically most consistent with ordinary chondrites. The diameters of the binary components are measured to be about 780 and 160 m [5]. A model of the short-term binary dynamics suggests possible librations of the secondary with up to ~10-deg amplitude, depending on its axial ratio. However, an equilibrium orbital and rotational solution is consistent with a libration amplitude of only ~1 deg. The primary, with an estimated 2.1 g/cc bulk density (uncertainty 30%) has a possibly super-critical rotation period of 2.26 h that may imply a cohesive strength of several tens of Pa. At this rate, perturbed regolith material may go through take-off/landing cycles and cause loss of fines due to solar radiation pressure. Based on a continuum analysis [6], the internal structure would likely fail before the equatorial region. A discrete analysis [7,8] shows that a minimum of 2.5 g/cc bulk density is needed for the structure to hold without cohesion. The system may be subject to weak thermal radiation forces (BYORP) with a period drift of no greater than 1 s/yr [9]. Experiments using the ISAE-SUPAERO drop tower [10] are underway to model the possible deployment of a lander on the secondary. References: [1] Michel et al. 2016, ASR 57, 2529; [2] Cheng et al. 2016, P&SS 127, 27; [3] Granvik et al. 2015, DPS 47, 214.07; [4] Dunn et al. 2013, LPSC 44, 1719; [5] Osip et al. 2016, this meeting; [6] Hirabayashi & Scheeres 2015, IAU 29, 2256185; [7] Barnouin et al. 2015, DPS 47, 402.09; [8] Zhang et al. 2016, this meeting; [9] McMahon et al. 2016, LPSC 47, 1903; [10] Sunday et al. 2016, Rev. Sci. Instr., accepted.

Enceladus's ice shell thickness and ocean depth from gravity, topography, and libration measurements

NASA Astrophysics Data System (ADS)

Trinh, A.; Rivoldini, A.; Beuthe, M.; Rekier, J.; Baland, R. M.; Van Hoolst, T.

2017-12-01

One of Cassini's major achievements is the discovery of a global ocean a few kilometres beneath Enceladus's south polar terrain. Here we infer the thickness of Enceladus's ice shell and ocean from Cassini's observations using our latest models of isostatic compensation, shell libration, and ocean dynamics.

The origin and evolution of a differentiated Mimas

NASA Astrophysics Data System (ADS)

Neveu, M.; Rhoden, A. R.

2017-11-01

In stark contrast with its neighbor moon Enceladus, Mimas is surprisingly geologically quiet, despite an eccentric orbit and distance to Saturn prone to levels of tidal dissipation 30 times higher. While Mimas' lack of geological activity could be due to a stiff, frigid interior, libration data acquired using the Cassini spacecraft suggest that its interior is not homogeneous. Here, we present one-dimensional models of the thermal, structural, and orbital evolution of Mimas under two accretion scenarios: primordial, undifferentiated formation in the Saturnian sub-nebula, and late, layered formation from a debris ring created by the disruption of one or more previous moons. We find it difficult to reproduce a differentiated, eccentric Mimas under a primordial accretion scenario: either Mimas never differentiates, or the internal warming that leads to differentiation increases tidal dissipation, yielding runaway heating that produces a persistent ocean, thereby circularizing Mimas' orbit. Only if Mimas accretes very early (so that the decay of short-lived radionuclides initiates differentiation) but its rheology is not highly dissipative (in order to stop runaway tidal heating even if the eccentricity is not negligible) can the simulations match the observational constraints. Alternatively, a late, layered accretion scenario yields a present-day Mimas that matches observational constraints, independently of the magnitude of tidal dissipation. Consistent with previous findings, these models do not produce an ocean on Enceladus unless its orbital eccentricity is higher than today's value.

Deformation of the Galactic Centre stellar cusp due to the gravity of a growing gas disc

NASA Astrophysics Data System (ADS)

Kaur, Karamveer; Sridhar, S.

2018-06-01

The nuclear star cluster surrounding the massive black hole at the Galactic Centre consists of young and old stars, with most of the stellar mass in an extended, cuspy distribution of old stars. The compact cluster of young stars was probably born in situ in a massive accretion disc around the black hole. We investigate the effect of the growing gravity of the disc on the orbits of the old stars, using an integrable model of the deformation of a spherical star cluster with anisotropic velocity dispersions. A formula for the perturbed phase-space distribution function is derived using linear theory, and new density and surface density profiles are computed. The cusp undergoes a spheroidal deformation with the flattening increasing strongly at smaller distances from the black hole; the intrinsic axis ratio ˜0.8 at ˜0.15 pc. Stellar orbits are deformed such that they spend more time near the disc plane and sample the dense inner parts of the disc; this could result in enhanced stripping of the envelopes of red giant stars. Linear theory accounts only for orbits whose apsides circulate. The non-linear theory of adiabatic capture into resonance is needed to understand orbits whose apsides librate. The mechanism is a generic dynamical process, and it may be common in galactic nuclei.

Dynamical spreading of small bodies in 1:1 resonance with planets by the diurnal Yarkovsky effect

NASA Astrophysics Data System (ADS)

Wang, Xuefeng; Hou, Xiyun

2017-10-01

A simple model is introduced to describe the inherent dynamics of Trojans in the presence of the diurnal Yarkovsky effect. For different spin statuses, the orbital elements of the Trojans (mainly semimajor axis, eccentricity and inclination) undergo different variations. The variation rate is generally very small, but the total variation of the semimajor axis or the orbit eccentricity over the age of the Solar system may be large enough to send small Trojans out of the regular region (or, vice versa, to capture small bodies in the regular region). In order to demonstrate the analytical analysis, we first carry out numerical simulations in a simple model, and then generalize these to two 'real' systems, namely the Sun-Jupiter system and the Sun-Earth system. In the Sun-Jupiter system, where the motion of Trojans is regular, the Yarkovsky effect gradually alters the libration width or the orbit eccentricity, forcing the Trojan to move from regular regionsto chaotic regions, where chaos may eventually cause it to escape. In the Sun-Earth system, where the motion of Trojans is generally chaotic, our limited numerical simulations indicate that the Yarkovsky effect is negligible for Trojans of 100 m in size, and even for larger ones. The Yarkovsky effect on small bodies captured in other 1:1 resonance orbits is also briefly discussed.

The Role of Cis-Lunar Space in Future Global Space Exploration

NASA Technical Reports Server (NTRS)

Bobskill, Marianne R.; Lupisella, Mark L.

2012-01-01

Cis-lunar space offers affordable near-term opportunities to help pave the way for future global human exploration of deep space, acting as a bridge between present missions and future deep space missions. While missions in cis-lunar space have value unto themselves, they can also play an important role in enabling and reducing risk for future human missions to the Moon, Near-Earth Asteroids (NEAs), Mars, and other deep space destinations. The Cis-Lunar Destination Team of NASA's Human Spaceflight Architecture Team (HAT) has been analyzing cis-lunar destination activities and developing notional missions (or "destination Design Reference Missions" [DRMs]) for cis-lunar locations to inform roadmap and architecture development, transportation and destination elements definition, operations, and strategic knowledge gaps. The cis-lunar domain is defined as that area of deep space under the gravitational influence of the earth-moon system. This includes a set of earth-centered orbital locations in low earth orbit (LEO), geosynchronous earth orbit (GEO), highly elliptical and high earth orbits (HEO), earth-moon libration or "Lagrange" points (E-ML1 through E-ML5, and in particular, E-ML1 and E-ML2), and low lunar orbit (LLO). To help explore this large possibility space, we developed a set of high level cis-lunar mission concepts in the form of a large mission tree, defined primarily by mission duration, pre-deployment, type of mission, and location. The mission tree has provided an overall analytical context and has helped in developing more detailed design reference missions that are then intended to inform capabilities, operations, and architectures. With the mission tree as context, we will describe two destination DRMs to LEO and GEO, based on present human space exploration architectural considerations, as well as our recent work on defining mission activities that could be conducted with an EML1 or EML2 facility, the latter of which will be an emphasis of this paper, motivated in part by recent interest expressed at the Global Exploration Roadmap Stakeholder meeting. This paper will also explore the links between this HAT Cis-Lunar Destination Team analysis and the recently released ISECG Global Exploration Roadmap and other potential international considerations, such as preventing harmful interference to radio astronomy observations in the shielded zone of the moon.

Pendulum motions of extended lunar space elevator

NASA Astrophysics Data System (ADS)

Burov, A. A.; Kosenko, I. I.

2014-09-01

In the usual everyday life, it is well known that the inverted pendulum is unstable and is ready to fall to "all four sides," to the left and to the right, forward and backward. The theoretical studies and the lunar experience of moon robots and astronauts also confirms this property. The question arises: Is this property preserved if the pendulum is "very, very long"? It turns out that the answer is negative; namely, if the pendulum length significantly exceeds the Moon radius, then the radial equilibria at which the pendulum is located along the straight line connecting the Earth and Moon centers are Lyapunov stable and the pendulum does not fall in any direction at all. Moreover, if the pendulum goes beyond the collinear libration points, then it can be extended and manufactured from cables. This property was noted by F. A. Tsander and underlies the so-called lunar space elevator (e.g., see [1]). In the plane of the Earth and Moon orbits, there are some other equilibria which turn out to be unstable. The question is, Are there equilibria at which the pendulum is located outside the orbital plane? In this paper, we show that the answer is positive, but such equilibria are unstable in the secular sense. We also study necessary conditions for the stability of lunar pendulum oscillations in the plane of the lunar orbit. It was numerically discovered that stable and unstable equilibria alternate depending on the oscillation amplitude and the angular velocity of rotation. The study of the lunar elevator dynamics originates in [2]. The concept of lunar elevator was developed in detail in [3, 4]. Several classes of equilibria with the finiteness of the Moon size taken into account were studied in [5]. The possibility of location of an orbital station fixed to the Moon surface by a pair of tethers was investigated in [6]. The problem of orientation of the terminal station of the lunar space elevator was studied in [7]. The influence of the tether length variations on the motion of the lunar tether system was considered in [8]. The alternation of stable and unstable flat oscillations is well known in the problem of satellite oscillations in a circular orbit [9, 10].

Development of Euler's ideas at the Moscow State Regional University

NASA Astrophysics Data System (ADS)

Vysikaylo, P. I.; Belyaev, V. V.

2018-03-01

In honor of the 250th anniversary of Euler's discovery of three libration points in Russia in 1767 in the area of two rotating gravitational attractors in 2017 an International Interdisciplinary Conference “Euler Readings MRSU 2017” was held in Moscow Region State University (MRSU). The Conference demonstrated that the Euler's ideas continue to remain relevant at the present time. This paper summarizes the main achievements on the basis of Leonard Euler's ideas presented at the Conference.

Resonant Capture and Tidal Evolution in Circumbinary Systems: Testing the Case of Kepler-38

NASA Astrophysics Data System (ADS)

Zoppetti, F. A.; Beaugé, C.; Leiva, A. M.

2018-04-01

Circumbinary planets are thought to form far from the central binary and migrate inwards by interactions with the circumbinary disk, ultimately stopping near their present location either by a planetary trap near the disk inner edge or by resonance capture. Here, we analyze the second possibility, presenting a detailed numerical study on the capture process, resonant dynamics and tidal evolution of circumbinary planets in high-order mean-motion resonances (MMRs). Planetary migration was modeled as an external acceleration in an N-body code, while tidal effects were incorporated with a weak-friction equilibrium tide model. As a working example we chose Kepler-38, a highly evolved system with a planet in the vicinity of the 5/1 MMR. Our simulations show that resonance capture is a high-probability event under a large range of system parameters, although several different resonant configuration are possible. We identified three possible outcomes: aligned librations, anti-aligned librations and chaotic solutions. All were found to be dynamically stable, even after the dissipation of the disk, for time-spans of the order of the system's age. We found that while tidal evolution decreases the binary's separation, the semimajor axis of the planet is driven outwards. Although the net effect is a secular increase in the mean-motion ratio, the system requires a planetary tidal parameter of the order of unity to reproduce the observed orbital configuration. The results presented here open an interesting outlook into the complex dynamics of high-order resonances in circumbinary systems.

Resonant capture and tidal evolution in circumbinary systems: testing the case of Kepler-38

NASA Astrophysics Data System (ADS)

Zoppetti, F. A.; Beaugé, C.; Leiva, A. M.

2018-07-01

Circumbinary planets are thought to form far from the central binary and migrate inwards by interactions with the circumbinary disc, ultimately stopping near their present location either by a planetary trap near the disc inner edge or by resonance capture. Here, we analyse the second possibility, presenting a detailed numerical study on the capture process, resonant dynamics, and tidal evolution of circumbinary planets in high-order mean-motion resonances (MMRs). Planetary migration was modelled as an external acceleration in an N-body code, while tidal effects were incorporated with a weak-friction equilibrium tide model. As a working example, we chose Kepler-38, a highly evolved system with a planet in the vicinity of the 5/1 MMR. Our simulations show that resonance capture is a high-probability event under a large range of system parameters, although several different resonant configuration are possible. We identified three possible outcomes: aligned librations, anti-aligned librations, and chaotic solutions. All were found to be dynamically stable, even after the dissipation of the disc, for time spans of the order of the system's age. We found that while tidal evolution decreases the binary's separation, the semimajor axis of the planet is driven outwards. Although the net effect is a secular increase in the mean-motion ratio, the system requires a planetary tidal parameter of the order of unity to reproduce the observed orbital configuration. The results presented here open an interesting outlook into the complex dynamics of high-order resonances in circumbinary systems.

Entropically Stabilized Colloidal Crystals Hold Entropy in Collective Modes

NASA Astrophysics Data System (ADS)

Antonaglia, James; van Anders, Greg; Glotzer, Sharon

Ordered structures can be stabilized by entropy if the system has more ordered microstates available than disordered ones. However, ``locating'' the entropy in an ordered system is challenging because entropic ordering is necessarily a collective effort emerging from the interactions of large numbers of particles. Yet, we can characterize these crystals using simple traditional tools, because entropically stabilized crystals exhibit collective motion and effective stiffness. For a two-dimensional system of hard hexagons, we calculate the dispersion relations of both vibrational and librational collective modes. We find the librational mode is gapped, and the gap provides an emergent, macroscopic, and density-dependent length scale. We quantify the entropic contribution of each collective mode and find that below this length scale, the dominant entropic contributions are librational, and above this length scale, vibrations dominate. This length scale diverges in the high-density limit, so entropy is found predominantly in libration near dense packing. National Science Foundation Graduate Research Fellowship Program Grant No. DGE 1256260, Advanced Research Computing at the University of Michigan, Ann Arbor, and the Simons Foundation.

DOE Office of Scientific and Technical Information (OSTI.GOV)

Caldecott, Ralph; Kamarulzaman, Dayangku N. S.; Kirrane, James P.

The concept of momentum exchange when applied to space tethers for propulsion is well established, and a considerable body of literature now exists on the on-orbit modelling, the dynamics, and also the control of a large range of tether system applications. The authors consider here a new application for the Motorised Momentum Exchange Tether by highlighting three key stages of development leading to a conceptualisation that can subsequently be developed into a technology for Active Debris Removal. The paper starts with a study of the on-orbit mechanics of a full sized motorised tether in which it is shown that amore » laden and therefore highly massasymmetrical tether can still be forced to spin, and certainly to librate, thereby confirming its possible usefulness for active debris removal (ADR). The second part of the paper concentrates on the modelling of the centripetal deployment of a symmetrical MMET in order to get it initialized for debris removal operations, and the third and final part of the paper provides an entry into scale modelling for low cost mission design and testing. It is shown that the motorised momentum exchange tether offers a potential solution to the removal of large pieces of orbital debris, and that dynamic methodologies can be implemented to in order to optimise the emergent design.« less

Rotational properties of planetary satellites

NASA Technical Reports Server (NTRS)

Peale, S. J.

1991-01-01

Properties of satellite rotation that are observable in principle, include the rotation period, the orientation of the spin axis relative to the orbit plane, precession of the spin axis due to gravitational torques, nonprincipal axis rotation or wobble, and deviations from uniform principle axis rotation or libration. Considerable order is observed in current satellite rotation states, and it is of interest to ascertain how this order came about and why some satellites do not conform to the dominant norm. There is a strong coupling between the spin and orbital motions that is primarily responsible for maintaining the ordered rotation states in most cases, but this coupling is equally responsible for destroying any chance of orderly rotation for Saturn's satellite Hyperion. Understanding the processes which constrain current rotation states as well as those of an evolutionary nature which could have brought the individual satellites to their observed rotation and orbit states allows us to sometimes infer interior properties of some satellite or even of its primary planet, although, attempts to deduce primordial rotation states are usually frustrated. The observed rotational properties of the planetary satellites are summarized, and the understanding of the processes maintaining and those leading to the observed states are outlined. Some of the inferences that can be drawn about intrinsic properties of the bodies themselves are indicated.

The long-term evolution of known resonant trans-Neptunian objects

NASA Astrophysics Data System (ADS)

Saillenfest, M.; Lari, G.

2017-07-01

Aims: Numerous trans-Neptunian objects are known to be in mean-motion resonance with Neptune. We aim to describe their long-term orbital evolution (both past and future) by means of a one-degree-of-freedom secular model. In this paper, we focus only on objects with a semi-major axis larger than 50 astronomical units (au). Methods: For each resonant object considered, a 500 000-year numerical integration is performed. The output is digitally filtered to get the parameters of the resonant secular model. Their long-term (Giga-year) orbital evolution is then represented by the level curves of the secular Hamiltonian. Results: For the majority of objects considered, the mean-motion resonance has little impact on the long-term trajectories (the secular dynamics is similar to a non-resonant one). However, a subset of objects is strongly affected by the resonance, producing moderately-high-amplitude oscillations of the perihelion distance and/or libration of the argument of perihelion around a fixed centre. Moreover, the high perihelion distance of the object 2015 FJ345 is plainly explained by long-term resonant dynamics, allowing us to also deduce its orbital elements at the time of capture in resonance (at least 15 million years ago). The same type of past evolution is expected for 2014 FZ71.

The mechanics of motorised momentum exchange tethers when applied to active debris removal from LEO

NASA Astrophysics Data System (ADS)

Caldecott, Ralph; Kamarulzaman, Dayangku N. S.; Kirrane, James P.; Cartmell, Matthew P.; Ganilova, Olga A.

2014-12-01

The concept of momentum exchange when applied to space tethers for propulsion is well established, and a considerable body of literature now exists on the on-orbit modelling, the dynamics, and also the control of a large range of tether system applications. The authors consider here a new application for the Motorised Momentum Exchange Tether by highlighting three key stages of development leading to a conceptualisation that can subsequently be developed into a technology for Active Debris Removal. The paper starts with a study of the on-orbit mechanics of a full sized motorised tether in which it is shown that a laden and therefore highly massasymmetrical tether can still be forced to spin, and certainly to librate, thereby confirming its possible usefulness for active debris removal (ADR). The second part of the paper concentrates on the modelling of the centripetal deployment of a symmetrical MMET in order to get it initialized for debris removal operations, and the third and final part of the paper provides an entry into scale modelling for low cost mission design and testing. It is shown that the motorised momentum exchange tether offers a potential solution to the removal of large pieces of orbital debris, and that dynamic methodologies can be implemented to in order to optimise the emergent design.

The Lunar Space Tug: A sustainable bridge between low Earth orbits and the Cislunar Habitat

NASA Astrophysics Data System (ADS)

Mammarella, M.; Paissoni, C. A.; Viola, N.; Denaro, A.; Gargioli, E.; Massobrio, F.

2017-09-01

The International Space Station is the first space human outpost and over the last 15 years, it has represented a peculiar environment where science, technology and human innovation converge together in a unique microgravity and space research laboratory. With the International Space Station entering the second part of its life and its operations running steadily at nominal pace, the global space community is starting planning how the human exploration could move further, beyond Low-Earth-Orbit. According to the Global Exploration Roadmap, the Moon represents the next feasible path-way for advances in human exploration towards the nal goal, Mars. Based on the experience of the ISS, one of the most widespread ideas is to develop a Cislunar Station in preparation of long duration missions in a deep space environment. Cislunar space is de ned as the area of deep space under the influence of Earth-Moon system, including a set of special orbits, e.g. Earth-Moon Libration points and Lunar Retrograde Orbit. This habitat represents a suitable environment for demonstrating and testing technologies and capabilities in deep space. In order to achieve this goal, there are several crucial systems and technologies, in particular related to transportation and launch systems. The Orion Multi-Purpose Crew Vehicle is a reusable transportation capsule designed to provide crew transportation in deep space missions, whereas NASA is developing the Space Launch System, the most powerful rocket ever built, which could provide the necessary heavy-lift launch capability to support the same kind of missions. These innovations would allow quite-fast transfers from Earth to the Cislunar Station and vice versa, both for manned and unmanned missions. However, taking into account the whole Concept of Operations for both the growth and sustainability of the Cislunar Space Station, the Lunar Space Tug can be considered as an additional, new and fundamental element for the mission architecture. The Lunar Space Tug represents an alternative to the SLS scenario, especially for what concerns all unmanned or logistic missions (e.g. cargo transfer, on orbit assembly, samples return), from Low Earth Orbit to Cislunar space. The paper focuses on the mission analysis and conceptual design of the Lunar Space Tug to support the growth and sustainment of the Cislunar Station. Particular attention is dedicated to the analysis of the propulsion subsystem effects of the Lunar Space Tug design. Main results are presented and discussed, and main conclusions are drawn.

LLR data analysis and impact on lunar dynamics from recent developments at OCA LLR Station

NASA Astrophysics Data System (ADS)

Viswanathan, Vishnu; Fienga, Agnes; Courde, Clement; Torre, Jean-Marie; Exertier, Pierre; Samain, Etienne; Feraudy, Dominique; Albanese, Dominique; Aimar, Mourad; Mariey, Hervé; Viot, Hervé; Martinot-Lagarde, Gregoire

2016-04-01

Since late 2014, OCA LLR station has been able to range with infrared wavelength (1064nm). IR ranging provides both temporal and spatial improvement in the LLR observations. IR detection also permits in densification of normal points, including the L1 and L2 retroreflectors due to better signal to noise ratio. This contributes to a better modelisation of the lunar libration. The hypothesis of lunar dust and environmental effects due to the chromatic behavior noticed on returns from L2 retroreflector is discussed. In addition, data analysis shows that the effect of retroreflector tilt and the use of calibration profile for the normal point deduction algorithm, contributes to improving the precision of normal points, thereby impacting lunar dynamical models and inner physics.

Stability and periodicity in the Sitnikov three-body problem when primaries are oblate spheroids

NASA Astrophysics Data System (ADS)

Rahman, M. A.; Garain, D. N.; Hassan, M. R.

2015-05-01

This paper deals with the effect of oblateness of the primaries of equal masses on the series solutions of the Sitnikov problem of three bodies. Effects of oblateness have also been shown on the stability of libration points and Poincare surface of section. Here series solutions have been developed with the help of iteration process of Green's function and by the Lindstedt-Poincare method. Following Murray and Dermott (Solar System Dynamics, Cambridge University Press, Cambridge, 1999) we have checked the stability of the equilibrium points in the Sitnikov problem. Periodicity and quasi-periodicity have been examined by drawing the Poincare surfaces of section using the mathematical software.

On-orbit radiometric calibration over time and between spacecraft using the moon

USGS Publications Warehouse

Kieffer, H.H.; Stone, T.C.; Barnes, R.A.; Bender, S.; Eplee, R.E.; Mendenhall, J.; Ong, L.; ,

2002-01-01

The Robotic Lunar Observatory (ROLO) project has developed a spectral irradiance model of the Moon that accounts for variations with lunar phase through the bright half of a month, lunar librations, and the location of an Earth-orbiting spacecraft. The methodology of comparing spacecraft observations of the Moon with this model has been developed to a set of standardized procedures so that comparisons can be readily made. In the cases where observations extend over several years (e.g., SeaWiFS), instrument response degradation has been determined with precision of about 0.1% per year. Because of the strong dependence of lunar irradiance on geometric angles, observations by two spacecraft cannot be directly compared unless acquired at the same time and location. Rather, the lunar irradiance based on each spacecraft instrument calibration can be compared with the lunar irradiance model. Even single observations by an instrument allow inter-comparison of its radiometric scale with other instruments participating in the lunar calibration program. Observations by SeaWiFS, ALI, Hyperion and MTI are compared here.

Terahertz VRT spectroscopy of the water hexamer-d12 prism: Dramatic enhancement of bifurcation tunneling upon librational excitation

NASA Astrophysics Data System (ADS)

Cole, William T. S.; Farrell, James D.; Sheikh, Akber A.; Yönder, Öezlem; Fellers, Raymond S.; Viant, Mark R.; Wales, David J.; Saykally, Richard J.

2018-03-01

Using diode laser vibration-rotation-tunneling spectroscopy near 15 Thz (500 cm-1), we have measured and assigned 142 transitions to three a-type librational subbands of the water hexamer-d12 prism. These subbands reveal dramatically enhanced (ca. 1000×) tunneling splittings relative to the ground state. This enhancement is in agreement with that observed for the water dimer, trimer, and pentamer in this same frequency region. The water prism tunneling motion has been predicted to potentially describe the motions of water in interfacial and confined environments; hence, the results presented here indicate that excitation of librational vibrations has a significant impact on the hydrogen bond dynamics in these macroscopic environments.

The librational band of water ice in AFGL 961: revisited

NASA Astrophysics Data System (ADS)

Smith, R. G.; Wright, C. M.

2011-07-01

Of all the water ice absorption bands seen in the laboratory, the librational band near 12-13 μ m has proven the most difficult to conclusively identify in observational spectra. Cox reported the detection of this band in the IRAS spectrum of the massive protostar AFGL 961 near 13.6 μ m; however, the details of the structure of the band were limited by the quality of the IRAS spectrum and the accuracy of the subtracted silicate absorption. AFGL 961 is also a double system comprising two point-like components separated by ˜6 arcsec (AFGL 961E and AFGL 961W) so the IRAS aperture included both components - it is unclear how the combination of the intrinsic spectra of these two sources may have affected the resultant IRAS spectrum. In this paper we report Spitzer and European Southern Observatory (ESO) 3.6-m mid-infrared spectroscopic observations of each component of AFGL 961. We find a broad absorption feature near 13.1 μ m common to both AFGL 961E and W. The profile and peak wavelength of this feature are well matched by the laboratory spectrum of the librational band of amorphous H2O ice in the temperature range 10-30 K, in agreement with the Cox result. Both AFGL 961E and W also have strong CO2 ice absorption near 15.2 μ m, indistinguishable in profile between the two. However, AFGL 961E shows silicates in absorption near 9.7 μ m, while AFGL 961W shows polycyclic aromatic hydrocarbons in emission and, in a small aperture, also silicates in emission. Uncertainty in where the true continuum lies in the 8-13 μ m spectral region for both AFGL 961E and W means we cannot rule out the possibility that a combination of silicate emission and absorption could be responsible for at least some of the features we see in this region. In this case, a much weaker librational band could still be present, but not as a distinct feature. In either case, the ice must be located in a cool, outer envelope surrounding both stars or a cool foreground cloud, far enough away that the ice is not appreciably modified by the local environment of either one.

A resonant family of dynamically cold small bodies in the near-Earth asteroid belt

NASA Astrophysics Data System (ADS)

de la Fuente Marcos, C.; de la Fuente Marcos, R.

2013-07-01

Near-Earth objects (NEOs) moving in resonant, Earth-like orbits are potentially important. On the positive side, they are the ideal targets for robotic and human low-cost sample return missions and a much cheaper alternative to using the Moon as an astronomical observatory. On the negative side and even if small in size (2-50 m), they have an enhanced probability of colliding with the Earth causing local but still significant property damage and loss of life. Here, we show that the recently discovered asteroid 2013 BS45 is an Earth co-orbital, the sixth horseshoe librator to our planet. In contrast with other Earth's co-orbitals, its orbit is strikingly similar to that of the Earth yet at an absolute magnitude of 25.8, an artificial origin seems implausible. The study of the dynamics of 2013 BS45 coupled with the analysis of NEO data show that it is one of the largest and most stable members of a previously undiscussed dynamically cold group of small NEOs experiencing repeated trappings in the 1:1 commensurability with the Earth. This new resonant family is well constrained in orbital parameter space and it includes at least 10 other transient members: 2003 YN107, 2006 JY26, 2009 SH2 and 2012 FC71 among them. 2012 FC71 represents the best of both worlds as it is locked in a Kozai resonance and is unlikely to impact the Earth. These objects are not primordial and may have originated within the Venus-Earth-Mars region or in the main-belt, then transition to Amor-class asteroid before entering Earth's co-orbital region. Objects in this group could be responsible for the production of Earth's transient irregular natural satellites.

The BepiColombo MORE gravimetry and rotation experiments with the ORBIT14 software

NASA Astrophysics Data System (ADS)

Cicalò, S.; Schettino, G.; Di Ruzza, S.; Alessi, E. M.; Tommei, G.; Milani, A.

2016-04-01

The BepiColombo mission to Mercury is an ESA/JAXA cornerstone mission, consisting of two spacecraft in orbit around Mercury addressing several scientific issues. One spacecraft is the Mercury Planetary Orbiter, with full instrumentation to perform radio science experiments. Very precise radio tracking from Earth, on-board accelerometer and optical measurements will provide large data sets. From these it will be possible to study the global gravity field of Mercury and its tidal variations, its rotation state and the orbit of its centre of mass. With the gravity field and rotation state, it is possible to constrain the internal structure of the planet. With the orbit of Mercury, it is possible to constrain relativistic theories of gravitation. In order to assess that all the scientific goals are achievable with the required level of accuracy, full cycle numerical simulations of the radio science experiment have been performed. Simulated tracking, accelerometer and optical camera data have been generated, and a long list of variables including the spacecraft initial conditions, the accelerometer calibrations and the gravity field coefficients have been determined by a least-squares fit. The simulation results are encouraging: the experiments are feasible at the required level of accuracy provided that some critical terms in the accelerometer error are moderated. We will show that BepiColombo will be able to provide at least an order of magnitude improvement in the knowledge of Love number k2, libration amplitudes and obliquity, along with a gravity field determination up to degree 25 with a signal-to-noise ratio of 10.

Modelling of Lunar Laser Ranging in the Geocentric Frame and Comparison with the Common-View Double-Difference Lunar Laser Ranging Approach

NASA Astrophysics Data System (ADS)

Svehla, D.; Rothacher, M.

2016-12-01

Is it possible to process Lunar Laser Ranging (LLR) measurements in the geocentric frame in a similar way SLR measurements are modelled for GPS satellites and estimate all global reference frame parameters like in the case of GPS? The answer is yes. We managed to process Lunar laser measurements to Apollo and Luna retro-reflectors on the Moon in a similar way we are processing SLR measurements to GPS satellites. We make use of the latest Lunar libration models and DE430 ephemerides given in the Solar system baricentric frame and model uplink and downlink Lunar laser ranges in the geocentric frame as one way measurements, similar to SLR measurements to GPS satellites. In the first part of this contribution we present the estimation of the Lunar orbit as well as the Earth orientation parameters (including UT1 or UT0) with this new formulation. In the second part, we form common-view double-difference LLR measurements between two Lunar retro-reflectors and two LLR telescopes to show the actual noise of the LLR measurements. Since, by forming double-differences of LLR measurements, all range biases are removed and orbit errors are significantly reduced (the Lunar orbit is much farther away than the GPS orbits), one can consider double-difference LLR as an "orbit-free" and "bias-free" differential approach. In the end, we make a comparison with the SLR double-difference approach with Galileo satellites, where we already demonstrated submillimeter precision, and discuss possible combination of LLR and SLR to GNSS satellites using double-difference approach.

Using Geological Implications of a Physical Libration to Constrain Enceladus' Libration State

NASA Technical Reports Server (NTRS)

Hurford, T. A.; Bills, B. G.; Helfenstein, P.; Greenberg, R.; Hoppa, G. V.; Hamilton, D. P.

2009-01-01

Observations of Enceladus' south pole revealed large rifts in the crust, called "tiger stripes", which exhibit higher temperatures than the surrounding terrain and are likely sources of observed eruptions. Tidal stress may periodically open the tiger stripe rifts, controlling the timing and location of eruptions. Moreover, shear motion along rifts may produce the heat to drive eruptions.

A resonant chain of four transiting, sub-Neptune planets.

PubMed

Mills, Sean M; Fabrycky, Daniel C; Migaszewski, Cezary; Ford, Eric B; Petigura, Erik; Isaacson, Howard

2016-05-26

Surveys have revealed many multi-planet systems containing super-Earths and Neptunes in orbits of a few days to a few months. There is debate whether in situ assembly or inward migration is the dominant mechanism of the formation of such planetary systems. Simulations suggest that migration creates tightly packed systems with planets whose orbital periods may be expressed as ratios of small integers (resonances), often in a many-planet series (chain). In the hundreds of multi-planet systems of sub-Neptunes, more planet pairs are observed near resonances than would generally be expected, but no individual system has hitherto been identified that must have been formed by migration. Proximity to resonance enables the detection of planets perturbing each other. Here we report transit timing variations of the four planets in the Kepler-223 system, model these variations as resonant-angle librations, and compute the long-term stability of the resonant chain. The architecture of Kepler-223 is too finely tuned to have been formed by scattering, and our numerical simulations demonstrate that its properties are natural outcomes of the migration hypothesis. Similar systems could be destabilized by any of several mechanisms, contributing to the observed orbital-period distribution, where many planets are not in resonances. Planetesimal interactions in particular are thought to be responsible for establishing the current orbits of the four giant planets in the Solar System by disrupting a theoretical initial resonant chain similar to that observed in Kepler-223.

Tidally modulated eruptions on Enceladus: Cassini ISS observations and models

DOE Office of Scientific and Technical Information (OSTI.GOV)

Nimmo, Francis; Porco, Carolyn; Mitchell, Colin, E-mail: carolyn@ciclops.org

2014-09-01

We use images acquired by the Cassini Imaging Science Subsystem (ISS) to investigate the temporal variation of the brightness and height of the south polar plume of Enceladus. The plume's brightness peaks around the moon's apoapse, but with no systematic variation in scale height with either plume brightness or Enceladus' orbital position. We compare our results, both alone and supplemented with Cassini near-infrared observations, with predictions obtained from models in which tidal stresses are the principal control of the eruptive behavior. There are three main ways of explaining the observations: (1) the activity is controlled by right-lateral strike slip motion;more » (2) the activity is driven by eccentricity tides with an apparent time delay of about 5 hr; (3) the activity is driven by eccentricity tides plus a 1:1 physical libration with an amplitude of about 0.°8 (3.5 km). The second hypothesis might imply either a delayed eruptive response, or a dissipative, viscoelastic interior. The third hypothesis requires a libration amplitude an order of magnitude larger than predicted for a solid Enceladus. While we cannot currently exclude any of these hypotheses, the third, which is plausible for an Enceladus with a subsurface ocean, is testable by using repeat imaging of the moon's surface. A dissipative interior suggests that a regional background heat source should be detectable. The lack of a systematic variation in plume scale height, despite the large variations in plume brightness, is plausibly the result of supersonic flow; the details of the eruption process are yet to be understood.« less

Primer Vector Optimization: Survey of Theory, new Analysis and Applications

NASA Astrophysics Data System (ADS)

Guzman

This paper presents a preliminary study in developing a set of optimization tools for orbit rendezvous, transfer and station keeping. This work is part of a large scale effort undergoing at NASA Goddard Space Flight Center and a.i. solutions, Inc. to build generic methods, which will enable missions with tight fuel budgets. Since no single optimization technique can solve efficiently all existing problems, a library of tools where the user could pick the method most suited for the particular mission is envisioned. The first trajectory optimization technique explored is Lawden's primer vector theory [Ref. 1]. Primer vector theory can be considered as a byproduct of applying Calculus of Variations (COV) techniques to the problem of minimizing the fuel usage of impulsive trajectories. For an n-impulse trajectory, it involves the solution of n-1 two-point boundary value problems. In this paper, we look at some of the different formulations of the primer vector (dependent on the frame employed and on the force model). Also, the applicability of primer vector theory is examined in effort to understand when and why the theory can fail. Specifically, since COV is based on "small variations", singularities in the linearized (variational) equations of motion along the arcs must be taken into account. These singularities are a recurring problem in analyzes that employ "small variations" [Refs. 2, 3]. For example, singularities in the (2-body problem) variational equations along elliptic arcs occur when [Ref. 4], 1) the difference between the initial and final times is a multiple of the reference orbit period, 2) the difference between the initial and final true anomalies are given by k, for k= 0, 1, 2, 3,..., note that this cover the 3) the time of flight is a minimum for the given difference in true anomaly. For the N-body problem, the situation is more complex and is still under investigation. Several examples, such as the initialization of an orbit (ascent trajectory) and rotation of the line of apsides, are utilized as test cases. Recommendations, future work, and the possible addition of other optimization techniques are also discussed. References: [1] Lawden D.F., Optimal Trajectories for Space Navigation, Butterworths, London, 1963. [2] Wilson, R.S., Howell, K.C., and, Lo, M, "Optimization of Insertion Cost for Transfer Trajectories to Libration Point Orbits", AIAA/AAS Astrodynamics Specialist Conference, AAS 99-041, Girdwood, Alaska, August 16-19, 1999. [3] Goodson, T, "Monte-Carlo Maneuver Analysis for the Microwave Anisotropy Probe", AAS/AIAA Astrodynamics Specialist Conference, AAS 01-331, Quebec City, Canada, July 30 - August 2, 2001. [4] Stern, R.G., "Singularities in the Analytic Solution of the Linearized Variational Equations of Elliptical Motion", Report RE-8, May 1964, Experimental Astronomy Lab., Massachusetts Institute of Technology, Cambridge, Massachusetts.

Autonomous NanoTechnology Swarm (ANTS) Prospecting Asteroid Mission (PAM), Asteroid Proximity Operations

NASA Technical Reports Server (NTRS)

Marr, Greg; Cooley, Steve; Roithmayr, Carlos; Kay-Bunnell, Linda; Williams, Trevor

2004-01-01

The Autonomous NanoTechnology Swarm (ANTS) is a generic mission architecture based on spatially distributed spacecraft, autonomous and redundant components, and hierarchical organization. The ANTS Prospecting Asteroid Mission (PAM) is an ANTS application which will nominally use a swarm of 1000 spacecraft. There would be 10 types of "specialists" with common spacecraft buses. There would be 10 subswarms of approximately 100 spacecraft each or approximately 10 of each specialist in each swarm. The ANTS PAM primary objective is the exploration of the asteroid belt in search of resources and material with astrobiologically relevant origins and signatures. The ANTS PAM spacecraft will nominally be released from a station in an Earth-Moon L1 libration point orbit, and they will use Solar sails for propulsion. The sail structure would be highly flexible, capable of changing morphology to change cross-section for capture of sunlight or to form effective "tip vanes" for attitude control. ANTS PAM sails would be capable of full to partial deployment, to change effective sail area and center of pressure, and thus allow attitude control. Results of analysis of a transfer trajectory from Earth to a sample target asteroid will be presented. ANTS PAM will require continuous coverage of different asteroid locations as close as one to two asteroid "diameters" from the surface of the asteroid for periods of science data collection during asteroid proximity operations. Hovering spacecraft could meet the science data collection objectives. The results of hovering analysis will be presented. There are locations for which hovering is not possible, for example on the illuminated side of the asteroid. For cases where hovering is not possible, the results of utilizing asteroid formations to orbit the asteroid and achieve the desired asteroid viewing will be presented for sample asteroids. The ability of ANTS PAM to reduce the area of the solar sail during asteroid proximity operations is critical to the maintenance of orbiting formations for a period of time. Results of analysis of potential "traffic" problems during asteroid proximity operations will be presented.

The Impact Imperative: A Space Infrastructure Enabling a Multi-Tiered Earth Defense

NASA Technical Reports Server (NTRS)

Campbell, Jonathan W.; Phipps, Claude; Smalley, Larry; Reilly, James; Boccio, Dona

2003-01-01

Impacting at hypervelocity, an asteroid struck the Earth approximately 65 million years ago in the Yucatan Peninsula a m . This triggered the extinction of almost 70% of the species of life on Earth including the dinosaurs. Other impacts prior to this one have caused even greater extinctions. Preventing collisions with the Earth by hypervelocity asteroids, meteoroids, and comets is the most important immediate space challenge facing human civilization. This is the Impact Imperative. We now believe that while there are about 2000 earth orbit crossing rocks greater than 1 kilometer in diameter, there may be as many as 200,000 or more objects in the 100 m size range. Can anything be done about this fundamental existence question facing our civilization? The answer is a resounding yes! By using an intelligent combination of Earth and space based sensors coupled with an infrastructure of high-energy laser stations and other secondary mitigation options, we can deflect inbound asteroids, meteoroids, and comets and prevent them &om striking the Earth. This can be accomplished by irradiating the surface of an inbound rock with sufficiently intense pulses so that ablation occurs. This ablation acts as a small rocket incrementally changing the shape of the rock's orbit around the Sun. One-kilometer size rocks can be moved sufficiently in about a month while smaller rocks may be moved in a shorter time span. We recommend that space objectives be immediately reprioritized to start us moving quickly towards an infrastructure that will support a multiple option defense capability. Planning and development for a lunar laser facility should be initiated immediately in parallel with other options. All mitigation options are greatly enhanced by robust early warning, detection, and tracking resources to find objects sufficiently prior to Earth orbit passage in time to allow significant intervention. Infrastructure options should include ground, LEO, GEO, Lunar, and libration point laser and sensor stations for providing early warning, tracking, and deflection. Other options should include space interceptors that will carry both laser and nuclear ablators for close range work. Response options must be developed to deal with the consequences of an impact should we move too slowly.

Mercury's gravity field, orientation, and ephemeris after MESSENGER's Low-Altitude Campaign

NASA Astrophysics Data System (ADS)

Genova, Antonio; Mazarico, Erwan; Goossens, Sander J.; Lemoine, Frank G.; Neumann, Gregory A.; Smith, David E.; Zuber, Maria T.; Solomon, Sean C.

2015-04-01

In April 2015, the MErcury Surface, Space ENvironment, GEochemistry, and Ranging (MESSENGER) spacecraft will complete more than 4 years of operations in orbit around Mercury. In its last year, as part of MESSENGER's Second Extended Mission (XM2) started in March 2013, the spacecraft has been collecting radio tracking data at unprecedented low altitudes in Mercury's northern hemisphere. During the first two years in orbit, the spacecraft periapsis altitude was kept between 200 and 500 km, while its location drifted slowly northward from 60˚N to 84˚N. The orbital period initially was 12 h, but it was decreased to 8 h in April 2012. The remaining fuel onboard the spacecraft enabled two extended missions, the last of which will end with an impact expected on or before 28 April 2015. During the second extended mission, the periapsis altitude has been as low as 15-25 km. NASA's Deep Space Network (DSN) tracked the spacecraft during periapsis passages from April to October 2014, when the spacecraft periapsis altitude was between 25 and 100 km. In the last six months of the mission, the closest approaches of MESSENGER were occulted by Mercury and were thus not visible from Earth. However, additional radio tracking data have been collected at altitudes (75-100 km) that are still substantially below the initial periapsis altitude. The new low-altitude radio tracking data have enabled an updated model of the gravity field of Mercury. With these data, the resolution of the field in the northern hemisphere has been improved, revealing features that were previously undetectable and that correlate well with topography. The zonal harmonics are in good agreement with those in previous models of the gravity field. We also focused our study on the determination of other geophysical parameters, such as the orientation of Mercury. The new data were acquired not only at lower altitudes but also at latitudes closer to the equator, so they provide important information on tides, the right ascension of the pole, and the physical libration in longitude. The new model of Mercury's gravity field includes the estimation of the declination and the right ascension of the pole, the Love number k2, and the amplitude of the longitudinal libration. We also report an update on the ephemeris of Mercury obtained from MESSENGER range data covering the entire mission period, from the flybys until the end of the mission.

Lattice dynamics of solid N2 with an ab initio intermolecular potential

NASA Astrophysics Data System (ADS)

Luty, T.; van der Avoird, A.; Berns, R. M.

1980-11-01

We have performed harmonic and self-consistent phonon lattice dynamics calculations for α and γ N2 crystals using an intermolecular potential from ab initio calculations. This potential contains electrostatic (multipole) interactions, up to all R-9 terms inclusive, anisotropic dispersion interactions up to all R-10 terms inclusive, and anisotropic overlap interactions caused by charge penetration and exchange between the molecules. The lattice constants, cohesion energy, the frequencies of the translational phonon modes and the Grüneisen parameters for the librational modes are in good agreement with experimental values, confirming the quality of the potential. The frequencies of the librational modes and those of the mixed modes are less well reproduced, especially at temperatures near the α-β phase transition. Probably, the self-consistent phonon method used does not fully account for the anharmonicity in the librations.

Electron spin control and spin-libration coupling of a levitated nanodiamond

NASA Astrophysics Data System (ADS)

Hoang, Thai; Ma, Yue; Ahn, Jonghoon; Bang, Jaehoon; Robicheaux, Francis; Gong, Ming; Yin, Zhang-Qi; Li, Tongcang

2017-04-01

Hybrid spin-mechanical systems have great potentials in sensing, macroscopic quantum mechanics, and quantum information science. Recently, we optically levitated a nanodiamond and demonstrated electron spin control of its built-in nitrogen-vacancy (NV) centers in vacuum. We also observed the libration (torsional vibration) of a nanodiamond trapped by a linearly polarized laser beam in vacuum. We propose to achieve strong coupling between the electron spin of a NV center and the libration of a levitated nanodiamond with a uniform magnetic field. With a uniform magnetic field, multiple spins can couple to the torsional vibration at the same time. We propose to use this strong coupling to realize the Lipkin-Meshkov-Glick (LMG) model and generate rotational superposition states. This work is supported by the National Science Foundation under Grant No. 1555035-PHY.

Absolute, SI-traceable lunar irradiance tie-points for the USGS Lunar Model

NASA Astrophysics Data System (ADS)

Brown, Steven W.; Eplee, Robert E.; Xiong, Xiaoxiong J.

2017-10-01

The United States Geological Survey (USGS) has developed an empirical model, known as the Robotic Lunar Observatory (ROLO) Model, that predicts the reflectance of the Moon for any Sun-sensor-Moon configuration over the spectral range from 350 nm to 2500 nm. The lunar irradiance can be predicted from the modeled lunar reflectance using a spectrum of the incident solar irradiance. While extremely successful as a relative exo-atmospheric calibration target, the ROLO Model is not SI-traceable and has estimated uncertainties too large for the Moon to be used as an absolute celestial calibration target. In this work, two recent absolute, low uncertainty, SI-traceable top-of-the-atmosphere (TOA) lunar irradiances, measured over the spectral range from 380 nm to 1040 nm, at lunar phase angles of 6.6° and 16.9° , are used as tie-points to the output of the ROLO Model. Combined with empirically derived phase and libration corrections to the output of the ROLO Model and uncertainty estimates in those corrections, the measurements enable development of a corrected TOA lunar irradiance model and its uncertainty budget for phase angles between +/-80° and libration angles from 7° to 51° . The uncertainties in the empirically corrected output from the ROLO model are approximately 1 % from 440 nm to 865 nm and increase to almost 3 % at 412 nm. The dominant components in the uncertainty budget are the uncertainty in the absolute TOA lunar irradiance and the uncertainty in the fit to the phase correction from the output of the ROLO model.

Earth Rings for Planetary Environment Control

NASA Astrophysics Data System (ADS)

Pearson, Jerome; Oldson, John; Levin, Eugene; Carroll, Joseph

2002-01-01

For most of its past, large parts of the Earth have experienced subtropical climates, with high sea levels and no polar icecaps. This warmer environment was punctuated 570, 280, and 3 million years ago with periods of glaciation that covered temperate regions with thick ice for millions of years. At the end of the current ice age, a warmer climate could flood coastal cities, even without human-caused global warming. In addition, asteroids bombard the Earth periodically, with impacts large enough to destroy most life on Earth, and the sun is warming inexorably. This paper proposes a concept to solve these problems simultaneously, by creating an artificial planetary ring about the Earth to shade it. Past proposals for space climate control have depended on gigantic engineering structures launched from Earth and placed in Earth orbit or at the Earth-Sun L1 libration point, requiring fabrication, large launch masses and expense, constant control, and repair. Our solution is to begin by using lunar material, and then mine and remove Earth-orbit-crossing asteroids and discard the tailings into Earth orbit, to form a broad, flat ring like those of Saturn. This solution is evaluated and compared with other alternatives. Such ring systems can persist for thousands of years, and can be maintained by shepherding satellites or by continual replenishment from new asteroids to replace the edges of the ring lost by diffusion. An Earth ring at R = 1.3-1.83 RE would shade only the equatorial regions, moderating climate extremes, and could reverse a century of global warming. It could also absorb particles from the radiation belts, making trips to high Earth orbit and GEO safer for humans and for electronics. It would also light the night many times as bright as the full moon. A preliminary design of the ring is developed, including its location, mass, composition, stability, and timescale required. A one-dimensional climate model is used to evaluate the Earth ring performance. Earth, lunar, and asteroidal material sources are evaluated; asteroid retrieval is addressed, along with techniques for processing and forming the ring to the proper thickness and density. The ring could consist of particles, or fabricated satellite structures. Environmental concerns and effects on existing satellites in various Earth orbits are addressed. There are uncertainties in our understanding of climate and its control. But it appears that the Earth ring could control the Earth's temperature and its latitudinal variation, make dangerous asteroids useful, reduce the intensity of the Van Allen radiation belts, provide nighttime illumination without power, and create an artificial ionosphere for radio communication.

AIDA DART asteroid deflection test: Planetary defense and science objectives

NASA Astrophysics Data System (ADS)

Cheng, Andrew F.; Rivkin, Andrew S.; Michel, Patrick; Atchison, Justin; Barnouin, Olivier; Benner, Lance; Chabot, Nancy L.; Ernst, Carolyn; Fahnestock, Eugene G.; Kueppers, Michael; Pravec, Petr; Rainey, Emma; Richardson, Derek C.; Stickle, Angela M.; Thomas, Cristina

2018-08-01

The Asteroid Impact & Deflection Assessment (AIDA) mission is an international cooperation between NASA and ESA. NASA plans to provide the Double Asteroid Redirection Test (DART) mission which will perform a kinetic impactor experiment to demonstrate asteroid impact hazard mitigation. ESA proposes to provide the Hera mission which will rendezvous with the target to monitor the deflection, perform detailed characterizations, and measure the DART impact outcomes and momentum transfer efficiency. The primary goals of AIDA are (i) to demonstrate the kinetic impact technique on a potentially hazardous near-Earth asteroid and (ii) to measure and characterize the deflection caused by the impact. The AIDA target will be the binary asteroid (65803) Didymos, which is of spectral type Sq, with the deflection experiment to occur in October, 2022. The DART impact on the secondary member of the binary at ∼6 km/s changes the orbital speed and the binary orbit period, which can be measured by Earth-based observatories with telescope apertures as small as 1 m. The DART impact will in addition alter the orbital and rotational states of the Didymos binary, leading to excitation of eccentricity and libration that, if measured by Hera, can constrain internal structure of the target asteroid. Measurements of the DART crater diameter and morphology can constrain target properties like cohesion and porosity based on numerical simulations of the DART impact.

Actual Romanian research in post-newtonian dynamics

NASA Astrophysics Data System (ADS)

Mioc, V.; Stavinschi, M.

2007-05-01

We survey the recent Romanian results in the study of the two-body problem in post-Newtonian fields. Such a field is characterized, in general, by a potential of the form U(q)=|q|^{-1}+ something (small, but not compulsorily). We distinguish some classes of post-Newtonian models: relativistic (Schwarzschild, Fock, Einstein PN, Reissner-Nordström, Schwarzschild - de Sitter, etc.) and nonrelativistic (Manev, Mücket-Treder, Seeliger, gravito-elastic, etc.). Generalized models (the zonal-satellite problem, quasihomogeneous fields), as well as special cases (anisotropic Manev-type and Schwarzschild-type models, Popovici or Popovici-Manev photogravitational problem), were also tackled. The methods used in such studies are various: analytical (using mainly the theory of perturbations, but also other theories: functions of complex variable, variational calculus, etc.), geometric (qualitative approach of the theory of dynamical systems), and numerical (especially using the Poincaré-section technique). The areas of interest and the general results obtained focus on: exact or approximate analytical solutions; characteristics of local flows (especially at limit situations: collision and escape); quasiperiodic and periodic orbits; equilibria; symmetries; chaoticity; geometric description of the global flow (and physical interpretation of the phase-space structure). We emphasize some special features, which cannot be met within the Newtonian framework: black-hole effect, oscillatory collisions, radial librations, bounded orbits for nonnegative energy, existence of unstable circular motion (or unstable rest), symmetric periodic orbits within anisotropic models, etc.

First Numerical Simulations of Turbulent Dynamos Driven by Libration, Precession and Tides in Triaxial Ellipsoids - An Alternative Route for Planetary Magnetism

NASA Astrophysics Data System (ADS)

Le Bars, M.; Kanuganti, S. R.; Favier, B.

2017-12-01

Most of the time, planetary dynamos are - tacitly or not - associated with thermo-solutal convection. The convective dynamo model has indeed proven successful to explain the current Earth's magnetic field. However, its results are sometimes difficult to reconcile with observational data and its validity can be questioned for several celestial bodies. For instance, the small size of the Moon and Ganymede makes it difficult to maintain a sufficient temperature gradient to sustain convection and to explain their past and present magnetic fields, respectively. The same caveat applies to the growing number of planetesimals shown to have generated magnetic fields in their early history. Finally, the energy budget of the early Earth is difficult to reconcile with a convective dynamo before the onset of inner core growth. Significant effort has thus been put into finding new routes for planetary dynamo. In particular, the rotational dynamics of planets, moons and small bodies, where their average spinning motion is periodically perturbed by the small mechanical forcings of libration, precession and/or tides, is now widely accepted as an efficient source of core turbulence. The underlying mechanism relies on a parametric instability where the inertial waves of the rotating fluid core are resonantly excited by the small forcing, leading to exponential growth and bulk filling intense motions, pumping their energy from the orbital dynamics. Dynamos driven by mechanical forcing have been suggested for the Moon, Mars, Io, the early Earth, etc. However, the real dynamo capacity of the corresponding flows has up-to-now been studied only in very limited cases, with simplified spherical/spheroidal geometries and/or overly viscous fluids. We will present here the first numerical simulations of dynamos driven by libration, precession and tides, in the triaxial ellipsoidal geometry and in the turbulent regime relevant for planetary cores. We will describe the numerical techniques required to tackle this challenge and present the first results describing the associated magnetic field in terms of amplitude, energy budget, and spatiotemporal signature. We hope to motivate others to participate in the exploration of the wide parameter space, a necessary work for addressing the variety of observed past and present magnetic fields.

Application of the NASCAP Spacecraft Simulation Tool to Investigate Electrodynamic Tether Current Collection in LEO

NASA Technical Reports Server (NTRS)

Adams, Mitzi; HabashKrause, Linda

2012-01-01

Recent interest in using electrodynamic tethers (EDTs) for orbital maneuvering in Low Earth Orbit (LEO) has prompted the development of the Marshall ElectroDynamic Tether Orbit Propagator (MEDTOP) model. The model is comprised of several modules which address various aspects of EDT propulsion, including calculation of state vectors using a standard orbit propagator (e.g., J2), an atmospheric drag model, realistic ionospheric and magnetic field models, space weather effects, and tether librations. The natural electromotive force (EMF) attained during a radially-aligned conductive tether results in electrons flowing down the tether and accumulating on the lower-altitude spacecraft. The energy that drives this EMF is sourced from the orbital energy of the system; thus, EDTs are often proposed as de-orbiting systems. However, when the current is reversed using satellite charged particle sources, then propulsion is possible. One of the most difficult challenges of the modeling effort is to ascertain the equivalent circuit between the spacecraft and the ionospheric plasma. The present study investigates the use of the NASA Charging Analyzer Program (NASCAP) to calculate currents to and from the tethered satellites and the ionospheric plasma. NASCAP is a sophisticated set of computational tools to model the surface charging of three-dimensional (3D) spacecraft surfaces in a time-varying space environment. The model's surface is tessellated into a collection of facets, and NASCAP calculates currents and potentials for each one. Additionally, NASCAP provides for the construction of one or more nested grids to calculate space potential and time-varying electric fields. This provides for the capability to track individual particles orbits, to model charged particle wakes, and to incorporate external charged particle sources. With this study, we have developed a model of calculating currents incident onto an electrodynamic tethered satellite system, and first results are shown here.

Pluto and Charon: A Case of Precession-Orbit Resonance?

NASA Technical Reports Server (NTRS)

Rubincam, David Parry; Smith, David E. (Technical Monitor)

2000-01-01

Pluto may be the only known case of precession-orbit resonance in the solar system. The Pluto-Charon system orbits the Sun with a period of 1 Plutonian year, which is 250.8 Earth years. The observed parameters of the system are such that Charon may cause Pluto to precess with a period near 250.8 Earth years. This gives rise to two possible resonances, heretofore unrecognized. The first is due to Pluto's orbit being highly eccentric, giving solar torques on Charon with a period of 1 Plutonian year. Charon in turn drives Pluto near its precession period. Volatiles, which are expected to shuttle across Pluto's surface between equator and pole as Pluto's obliquity oscillates, might change the planet's dynamical flattening enough so that Pluto crosses the nearby resonance, forcing the planet's equatorial plane to depart from Charon's orbital plane. The mutual tilt can reach as much as 2 deg after integrating over 5.6 x 10(exp 6) years, depending upon how close Pluto is to the resonance and the supply of volatiles. The second resonance is due to the Sun's traveling above and below Charon's orbital plane; it has a period half that of the eccentricity resonance. Reaching this half-Plutonian year resonance requires a much larger but still theoretically possible amount of volatiles. In this case the departure of Charon from an equatorial orbit is about 1 deg after integrating for 5.6 x 10(exp 6) years. The calculations ignore libration and tidal friction. It is not presently known how large the mutual tilt can grow over the age of the solar system, but if it remains only a few degrees, then observing such small angles from a Pluto flyby mission would be difficult. It is not clear why the parameters of the Pluto-Charon system are so close to the eccentricity resonance.

Establishing a Near Term Lunar Farside Gravity Model via Inexpensive Add-on Navigation Payload

NASA Technical Reports Server (NTRS)

Folta, David; Mesarch, Michael; Miller, Ronald; Bell, David; Jedrey, Tom; Butman, Stanley; Asmar, Sami

2007-01-01

The Space Communications and Navigation, Constellation Integration Project (SCIP) is tasked with defining, developing, deploying and operating an evolving multi-decade communications and navigation (C/N) infrastructure including services and subsystems that will support both robotic and human exploration activities at the Moon. This paper discusses an early far side gravitational mapping service and related telecom subsystem that uses an existing spacecraft (WIND) and the Lunar Reconnaissance Orbiter (LRO) to collect data that would address several needs of the SCIP. An important aspect of such an endeavor is to vastly improve the current lunar gravity model while demonstrating the navigation and stationkeeping of a relay spacecraft. We describe a gravity data acquisition activity and the trajectory design of the relay orbit in an Earth-Moon L2 co-linear libration orbit. Several phases of the transfer from an Earth-Sun to the Earth-Moon region are discussed along with transfers within the Earth-Moon system. We describe a proposed, but not integrated, add-on to LRO scheduled to be launched in October of 2008. LRO provided a real host spacecraft against which we designed the science payload and mission activities. From a strategic standpoint, LRO was a very exciting first flight opportunity for gravity science data collection. Gravity Science data collection requires the use of one or more low altitude lunar polar orbiters. Variations in the lunar gravity field will cause measurable variations in the orbit of a low altitude lunar orbiter. The primary means to capture these induced motions is to monitor the Doppler shift of a radio signal to or from the low altitude spacecraft, given that the signal is referenced to a stable frequency reference. For the lunar far side, a secondary orbiting radio signal platform is required. We provide an in-depth look at link margins, trajectory design, and hardware implications. Our approach posed minimum risk to a host mission while maintaining a very low implementation and operations cost.

Mapping the Topography of Mercury with MESSENGER Laser Altimetry

NASA Technical Reports Server (NTRS)

Sun, Xiaoli; Cavanaugh, John F.; Neumann, Gregory A.; Smith, David E..; Zubor, Maria T.

2012-01-01

The Mercury Laser Altimeter onboard MESSENGER involves unique design elements that deal with the challenges of being in orbit around Mercury. The Mercury Laser Altimeter (MLA) is one of seven instruments on NASA's MErcury Surface, Space ENvironment, GEochemistry, and Ranging (MESSENGER) spacecraft. MESSENGER was launched on 3 August 2004, and entered into orbit about Mercury on 18 March 2011 after a journey through the inner solar system. This involved six planetary flybys, including three of Mercury. MLA is designed to map the topography and landforms of Mercury's surface. It also measures the planet's forced libration (motion about the spin axis), which helps constrain the state of the core. The first science measurements from orbit taken with MLA were made on 29 March 2011 and continue to date. MLA had accumulated about 8.3 million laser ranging measurements to Mercury's surface, as of 31 July 2012, i.e., over six Mercury years (528 Earth days). Although MLA is the third planetary lidar built at the NASA Goddard Space Flight Center (GSFC), MLA must endure a much harsher thermal environment near Mercury than the previous instruments on Mars and Earth satellites. The design of MLA was derived in part from that of the Mars Orbiter Laser Altimeter on Mars Global Surveyor. However, MLA must range over greater distances and often in off-nadir directions from a highly eccentric orbit. In MLA we use a single-mode diode-pumped Nd:YAG (neodymium-doped yttrium aluminum garnet) laser that is highly collimated to maintain a small footprint on the planet. The receiver has both a narrow field of view and a narrow spectral bandwidth to minimize the amount of background light detected from the sunlit hemisphere of Mercury. We achieve the highest possible receiver sensitivity by employing the minimum receiver detection threshold.

A note on an attempt at more efficient Poisson series evaluation. [for lunar libration

NASA Technical Reports Server (NTRS)

Shelus, P. J.; Jefferys, W. H., III

1975-01-01

A substantial reduction has been achieved in the time necessary to compute lunar libration series. The method involves eliminating many of the trigonometric function calls by a suitable transformation and applying a short SNOBOL processor to the FORTRAN coding of the transformed series, which obviates many of the multiplication operations during the course of series evaluation. It is possible to accomplish similar results quite easily with other Poisson series.

Europa Tide Movie

NASA Technical Reports Server (NTRS)

2007-01-01

[figure removed for brevity, see original site] Click on the image for Europa Tide Movie

In this movie Europa is seen in a cutaway view through two cycles of its 3.5 day orbit about the giant planet Jupiter. Like Earth, Europa is thought to have an iron core, a rocky mantle and a surface ocean of salty water. Unlike on Earth, however, this ocean is deep enough to cover the whole moon, and being far from the sun, the ocean surface is globally frozen over. Europa's orbit is eccentric, which means as it travels around Jupiter, large tides, raised by Jupiter, rise and fall. Jupiter's position relative to Europa is also seen to librate, or wobble, with the same period. This tidal kneading causes frictional heating within Europa, much in the same way a paper clip bent back and forth can get hot to the touch, as illustrated by the red glow in the interior of Europa's rocky mantle and in the lower, warmer part of its ice shell. This tidal heating is what keeps Europa's ocean liquid and could prove critical to the survival of simple organisms within the ocean, if they exist.

The Influence of Eccentricity Cycles on Exoplanet Habitability

NASA Astrophysics Data System (ADS)

Baskin, N. J. K.; Fabrycky, D. C.; Abbot, D. S.

2015-12-01

In our search for habitable exoplanets, it is important to understand how planetary habitability is influenced by orbital configurations that differ from those of the terrestrial planets in our Solar system. In particular, observational surveys have revealed the prevalence of planetary systems around binary stars. Within these systems, the gravitational influence of a companion star can induce libration in the eccentricity of the planet's orbit (referred to as Kozai Cycles) on timescales as short as thousands of years. The resulting fluctuations in stellar flux at the top of the atmosphere can potentially induce dramatic variations in surface temperatures, with direct implications for the planet's habitability prospects. We investigate this research problem using two steps. First, we utilize the MERCURY N-body integrator in order to calculate the eccentricity of a hypothetical Earth-analogue under the gravitational influence of a stellar companion. Second, we run a coupled Global Climate Model (GCM) at various stages of a cycle provided by the MERCURY runs in order to examine if the increase in insolation renders the planet uninhabitable. This work will allow us to better understand how Kozai cycles influence the boundaries of a planet's habitable zone.

On-Orbit Cross-Calibration of AM Satellite Remote Sensing Instruments using the Moon

NASA Technical Reports Server (NTRS)

Butler, James J.; Kieffer, Hugh H.; Barnes, Robert A.; Stone, Thomas C.

2003-01-01

On April 14,2003, three Earth remote sensing spacecraft were maneuvered enabling six satellite instruments operating in the visible through shortwave infrared wavelength region to view the Moon for purposes of on-orbit cross-calibration. These instruments included the Moderate Resolution Imaging Spectroradiometer (MODIS), the Multi-angle Imaging SpectroRadiometer (MISR), the Advanced Spaceborne Thermal Emission and Reflection (ASTER) radiometer on the Earth Observing System (EOS) Terra spacecraft, the Advanced Land Imager (ALI) and Hyperion instrument on Earth Observing-1 (EO-1) spacecraft, and the Sea-viewing Wide Field-of-view Sensor (SeaWiFS) on the SeaStar spacecraft. Observations of the Moon were compared using a spectral photometric mode for lunar irradiance developed by the Robotic Lunar Observatory (ROLO) project located at the United States Geological Survey in Flagstaff, Arizona. The ROLO model effectively accounts for variations in lunar irradiance corresponding to lunar phase and libration angles, allowing intercomparison of observations made by instruments on different spacecraft under different time and location conditions. The spacecraft maneuvers necessary to view the Moon are briefly described and results of using the lunar irradiance model in comparing the radiometric calibration scales of the six satellite instruments are presented here.

Formation of the Wide Asynchronous Binary Asteroid Population

NASA Astrophysics Data System (ADS)

Jacobson, Seth A.; Scheeres, Daniel J.; McMahon, Jay

2014-01-01

We propose and analyze a new mechanism for the formation of the wide asynchronous binary population. These binary asteroids have wide semimajor axes relative to most near-Earth and main belt asteroid systems. Confirmed members have rapidly rotating primaries and satellites that are not tidally locked. Previously suggested formation mechanisms from impact ejecta, from planetary flybys, and directly from rotational fission events cannot satisfy all of the observations. The newly hypothesized mechanism works as follows: (1) these systems are formed from rotational fission, (2) their satellites are tidally locked, (3) their orbits are expanded by the binary Yarkovsky-O'Keefe-Radzievskii-Paddack (BYORP) effect, (4) their satellites desynchronize as a result of the adiabatic invariance between the libration of the secondary and the mutual orbit, and (5) the secondary avoids resynchronization because of the YORP effect. This seemingly complex chain of events is a natural pathway for binaries with satellites that have particular shapes, which define the BYORP effect torque that acts on the system. After detailing the theory, we analyze each of the wide asynchronous binary members and candidates to assess their most likely formation mechanism. Finally, we suggest possible future observations to check and constrain our hypothesis.

Forming the wide asynchronous binary asteroid population

NASA Astrophysics Data System (ADS)

Jacobson, S.; Scheeres, D.; McMahon, J.

2014-07-01

We propose and analyze a new mechanism for the formation of the wide asynchronous binary population. These binary asteroids have wide semi-major axes relative to most near-Earth-asteroid and main-belt-asteroid systems as shown in the attached table. Confirmed members have rapidly rotating primaries and satellites that are not tidally locked. Previously suggested formation mechanisms from impact ejecta, from planetary flybys, and directly from rotational-fission events cannot satisfy all of the observations. The newly hypothesized mechanism works as follows: (1) these systems are formed from rotational fission, (2) their satellites are tidally locked, (3) their orbits are expanded by the binary Yarkovsky-O'Keefe-Radzievskii-Paddack (BYORP) effect, (4) their satellites desynchronize as a result of the adiabatic invariance between the libration of the secondary and the mutual orbit, and (5) the secondary avoids resynchronization because of the YORP effect. This seemingly complex chain of events is a natural pathway for binaries with satellites that have particular shapes, which define the BYORP effect torque that acts on the system. After detailing the theory, we analyze each of the wide-asynchronous-binary members and candidates to assess their most likely formation mechanism. Finally, we suggest possible future observations to check and constrain our hypothesis.

Inertial wave beams and inertial wave modes in a rotating cylinder with time-modulated rotation rate

NASA Astrophysics Data System (ADS)

Borcia, Ion D.; Ghasemi V., Abouzar; Harlander, Uwe

2014-05-01

Inertial gravity waves play an crucial role in atmospheres, oceans, and the fluid inside of planets and moons. In the atmosphere, the effect of rotation is neglected for small wavelength and the waves bear the character of internal gravity waves. For long waves, the hydrostatic assumption is made which in turn makes the atmosphere inelastic with respect to inertial motion. In contrast, in the Earth's interior, pure inertial waves are considered as an important fundamental part of the motion. Moreover, as the deep ocean is nearly homogeneous, there the inertial gravity waves bear the character of inertial waves. Excited at the oceans surface mainly due to weather systems the waves can propagate downward and influence the deep oceans motion. In the light of the aforesaid it is important to understand better fundamental inertial wave dynamics. We investigate inertial wave modes by experimental and numerical methods. Inertial modes are excited in a fluid filled rotating annulus by modulating the rotation rate of the outer cylinder and the upper and lower lids. This forcing leads to inertial wave beams emitted from the corner regions of the annulus due to periodic motions in the boundary layers (Klein et al., 2013). When the forcing frequency matches with the eigenfrequency of the rotating annulus the beam pattern amplitude is increasing, the beams broaden and mode structures can be observed (Borcia et al., 2013a). The eigenmodes are compared with analytical solutions of the corresponding inviscid problem (Borcia et al, 2013b). In particular for the pressure field a good agreement can be found. However, shear layers related to the excited wave beams are present for all frequencies. This becomes obvious in particular in the experimental visualizations that are done by using Kalliroscope particles, highlighting relative motion in the fluid. Comparing the eigenfrequencies we find that relative to the analytical frequencies, the experimental and numerical ones show a small shift towards higher frequencies. This frequency shift is due to the reduction of the effective resonance volume that results from the existence of a Stokes boundary layer at the outer librating wall. Due to the symmetry of the forcing not all possible modes can be excited. It is shown that only symmetric modes with respect to the rotation axis exist. From a fundamental perspective, the study might help to understand better inertial mode excitation in librating planets and moons where inertial waves are emitted from critical points on the inner or outer spherical boundary. Recently, Zhang et al. (2013) pointed out the resonance should not occur in symmetric librating bodies without precession. We will discuss how this assumption depends on the boundary conditions. It might turn out that even when the projection of the Euler (or Poincare) force on the modes is zero, the projection of the excited wave beams on the modes is non-zero. K. Zhang, K. H. Chan, X. Liao, and J. M. Aurnou. The non-resonant response of fluid in a rapidly rotating sphere undergoing longitudinal libration, J. Fluid Mech.,720, 212-235, 2013. I. D. Borcia and U. Harlander. Inertial waves in a rotating annulus with inclined inner cylinder, Theoret. Comp. Fluid Dynamics, 27, 397-413, 2013. I. D. Borcia, A. Ghasemi V., and U. Harlander. Inertial wave mode excitation inside a rotating cylindrical container with librating walls, submitted to Fluid Dyn. Res.,2013. M. Klein, T. Seelig, M. V. Kurgansky, A. Ghasemi V., I. D. Borcia, A. Will, E. Schaller, C. Egbers, and Uwe Harlander. Inertial wave excitation and focusing in a liquid bounded by a frustum and a cylinder, submitted to J. Fluid Mech., 2013.

Computation of the Quantities Describing the Lunar Librations in the Astronomical Almanac

DTIC Science & Technology

2010-08-01

this system ~e ( COS( -(3) cost >. + 180’ - tt)) cost -(3) sine>. + 180’ - tt) sin(-(3) , (1) Consid~r neXt, point M referred to axes OX’’z’ iIi...now write (7) as the three equl\\tions " cos b cos(1 + LM - tt) = cosj3 cost >. - tt - N) cos b sin(1 + LM - tt) ,= cos Lcosj3si,n(>’,- tt -’N) ,- sin...8217?’~ on . .the sel~~~centric sphere. The geocentric right ascension and declination of the Moon are 0:, 0 and so the right ascension and declination of

Resonance capture and dynamics of three-planet systems

NASA Astrophysics Data System (ADS)

Charalambous, C.; Martí, J. G.; Beaugé, C.; Ramos, X. S.

2018-06-01

We present a series of dynamical maps for fictitious three-planet systems in initially circular coplanar orbits. These maps have unveiled a rich resonant structure involving two or three planets, as well as indicating possible migration routes from secular to double resonances or pure three-planet commensurabilities. These structures are then compared to the present-day orbital architecture of observed resonant chains. In a second part of the paper, we describe N-body simulations of type-I migration. Depending on the orbital decay time-scale, we show that three-planet systems may be trapped in different combinations of independent commensurabilities: (i) double resonances, (ii) intersection between a two-planet and a first-order three-planet resonances, and (iii) simultaneous libration in two first-order three-planet resonances. These latter outcomes are found for slow migrations, while double resonances are almost always the final outcome in high-density discs. Finally, we discuss an application to the TRAPPIST-1 system. We find that, for low migration rates and planetary masses of the order of the estimated values, most three-planet sub-systems are able to reach the observed double resonances after following evolutionary routes defined by pure three-planet resonances. The final orbital configuration shows resonance offsets comparable with present-day values without the need of tidal dissipation. For the 8/5 resonance proposed to dominate the dynamics of the two inner planets, we find little evidence of its dynamical significance; instead, we propose that this relation between mean motions could be a consequence of the interaction between a pure three-planet resonance and a two-planet commensurability between planets c and d.

Use of the moon to support on-orbit sensor calibration for climate change measurements

USGS Publications Warehouse

Stone, T.C.; Kieffer, H.H.

2006-01-01

Production of reliable climate datasets from multiple observational measurements acquired by remote sensing satellite systems available now and in the future places stringent requirements on the stability of sensors and consistency among the instruments and platforms. Detecting trends in environmental parameters measured at solar reflectance wavelengths (0.3 to 2.5 microns) requires on-orbit instrument stability at a level of 1% over a decade. This benchmark can be attained using the Moon as a radiometric reference. The lunar calibration program at the U.S. Geological Survey has an operational model to predict the lunar spectral irradiance with precision ???1%, explicitly accounting for the effects of phase, lunar librations, and the lunar surface photometric function. A system for utilization of the Moon by on-orbit instruments has been established. With multiple lunar views taken by a spacecraft instrument, sensor response characterization with sub-percent precision over several years has been achieved. Meteorological satellites in geostationary orbit (GEO) capture the Moon in operational images; applying lunar calibration to GEO visible-channel image archives has the potential to develop a climate record extending decades into the past. The USGS model and system can provide reliable transfer of calibration among instruments that have viewed the Moon as a common source. This capability will be enhanced with improvements to the USGS model absolute scale. Lunar calibration may prove essential to the critical calibration needs to cover a potential gap in observational capabilities prior to deployment of NPP/NPOESS. A key requirement is that current and future instruments observe the Moon.

Determination of Phobos' rotational parameters by an inertial frame bundle block adjustment

NASA Astrophysics Data System (ADS)

Burmeister, Steffi; Willner, Konrad; Schmidt, Valentina; Oberst, Jürgen

2018-01-01

A functional model for a bundle block adjustment in the inertial reference frame was developed, implemented and tested. This approach enables the determination of rotation parameters of planetary bodies on the basis of photogrammetric observations. Tests with a self-consistent synthetic data set showed that the implementation converges reliably toward the expected values of the introduced unknown parameters of the adjustment, e.g., spin pole orientation, and that it can cope with typical observational errors in the data. We applied the model to a data set of Phobos using images from the Mars Express and the Viking mission. With Phobos being in a locked rotation, we computed a forced libration amplitude of 1.14^circ ± 0.03^circ together with a control point network of 685 points.

Computer simulating observations of the Lunar physical libration for the Japanese Lunar project ILOM

NASA Astrophysics Data System (ADS)

Petrova, Natalia; Hanada, Hideo

2010-05-01

In the frame of the second stage of the Japanese space mission SELENE-2 (Hanada et al. 2009) the project ILOM (In-situ Lunar Orientation Measurement) planned after 2017years is a kind of instrument for positioning on the Moon. It will be set near the lunar pole and will determine parameters of lunar physical libration by positioning of several tens of stars in the field of view regularly for longer than one year. Presented work is dedicated to analyses of computer simulating future observations. It's proposed that for every star crossing lunar prime meridian its polar distance will be to measure. The methods of optimal star observation are being developed for the future experiment. The equations are constructed to determine libration angles ? (t),ρ(t),σ(t)- on the basis of observed polar distances pobs: (| f1(?,ρ,Iσ,pobs) = 0 |{ f2(?,ρ,Iσ,pobs) = 0 | f3(?,ρ,Iσ,pobs) = 0 |( or f(X) = 0, where ; f = ? f1 ? | f2 | |? f3 |? X = ? ? ? | ρ | |? Iσ |? (1) At the present stage we have developed the software for selection of stars for these future polar observations. Stars were taken from various stellar catalogues, such as the UCAC2-BSS, Hipparcos, Tycho and FK6. The software reduces ICRS coordinates of star to selenographical system at the epoch of observation (Petrova et al., 2009). For example, to the epochs 2017 - 2018 more than 50 stars brighter than m = 12 were selected for the northern pole. In total, these stars give about 600 crossings of the prime meridian during one year. Nevertheless, only a few stars (2-5) may be observed in a vicinity of the one moment. This is not enough to have sufficient sample to exclude various kind of errors. The software includes programmes which can determine the moment of transition of star across the meridian and theoretical values of libration angles at this moments. A serious problem arises when we try to solve equations (1) with the purpose to determine libration angles on the basis of simulated pobs.. Polar distances are calculated using the analytical theory of physical libration Petrova et al. (2008; 2009). We cannot use Newton's method for solution of the equation, because the Jacobian | | || δδfx11 δδfx12 δδf1x3-|| || δδfx2 δδfx2 δδf2x-|| J(X ) = || δf13 δf23 δ3f3-|| = 0. || δx1 δx2 δx3 || We transformed equations to the iteration form xi = φi(X). Used iteration methods have unsatisfactory convergence: inaccuracy in polar distance of 1 milliseconds of arc causes inaccuracy of 0.01arcsec in ρ and in Iσ, and 0.1 arcsec in ?. Results of our computer simulating showed It's necessary to carry out measuring of polar distances of stars in several meridians simultaneously to increase sample of stars. It's necessary to find additional links (relations) between observed parameters and libration angles to have stable mathematical methods to receive solutions for lunar rotation with high accuracy. The research was supported by the Russian-Japanese grant RFFI-JSPS 09-02-92113, (2009-2010) References: Hanada H., Noda H., Kikuchi F. et al., 2009. Different kind of observations of lunar rotation and gravity for SELENE-2. Proc of conf. Astrokazan-2009, August 19 - 26, Kazan, Russia. p. 172-175 Petrova N., Gusev A., Kawano N., Hanada H., 2008. Free librations of the two-layer Moon and the possibilities of their detection. Advances in Space Res., v 42, p. 1398-1404 Petrova N., Gusev A., Hanada H., Ivanova T., Akutina V., 2009. Application of the analytical theory of Lunar physical libration for simulating observations of stars for the future Japanese project ILOM. Proc of conf. Astrokazan-2009, August 19 - 26, Kazan, Russia. p.197 - 201.

A technique for processing of planetary images with heterogeneous characteristics for estimating geodetic parameters of celestial bodies with the example of Ganymede

NASA Astrophysics Data System (ADS)

Zubarev, A. E.; Nadezhdina, I. E.; Brusnikin, E. S.; Karachevtseva, I. P.; Oberst, J.

2016-09-01

The new technique for generation of coordinate control point networks based on photogrammetric processing of heterogeneous planetary images (obtained at different time, scale, with different illumination or oblique view) is developed. The technique is verified with the example for processing the heterogeneous information obtained by remote sensing of Ganymede by the spacecraft Voyager-1, -2 and Galileo. Using this technique the first 3D control point network for Ganymede is formed: the error of the altitude coordinates obtained as a result of adjustment is less than 5 km. The new control point network makes it possible to obtain basic geodesic parameters of the body (axes size) and to estimate forced librations. On the basis of the control point network, digital terrain models (DTMs) with different resolutions are generated and used for mapping the surface of Ganymede with different levels of detail (Zubarev et al., 2015b).

Fracture formation post impact on Enceladus?

NASA Astrophysics Data System (ADS)

Craft, Kathleen; Roberts, James

2017-10-01

Saturn’s small icy moon Enceladus was observed by the Cassini mission to have jets of ice and vapor emanating from its southern polar terrain (SPT), creating a plume. The fact that the activity is only observed in one region has not been well explained. Hypotheses include a regional sea beneath the SPT or a global ocean that is thicker beneath the SPT, which feeds a group of fractures observed there called the tiger stripes. As Enceladus orbits Saturn, stresses acting on the moon may open and close the fractures enabling interior volatiles to escape and form the plume. Here we investigate how these fractures could have formed and the activity begun. We propose that an impact could have either punctured through or caused substantial melt and fracturing in an ice shell connecting to a liquid layer below. Our goal is to determine whether a formation of fractures resembling the tiger stripes could emerge post-impact.Previous work by Roberts and Stickle (LPSC 2017, #1955) modeled an impact into an ice shell over an ocean and calculated penetration depth and melt temperatures and volumes through the shell thickness. Fracturing would occur during and after the impact, the crater would collapse, water would begin to refreeze and subsequent fluid exchange would occur. Working forward from a point after impact and as the ice shell begins refreezing, we performed finite element modeling to simulate the probable formation of fractures based on the resulting stress regime. Here we explore fracture formation for shells ranging from 1 km to 5 km thick (consistent with gravity and libration studies), to explore formation as the shell cools and thickens through time. We emplaced several fractures, penetrating either entirely or partially across the base to surface. Fracture interactions, tidal stress forcing with orbital true anomalies and ocean water pressurization are considered free parameters in the model. We present results for a number of parameter value combinations and quantify fracture formation sensitivities to model parameters.

Tidal dissipation in a homogeneous spherical body. II. Three examples: Mercury, Io, and Kepler-10 b

DOE Office of Scientific and Technical Information (OSTI.GOV)

Makarov, Valeri V.; Efroimsky, Michael, E-mail: vvm@usno.navy.mil, E-mail: michael.efroimsky@usno.navy.mil

In Efroimsky and Makarov (Paper I), we derived from the first principles a formula for the tidal heating rate in a homogeneous sphere, compared it with the previously used formulae, and noted the differences. Now we present case studies: Mercury, Kepler-10 b, and a triaxial Io. A sharp frequency dependence of k {sub 2}/Q near spin-orbit resonances yields a sharp dependence of k {sub 2}/Q (and, therefore, of tidal heating) upon the spin rate. Thereby physical libration plays a major role in tidal heating of synchronously rotating planets. The magnitude of libration in the spin rate being defined by themore » planet's triaxiality, the latter becomes a factor determining the dissipation rate. Other parameters equal, a strongly triaxial synchronized body generates more heat than a similar body of a more symmetrical shape. After an initially triaxial object melts and loses its triaxiality, dissipation becomes less intensive; the body can solidify, with the tidal bulge becoming a new figure with triaxiality lower than the original. We derive approximate expressions for the dissipation rate in a Maxwell planet with the Maxwell time longer than the inverse tidal frequency. The expressions derived pertain to the 1:1 and 3:2 resonances and a nonresonant case; so they are applicable to most close-in super-Earths detected. In these planets, the heating outside synchronism is weakly dependent on the eccentricity and obliquity, provided both these parameters's values are moderate. According to our calculation, Kepler-10 b could hardly survive the intensive tidal heating without being synchronized, circularized, and reshaped through a complete or partial melt-down.« less

Exploration Platform in the Earth-Moon Libration System Based on ISS

NASA Technical Reports Server (NTRS)

Raftery, Michael; Derechin, Alexander

2012-01-01

International Space Station (ISS) industry partners have been working for the past two years on concepts using ISS development methods and residual assets to support a broad range of exploration missions. These concepts have matured along with planning details for NASA's Space Launch System (SLS) and Multi-Purpose Crew Vehicle (MPCV) to allow serious consideration for a platform located in the Earth-Moon Libration (EML) system. This platform would provide a flexible basis for future exploration missions and would significantly reduce costs because it will enable re-use of expensive spacecraft and reduce the total number of launches needed to accomplish these missions. ISS provides a robust set of methods which can be used to test systems and capabilities needed for missions to the Moon, Mars, asteroids and other potential destinations. We will show how ISS can be used to reduce risk and improve operational flexibility for missions beyond low earth orbit through the development of a new Exploration Platform based in the EML system. The benefits of using the EML system as a gateway will be presented along with additional details of a lunar exploration mission concept. International cooperation is a critical enabler and ISS has already demonstrated successful management of a large multi-national technical endeavor. We will show how technology developed for ISS can be evolved and adapted to the new exploration challenge. New technology, such as electric propulsion and advanced life support systems can be tested and proven at ISS as part of an incremental development program. Finally, we will describe how the EML Platform could be built and deployed and how International access for crew and cargo could be provided.

Measurements of Mercury's spin state and inferences about its interior

NASA Astrophysics Data System (ADS)

Margot, J.; Padovan, S.; Peale, S. J.; Solomon, S. C.

2011-12-01

Over the past nine years we have used the Green Bank Telescope (GBT) in conjunction with the Goldstone Solar System Radar (GSSR) to characterize the spin state and interior of Mercury. We implemented a technique [1,2] that provides instantaneous spin rate measurements with 10-5 fractional precision and spin orientation measurements at the arcsecond level. On the basis of measurements at 21 distinct epochs between 2002 and 2006, we found observational evidence that Mercury closely follows a Cassini state and that it exhibits forced librations in longitude [3], as predicted by theory [4,5]. A long-period (˜12 year) libration signature may be present in the data. Since 2006 we have secured measurements at 11 additional epochs (out of 23 attempts). We are in the process of re-analyzing the entire set of observations with the goals of (1) refining the determination of the obliquity and of the libration amplitude, two parameters that are critical in the determination of the core size; (2) confirming the presence or absence of a long-period libration component, with the prospect of elucidating the excitation mechanism; (3) quantifying deviations of the pole from the strict Cassini state, which could inform us about dissipation due to solid-body tides and core-mantle interactions. Our first goal is particularly important now that MESSENGER is securing measurements of the low-degree gravitational harmonics with an expected precision of better than 1%. The core-size error budget indicates that the precision of the ground-based estimates of obliquity and librations will ultimately dictate the quality of the core size determination, as well as the attendant inferences regarding the interior structure, thermal evolution, and magnetic field generation of the planet. [1] Green, in Radar Astronomy, McGraw-Hill, 1968. [2] Holin, Radiophys. Quant. Elec. 31, 1988. [3] Margot et al, Science 316, 2007. [4] Peale, Nature 262, 1976. [5] Peale, in Mercury, U. of Arizona Press, 1988.

Breaking mean-motion resonances during Type I planet migration

NASA Astrophysics Data System (ADS)

Hands, T. O.; Alexander, R. D.

2018-03-01

We present 2D hydrodynamical simulations of pairs of planets migrating simultaneously in the Type I regime in a protoplanetary disc. Convergent migration naturally leads to the trapping of these planets in mean-motion resonances. Once in resonance the planets' eccentricity grows rapidly, and disc-planet torques cause the planets to escape resonance on a time-scale of a few hundred orbits. The effect is more pronounced in highly viscous discs, but operates efficiently even in inviscid discs. We attribute this resonance-breaking to overstable librations driven by moderate eccentricity damping, but find that this mechanism operates differently in hydrodynamic simulations than in previous analytic calculations. Planets escaping resonance in this manner can potentially explain the observed paucity of resonances in Kepler multitransiting systems, and we suggest that simultaneous disc-driven migration remains the most plausible means of assembling tightly packed planetary systems.

Radio Navigation Beacons on the Moon, Lunar Geodetic VLBI System, Physical Libration of the Moon for Chang'E-3/4, Luna-Glob, Luna-Resource and SELENE-2 Projects

NASA Astrophysics Data System (ADS)

Gusev, Alexander; Ping, Jinsong; Hanada, Hideo; Kikuchi, Fuyuhiko; Kosov, Alexander; Li, Jinling; Titov, Oleg

2014-12-01

The future lunar missions of Chang'E-3/4, Luna-Glob, Luna-Resource, and SELENE-2 will consist of a lander and an orbiter. Using the Lunar Same Beam, Differential and Inverse VLBI technologies, we anticipate to determine the coordinates of the radio beacons on the lunar surface with an accuracy of 1 mm for various space projects on the Moon. Small radio telescopes being installed on the surface of the Moon and incorporated into the existing network will help to improve the traditional IVS products by a factor of ten or even more. The model of the two-layer Moon gives several normal rotational modes--Chandler Wobble and Free Core Nutation. They can play an important role in the determination of the core parameters.

Rotation-libration in a hierarchic supramolecular rotor-stator system: arrhenius activation and retardation by local interaction.

PubMed

Wahl, Markus; Stöhr, Meike; Spillmann, Hannes; Jung, Thomas A; Gade, Lutz H

2007-04-07

Fourfold symmetric zinc-octaethylporphyrin (OEP) has been incorporated in the holes of the hexagonal molecular network generated by thermal dehydrogenation of 4,9-diaminoperylene-quinone-3,10-diimine (DPDI) on a Cu(111) surface and displayed hindered rotation; the reorganization between the potential minima, a rotation-libration, which is characterized by an activation energy of ED=0.17+/-0.03 eV, has been monitored in the STM tunnelling currents as a bi-state "switching".

LASER APPLICATIONS AND OTHER TOPICS IN QUANTUM ELECTRONICS: Study of the subpicosecond rotational molecular dynamics in liquids

NASA Astrophysics Data System (ADS)

Nikiforov, V. G.; Lobkov, Vladimir S.

2006-10-01

The parameters of the femtosecond vibration—rotation molecular dynamics of liquid acetonitrile CH3CN, trimethylacetonitrile (CH3)3CCN, propionitrile CH3CH2CN, fluoroform CHF3, and chloroform CHCl3 are found by analysing the ultrafast optical Kerr effect. The influence of the molecular structure on the features of rotational (diffusion and libration) motions is studied. It is shown that the distribution of libration frequencies is described by the Maxwell distribution.

Orbit Determination of Spacecraft in Earth-Moon L1 and L2 Libration Point Orbits

NASA Technical Reports Server (NTRS)

Woodard, Mark; Cosgrove, Daniel; Morinelli, Patrick; Marchese, Jeff; Owens, Brandon; Folta, David

2011-01-01

The ARTEMIS mission, part of the THEMIS extended mission, is the first to fly spacecraft in the Earth-Moon Lissajous regions. In 2009, two of the five THEMIS spacecraft were redeployed from Earth-centered orbits to arrive in Earth-Moon Lissajous orbits in late 2010. Starting in August 2010, the ARTEMIS P1 spacecraft executed numerous stationkeeping maneuvers, initially maintaining a lunar L2 Lissajous orbit before transitioning into a lunar L1 orbit. The ARTEMIS P2 spacecraft entered a L1 Lissajous orbit in October 2010. In April 2011, both ARTEMIS spacecraft will suspend Lissajous stationkeeping and will be maneuvered into lunar orbits. The success of the ARTEMIS mission has allowed the science team to gather unprecedented magnetospheric measurements in the lunar Lissajous regions. In order to effectively perform lunar Lissajous stationkeeping maneuvers, the ARTEMIS operations team has provided orbit determination solutions with typical accuracies on the order of 0.1 km in position and 0.1 cm/s in velocity. The ARTEMIS team utilizes the Goddard Trajectory Determination System (GTDS), using a batch least squares method, to process range and Doppler tracking measurements from the NASA Deep Space Network (DSN), Berkeley Ground Station (BGS), Merritt Island (MILA) station, and United Space Network (USN). The team has also investigated processing of the same tracking data measurements using the Orbit Determination Tool Kit (ODTK) software, which uses an extended Kalman filter and recursive smoother to estimate the orbit. The orbit determination results from each of these methods will be presented and we will discuss the advantages and disadvantages associated with using each method in the lunar Lissajous regions. Orbit determination accuracy is dependent on both the quality and quantity of tracking measurements, fidelity of the orbit force models, and the estimation techniques used. Prior to Lissajous operations, the team determined the appropriate quantity of tracking measurements that would be needed to meet the required orbit determination accuracies. Analysts used the Orbit Determination Error Analysis System (ODEAS) to perform covariance analyses using various tracking data schedules. From this analysis, it was determined that 3.5 hours of DSN TRK-2-34 range and Doppler tracking data every other day would suffice to meet the predictive orbit knowledge accuracies in the Lissajous region. The results of this analysis are presented. Both GTDS and ODTK have high-fidelity environmental orbit force models that allow for very accurate orbit estimation in the lunar Lissajous regime. These models include solar radiation pressure, Earth and Moon gravity models, third body gravitational effects from the Sun, and to a lesser extent third body gravitational effects from Jupiter, Venus, Saturn, and Mars. Increased position and velocity uncertainties following each maneuver, due to small execution performance errors, requires that several days of post-maneuver tracking data be processed to converge on an accurate post-maneuver orbit solution. The effects of maneuvers on orbit determination accuracy will be presented, including a comparison of the batch least squares technique to the extended Kalman filter/smoother technique. We will present the maneuver calibration results derived from processing post-maneuver tracking data. A dominant error in the orbit estimation process is the uncertainty in solar radiation pressure and the resultant force on the spacecraft. An estimation of this value can include many related factors, such as the uncertainty in spacecraft reflectivity and surface area which is a function of spacecraft orientation (spin-axis attitude), uncertainty in spacecraft wet mass, and potential seasonal variability due to the changing direction of the Sun line relative to the Earth-Moon Lissajous reference frame. In addition, each spacecraft occasionally enters into Earth or Moon penumbra or umbra and these shadow crossings reduche solar radiation force for several hours. The effects of these events on orbit determination accuracy will be presented. In order to plan for upcoming stationkeeping maneuvers, the maneuver planning team must take the current orbit estimate, propagate it forward to the planned maneuver time, and determine the optimal maneuver to maintain the Lissajous orbit for one or more revolutions. The propagation is performed using a Runge-Kutta 7/8 integrator and typically the position and velocity uncertainty increases with propagation time, increasing the overall uncertainty of the orbit state at the maneuver execution time. The effect of orbit knowledge uncertainty on stationkeeping operations will be presented.

Significance of specific force models in two applications: Solar sails to sun-earth L4/L5 and grail data analysis suggesting lava tubes and buried craters on the moon

NASA Astrophysics Data System (ADS)

Sood, Rohan

In the trajectory design process, gravitational interaction between the bodies of interest plays a key role in developing the over-arching force model. However, non-gravitational forces, such as solar radiation pressure (SRP), can significantly influence the motion of a spacecraft. Incorporating SRP within the dynamical model can assist in estimating the trajectory of a spacecraft with greater precision, in particular, for a spacecraft with a large area-to-mass ratio, i.e., solar sails. Subsequently, in the trajectory design process, solar radiation pressure can be leveraged to maneuver the sail-based spacecraft. First, to construct low energy transfers, the invariant manifolds are explored that form an important tool in the computation and design of complex trajectories. The focus is the investigation of trajectory design options, incorporating solar sail dynamics, from the Earth parking orbit to the vicinity of triangular Lagrange points. Thereafter, an optimization scheme assisted in investigating the ?V requirement to depart from the Earth parking orbit. Harnessing the solar radiation pressure, the spacecraft is delivered to the vicinity of the displaced Lagrange point and maintains a trajectory close to the artificial libration point with the help of the solar sail. However, these trajectories are converged in a model formulated as a three-body problem with additional acceleration from solar radiation pressure. Thus, the trajectories are transitioned to higher fidelity ephemeris model to account for additional perturbing accelerations that may dominate the sail-craft dynamics and improve upon the trajectory design process. Alternatively, precise knowledge of the motion of a spacecraft about a central body and the contribution of the SRP can assist in deriving a highly accurate gravity field model. The high resolution gravity data can potentially assist in exploring the surface and subsurface properties of a particular body. With the goal of expanding human presence beyond Earth, sub-surface empty lava tubes on other worlds form ideal candidates for creating a permanent habitation environment safe from cosmic radiation, micrometeorite impacts and temperature extremes. In addition, gravitational analysis has also revealed large buried craters under thick piles of mare basalt, shedding light on Moon's dynamic and hostile past. In this work, gravity mapping observations from NASA's Gravity Recovery and Interior Laboratory (GRAIL) are employed to detect the presence of potential empty lava tubes and large impact craters buried beneath the lunar maria.

Periodic orbits around areostationary points in the Martian gravity field

NASA Astrophysics Data System (ADS)

Liu, Xiao-Dong; Baoyin, Hexi; Ma, Xing-Rui

2012-05-01

This study investigates the problem of areostationary orbits around Mars in three-dimensional space. Areostationary orbits are expected to be used to establish a future telecommunication network for the exploration of Mars. However, no artificial satellites have been placed in these orbits thus far. The characteristics of the Martian gravity field are presented, and areostationary points and their linear stability are calculated. By taking linearized solutions in the planar case as the initial guesses and utilizing the Levenberg-Marquardt method, families of periodic orbits around areostationary points are shown to exist. Short-period orbits and long-period orbits are found around linearly stable areostationary points, but only short-period orbits are found around unstable areostationary points. Vertical periodic orbits around both linearly stable and unstable areostationary points are also examined. Satellites in these periodic orbits could depart from areostationary points by a few degrees in longitude, which would facilitate observation of the Martian topography. Based on the eigenvalues of the monodromy matrix, the evolution of the stability index of periodic orbits is determined. Finally, heteroclinic orbits connecting the two unstable areostationary points are found, providing the possibility for orbital transfer with minimal energy consumption.

Work on a New Solar-System Ephemeris: Status Report

NASA Astrophysics Data System (ADS)

Mai, Enrico; Müller, Jürgen

2014-05-01

Currently, within a coordinated project in Germany, integrated methods and procedures for a consistent definition and realization of reference systems on Earth and in space are being developed. Barycentric ephemerides represent a dynamical realization of the Barycentric Celestial Reference System (BCRS), which is fundamental not only for the problem of interplanetary navigation but through its intimate relation to the Geocentric Celestial Reference System (GCRS). In accordance with existing renowned ephemerides (INPOP, DE, EPM) we want to lay the foundation for a new solar-system ephemeris. We collected available observational data for the planets as well as high-precise tracking data to various spacecrafts (interplanetary probes, planetary orbiters and landers). Furthermore, we set up the usual relativistic (post-Newtonian) force model in line with the latest French INPOP ephemeris, with a few exceptions. The focus in modeling is on the lunar librations and asteroid perturbations. Regarding the treatment of the Moon, we draw upon the elaborated modeling within the existing LLR analysis software at IfE and its ongoing improvements. Nowadays, any modern ephemeris, besides perturbations due to general mass inhomogeneities (at least for the Earth and the Moon) and solar flattening, respective figure-figure interactions and tidal effects, proper rotations and librations etc., has to account for the significant gravitational effect of the vast number of minor bodies in the solar-system (especially within the major asteroid belt between Mars and Jupiter) on the long-term evolution of planetary orbits. Due to limited computational resources, one is able to integrate the equations of motion (EOM) of only a comparatively small selection of asteroids simultaneously with the EOM of the major solar-system bodies (i.e., planets, Sun, Moon). On the other hand, one can efficiently account for the remaining asteroids by the introduction of at least one mass ring, the parameters of which (radius, total mass) have to be carefully modeled. Regarding the latter issue we will test the usability of an evolution strategy instead of a simple Monte Carlo method. In future, asteroid modeling will strongly benefit from observational data of the recently started GAIA mission. Here we present a few statistics on the collected observational data, the fundamental force model of the EOM in detail, and first computational results in comparison with the INPOP ephemeris.

Ultrafast dynamics of liquid water: Energy relaxation and transfer processes of the OH stretch and the HOH bend

DOE Office of Scientific and Technical Information (OSTI.GOV)

Imoto, Sho; Xantheas, Sotiris S.; Saito, Shinji

2015-08-27

The vibrational energy relaxation and transfer processes of the OH stretching and the HOH bending vibrations in liquid water are investigated via the theoretical calculation of the pump-probe spectra obtained from non-equilibrium molecular dynamics simulations with the TTM3-F interaction potential. The excitation of the OH stretch induces an instantaneous response of the high frequency librational motions in the 600-1000 cm-1 range. In addition, the excess energy of the OH stretch of a water molecule quickly transfers to the OH stretches of molecules in its first hydration shell with a time constant of ~50 fs, followed by relaxation to the HOHmore » bends of the surrounding molecules with a time constant of 230 fs. The excitation of the HOH bend also results in the ultrafast excitation of the high frequency librational motions. The energy of the excited HOH bend of a water molecule decays, with a time constant of 200 fs, mainly to the relaxation of the HOH bends of its surrounding molecules. The energies of the HOH bends were found to transfer quickly to the intermolecular motions via the coupling with the high frequency librational motions. The excess energy of the OH stretch or the HOH bend relaxes to the high frequency intermolecular librational motions and eventually to the hot ground state with a time scale of ~1 ps via the coupling with the librational and translational motions. The energy relaxation and transfer processes were found to depend on the local hydrogen bonding network; the relaxations of the excess energy of the OH stretch and the HOH bend of four- and five-coordinated molecules are faster than those of a three-coordinated molecule due to the delocalization of the vibrational motions of the former (four- and five-coordinated molecules) compared to those of the later (three-coordinated molecules). The present results highlight the importance of the high frequency intermolecular librational modes in facilitating the ultrafast energy relaxation process in liquid water via their strong nonlinear couplings with the intramolecular OH stretching and HOH bending vibrations. S.S.X. acknowledges the support of the U.S. Department of Energy, Office of Science, Office of Basic Energy Sciences, Division of Chemical Sciences, Geosciences, and Biosciences. Pacific Northwest National Laboratory (PNNL) is a multiprogram national laboratory operated for DOE by Battelle. The calculation was carried out using the computing resources at the Research Center for Computational Science in Okazaki, Japan.« less

Nucleic acid binding drugs. Part XIII. Molecular motion in a drug-nucleic acid model system: thermal motion analysis of a proflavine-dinucleoside crystal structure.

PubMed Central

Aggarwal, A K; Neidle, S

1985-01-01

The high-resolution crystal structure of the intercalation complex between proflavine and cytidylyl-3',5'-guanosine (CpG) has been studied by thermalmotion analysis. This has provided information on the translational and librational motions of individual groups in the complex. Many of these motions are similar to, though of larger magnitude than in uncomplexed dinucleosides. Pronounced librational effects were observed along the base pairs and in the plane of the drug chromophore. PMID:4034394

The analytical and numerical approaches to the theory of the Moon's librations: Modern analysis and results

NASA Astrophysics Data System (ADS)

Petrova, N.; Zagidullin, A.; Nefedyev, Y.; Kosulin, V.; Andreev, A.

2017-11-01

Observing physical librations of celestial bodies and the Moon represents one of the astronomical methods of remotely assessing the internal structure of a celestial body without conducting expensive space experiments. The paper contains a review of recent advances in studying the Moon's structure using various methods of obtaining and applying the lunar physical librations (LPhL) data. In this article LPhL simulation methods of assessing viscoelastic and dissipative properties of the lunar body and lunar core parameters, whose existence has been recently confirmed during the seismic data reprocessing of ;Apollo; space mission, are described. Much attention is paid to physical interpretation of the free librations phenomenon and the methods for its determination. In the paper the practical application of the most accurate analytical LPhL tables (Rambaux and Williams, 2011) is discussed. The tables were built on the basis of complex analytical processing of the residual differences obtained when comparing long-term series of laser observations with the numerical ephemeris DE421. In the paper an efficiency analysis of two approaches to LPhL theory is conducted: the numerical and the analytical ones. It has been shown that in lunar investigation both approaches complement each other in various aspects: the numerical approach provides high accuracy of the theory, which is required for the proper processing of modern observations, the analytical approach allows to comprehend the essence of the phenomena in the lunar rotation, predict and interpret new effects in the observations of lunar body and lunar core parameters.

Inelastic neutron scattering and molecular simulation of the dynamics of interlayer water in smectite clay minerals

DOE PAGES

Cygan, Randall T.; Daemen, Luke L.; Ilgen, Anastasia G.; ...

2015-11-16

The study of mineral–water interfaces is of great importance to a variety of applications including oil and gas extraction, gas subsurface storage, environmental contaminant treatment, and nuclear waste repositories. Understanding the fundamentals of that interface is key to the success of those applications. Confinement of water in the interlayer of smectite clay minerals provides a unique environment to examine the interactions among water molecules, interlayer cations, and clay mineral surfaces. Smectite minerals are characterized by a relatively low layer charge that allows the clay to swell with increasing water content. Montmorillonite and beidellite varieties of smectite were investigated to comparemore » the impact of the location of layer charge on the interlayer structure and dynamics. Inelastic neutron scattering of hydrated and dehydrated cation-exchanged smectites was used to probe the dynamics of the interlayer water (200–900 cm –1 spectral region) and identify the shift in the librational edge as a function of the interlayer cation. Molecular dynamics simulations of equivalent phases and power spectra, derived from the resulting molecular trajectories, indicate a general shift in the librational behavior with interlayer cation that is generally consistent with the neutron scattering results for the monolayer hydrates. Both neutron scattering and power spectra exhibit librational structures affected by the location of layer charge and by the charge of the interlayer cation. Furthermore, divalent cations (Ba 2+ and Mg 2+) characterized by large hydration enthalpies typically exhibit multiple broad librational peaks compared to monovalent cations (Cs + and Na +), which have relatively small hydration enthalpies.« less

Mean flow generation mechanism by inertial waves and normal modes

NASA Astrophysics Data System (ADS)

Will, Andreas; Ghasemi, Abouzar

2016-04-01

The mean flow generation mechanism by nonlinearity of the inertial normal modes and inertial wave beams in a rotating annular cavity with longitudinally librating walls in stable regime is discussed. Inertial normal modes (standing waves) are excited when libration frequency matches eigenfrequencies of the system. Inertial wave beams are produced by Ekman pumping and suction in a rotating cylinder and form periodic orbits or periodic ray trajectories at selected frequencies. Inertial wave beams emerge as concentrated shear layers in a librating annular cavity, while normal modes appear as global recirculation cells. Both (inertial wave beam and mode) are helical and thus intrinsically non-linear flow structures. No second mode or wave is necessary for non-linearity. We considered the low order normal modes (1,1), (2,1) and (2,2) which are expected to be excited in the planetary objects and investigate the mean flow generation mechanism using two independent solutions: 1) analytical solution (Borcia 2012) and 2) the wave component of the flow (ω0 component) obtained from the direct numerical simulation (DNS). It is well known that a retrograde bulk mean flow is generated by the Ekman boundary layer and E1/4-Stewartson layer close to the outer cylinder side wall due to libration. At and around the normal mode resonant frequencies we found additionally a prograde azimuthal mean flow (Inertial Normal Mode Mean Flow: INMMF) in the bulk of the fluid. The fluid in the bulk is in geostrophic balance in the absence of the inertial normal modes. However, when INMMF is excited, we found that the geostrophic balance does not hold in the region occupied by INMMF. We hypothesize that INMMF is generated by the nonlinearity of the normal modes or by second order effects. Expanding the velocity {V}(u_r,u_θ,u_z) and pressure (p) in a power series in ɛ (libration amplitude), the Navier-Stokes equations are segregated into the linear and nonlinear parts at orders ɛ1 and ɛ^2, respectively. The former is used to find the analytical solution of the normal modes (Borcia 2012). Plugging two independent solutions into the latter we investigate the generation mechanism of INMMF. We found R1^1=overbar{partial_z(u_r1 u_z^1)}, R2^1=overbar{partial_r(u_r1 u_r^1)} as source terms responsible for the generation of INMMF. The helical structure of the inertial waves causes the nonlinear terms R1 and R2 to be nonzero, contributing to the generation of INMMF. We used u_ra and u_za obtained from the analytical solution (Borcia 2012) and computed the source terms R1a and R2a and found a structural correspondence with the corresponding field computed from the DNS solution for the three normal modes investigated. The sum of R11 and R21 exhibits a good structural correspondence with INMMF. Interestingly, INMMF magnitude depends on the inertial wave beams and normal modes. For instance we found that INMMF is generated more efficiently for the libration frequency ω=1.58, although the resonant frequency is predicted by the analytical solution to be at ω=1.576 (normal mode (2,1)). Separating the inertial wave beams from the flow field obtained by DNS, using the analytical normal mode solution, we explored the phase lag between inertial wave beams and normal mode. We inferred that the normal mode amplitude is high only if the phase lag between the inertial wave beam and the normal mode is predominantly positive. In this case a high amplitude INMMF amplitude can be found. This supports the hypothesis that the normal modes are generated by the inertial wave beam in analogy to resonant forcing in classical mechanics. Interestingly, the 'optimum' phase lag found is much smaller than π/2. {Acknowledgement:} This work is a part of the project "Mischung und Grundstromanregung durch propagierende Trgheitswellen: Theorie, Experiment und Simulation" supported by the German Science Foundation (DFG). We would like to thank M. Klein, U. Harlander, I. Borcia and E. Schaller for helpful discussions and invaluable contributions. {References:} Borcia, I. D. & Harlander, U. 2012 Inertial waves in a rotating annulus with inclined inner cylinder: comparing the spectrum of wave attractor frequency bands and the eigenspectrum in the limit of zero inclination. Theor. Comput. Fluid Dyn. 27, 397-413.

Laser spectroscopy and dynamics of crystal lattices of chirally pure and racemic phases of amino acids

NASA Astrophysics Data System (ADS)

Belyanchikov, M. A.; Gorelik, V. S.; Gorshunov, B. P.; Pyatyshev, A. Yu.

2017-03-01

Strong sharp lines due to the librational modes characterized by a pseudoscalar symmetry type have been found in the low-frequency Raman spectra of the lattices of glycine and tyrosine amino acids. The intensities of these lines exceed those for Raman scattering in the region of intramolecular vibrations. The spectra of chirally pure and racemic phases of amino acids differ significantly. The results obtained can be used to observe stimulated Raman scattering from the librational modes of crystalline amino acids and monitor the chiral purity of bioactive preparations containing amino acids.

BIDIRECTIONAL FLUXES OF NEARLY RELATIVISTIC ELECTRONS DURING THE ONSET OF SOLAR ENERGETIC PARTICLE EVENTS

DOE Office of Scientific and Technical Information (OSTI.GOV)

Sun, L. P.; Li, C., E-mail: pmo_sunlp@msn.com

2013-03-10

We report intensity and anisotropy measurements of energetic electrons in the energy range of {approx}27-{approx}500 keV as observed with the Wind and Advanced Composition Explorer (ACE) spacecraft in 2000 June for several solar energetic particle (SEP) events. The solar sources of the SEP events are inferred from observations from the Solar and Heliospheric Observatory spacecraft. All of the events originate from the western limb active regions (ARs), which are well connected by interplanetary magnetic field (IMF) lines linking the Sun to near-Earth space. The observations on board Wind show bimodal pitch angle distributions (PADs), whereas ACE shows PADs with onemore » peak, as is usually observed for impulsive injection of electrons at the Sun. During the time of observations, Wind was located, upstream of the Earth's bow shock in the dawn-noon sector, at distances of {approx}40-{approx}80 R{sub E} from the Earth, and we infer that it was magnetically connected to the quasi-parallel bow shock. Meanwhile, ACE, orbiting the Sun-Earth libration point L1, was not connected to the bow shock. The electron intensity-time profiles and the energy spectra show that the backstreaming electrons observed at Wind are not of magnetospheric origin. The observations suggest rather that the bidirectional electron fluxes are due to reflection or scattering by an obstacle located at a distance of less than {approx}150 R{sub E} in the anti-sunward direction, which is compatible with the obstacle being the Earth's bow shock or magnetosheath.« less

Summary and status of the Horizons ephemeris system

NASA Astrophysics Data System (ADS)

Giorgini, J.

2011-10-01

Since 1996, the Horizons system has provided searchable access to JPL ephemerides for all known solar system bodies, several dozen spacecraft, planetary system barycenters, and some libration points. Responding to 18 400 000 requests from 300 000 unique addresses, the system has recently averaged 420 000 ephemeris requests per month. Horizons is accessed and automated using three interfaces: interactive telnet, web-browser form, and e-mail command-file. Asteroid and comet ephemerides are numerically integrated from JPL's database of initial conditions. This small-body database is updated hourly by a separate process as new measurements and discoveries are reported by the Minor Planet Center and automatically incorporated into new JPL orbit solutions. Ephemerides for other objects are derived by interpolating previously developed solutions whose trajectories have been represented in a file. For asteroids and comets, such files may be dynamically created and transferred to users, effectively recording integrator output. These small-body SPK files may then be interpolated by user software to reproduce the trajectory without duplicating the numerically integrated n-body dynamical model or PPN equations of motion. Other Horizons output is numerical and in the form of plain-text observer, vector, osculating element, or close-approach tables, typically expected be read by other software as input. About one hundred quantities can be requested in various time-scales and coordinate systems. For JPL small-body solutions, this includes statistical uncertainties derived from measurement covariance and state transition matrices. With the exception of some natural satellites, Horizons is consistent with DE405/DE406, the IAU 1976 constants, ITRF93, and IAU2009 rotational models.

Lunar Cube Transfer Trajectory Options

NASA Technical Reports Server (NTRS)

Folta, David C.; Dichman, Don; Clark, Pamela; Haapala, Amanda; Howell, Kathleen

2014-01-01

Contingent upon the modification of an initial condition of the injected or deployed orbit. Additionally, these designs can be restricted by the selection of the Cubesat subsystem design such as propulsion or communication. Nonetheless, many trajectory options can be designed with have a wide range of transfer durations, fuel requirements, and final destinations. Our investigation of potential trajectories highlights several design options including deployment into low Earth orbit (LEO), geostationary transfer orbits (GTO), and higher energy direct lunar transfer orbits. In addition to direct transfer options from these initial orbits, we also investigate the use of longer duration Earth-Moon dynamical systems. For missions with an intended lunar orbit, much of the design process is spent optimizing a ballistic capture while other science locations such as Sun-Earth libration or heliocentric orbits may simply require a reduced Delta-V imparted at a convenient location along the trajectory. In this article we examine several design options that meet the above limited deployment and subsystem drivers. We study ways that both impulsive and low-thrust Solar Electric Propulsion (SEP) engines can be used to place the Cubesat first into a highly eccentric Earth orbit, enter the Moon's Sphere of Influence, and finally achieve a highly eccentric lunar orbit. We show that such low-thrust transfers are feasible with a realistic micro-thruster model, assuming that the Cubesat can generate sufficient power for the SEP. Two examples are shown here: (1) A Cubestat injected by Exploration Mission 1 (EM-1) then employing low thrust; and (2) a CubSat deployed in a GTO, then employing impulsive maneuvers. For the EM-1 injected initial design, we increase the EM-1 targeted lunar flyby distance to reduce the energy of the lunar flyby to match that of a typical lMoon system heteroclinic manifold. Figure 1 presents an option that encompasses the similar dynamics as that of the ARTEMIS mission design. Low-thrust maneuvers are used along the manifold trajectory to raise perigee to that of a lunar orbit, adjust the timing with respect to the Moon, rotate the line of apsides, and target a ballistic lunar encounter. In this design a second flyby decreases the orbital energy with respect to the Moon, so that C3 -0.1 km2s2. Another design, shown in Figure 2 emanates from a GTO then uses impulsive maneuvers to phase onto a local Earth-Moon manifold, which then transfers the CubeSat to a lunar encounter.

Environmental control and life support technologies for advanced manned space missions

NASA Technical Reports Server (NTRS)

Powell, F. T.; Wynveen, R. A.; Lin, C.

1986-01-01

Regenerative environmental control and life support system (ECLSS) technologies are found by the present evaluation to have reached a degree of maturity that recommends their application to long duration manned missions. The missions for which regenerative ECLSSs are attractive in virtue of the need to avoid expendables and resupply requirements have been identified as that of the long duration LEO Space Station, long duration stays at GEO, a permanently manned lunar base (or colony), manned platforms located at the earth-moon libration points L4 or L5, a Mars mission, deep space exploration, and asteroid exploration. A comparison is made between nonregenerative and regenerative ECLSSs in the cases of 10 essential functions.

Jovian Trojans: Orbital structures versus the WISE data

NASA Astrophysics Data System (ADS)

Rozehnal, Jakub; Broz, M.

2013-10-01

In this work, we study the relation between orbital characteristics of Jovian Trojans and their albedos and diameters as measured by the WISE/NEOWISE mission (Grav et al. 2011, 2012). In our previous work (Broz & Rozehnal 2011), we concluded that there is only one collisional family with parent body size larger than 100 km among Trojans, namely the Eurybates. This finding was based on the analysis of the observed size distributions, colour data from the Sloan Digital Sky Survey, and simulations of orbital evolution. The WISE albedos serve as an independent source of information which allows us to verify our previous results. We also update our database of suitable resonant elements (i.e. the libration amplidude D, eccentricity e, inclination I) of Trojans and we look for new (to-be-discovered) clusters by the Hierarchical Clustering Method. Using the WISE diameters, we can construct more precise size-frequency distributions of Trojans in both the leading/trailing clouds which we compare to SFD of the cluster(s) mentioned above. We then prepare a collisional model (based on the Boulder code, Morbidelli et al. 2009). Initial conditions of our model are based on an assumption that the Trojans were captured from a destabilised transplanetary disc while Jupiter jumped during its close encounter with a Neptune-mass planet - the so-called "jump capture" (Nesvorny et al. 2013). Within the framework of this model we try to constrain the age of the Eurybates family. The work of MB was supported by grant GACR 13-013085 of the Czech Science Foundation and the Research Programme MSM0021620860 of the Czech Ministry of Education.

NASA's Decadal Planning Team Mars Mission Analysis Summary

NASA Astrophysics Data System (ADS)

Drake, Bret G.

2007-02-01

In June 1999 the NASA Administrator chartered an internal NASA task force, termed the Decadal Planning Team, to create new integrated vision and strategy for space exploration. The efforts of the Decadal Planning Team evolved into the Agency-wide team known as the NASA Exploration Team (NEXT). This team was also instructed to identify technology roadmaps to enable the science-driven exploration vision, established a cross-Enterprise, cross-Center systems engineering team with emphasis focused on revolutionary not evolutionary approaches. The strategy of the DPT and NEXT teams was to "Go Anywhere, Anytime" by conquering key exploration hurdles of space transportation, crew health and safety, human/robotic partnerships, affordable abundant power, and advanced space systems performance. Early emphasis was placed on revolutionary exploration concepts such as rail gun and electromagnetic launchers, propellant depots, retrograde trajectories, nano structures, and gas core nuclear rockets to name a few. Many of these revolutionary concepts turned out to be either not feasible for human exploration missions or well beyond expected technology readiness for near-term implementation. During the DPT and NEXT study cycles, several architectures were analyzed including missions to the Earth-Sun Libration Point (L2), the Earth-Moon Gateway and L1, the lunar surface, Mars (both short and long stays), one-year round trip Mars, and near-Earth asteroids. Common emphasis of these studies included utilization of the Earth-Moon Libration Point (L1) as a staging point for exploration activities, current (Shuttle) and near-term launch capabilities (EELV), advanced propulsion, and robust space power. Although there was much emphasis placed on utilization of existing launch capabilities, the team concluded that missions in near-Earth space are only marginally feasible and human missions to Mars were not feasible without a heavy lift launch capability. In addition, the team concluded that missions in Earth s neighborhood, such as to the Moon, can serve as stepping-stones toward further deep-space missions in terms of proving systems, technologies, and operational concepts. The material contained in this presentation was compiled to capture the work performed by the Mars Sub-Team of the DPT NEXT efforts in the late 1999-2001 timeframe.

NASA's Decadal Planning Team Mars Mission Analysis Summary

NASA Technical Reports Server (NTRS)

Drake, Bret G. (Editor)

2007-01-01

In June 1999 the NASA Administrator chartered an internal NASA task force, termed the Decadal Planning Team, to create new integrated vision and strategy for space exploration. The efforts of the Decadal Planning Team evolved into the Agency-wide team known as the NASA Exploration Team (NEXT). This team was also instructed to identify technology roadmaps to enable the science-driven exploration vision, established a cross-Enterprise, cross-Center systems engineering team with emphasis focused on revolutionary not evolutionary approaches. The strategy of the DPT and NEXT teams was to "Go Anywhere, Anytime" by conquering key exploration hurdles of space transportation, crew health and safety, human/robotic partnerships, affordable abundant power, and advanced space systems performance. Early emphasis was placed on revolutionary exploration concepts such as rail gun and electromagnetic launchers, propellant depots, retrograde trajectories, nano structures, and gas core nuclear rockets to name a few. Many of these revolutionary concepts turned out to be either not feasible for human exploration missions or well beyond expected technology readiness for near-term implementation. During the DPT and NEXT study cycles, several architectures were analyzed including missions to the Earth-Sun Libration Point (L2), the Earth-Moon Gateway and L1, the lunar surface, Mars (both short and long stays), one-year round trip Mars, and near-Earth asteroids. Common emphasis of these studies included utilization of the Earth-Moon Libration Point (L1) as a staging point for exploration activities, current (Shuttle) and near-term launch capabilities (EELV), advanced propulsion, and robust space power. Although there was much emphasis placed on utilization of existing launch capabilities, the team concluded that missions in near-Earth space are only marginally feasible and human missions to Mars were not feasible without a heavy lift launch capability. In addition, the team concluded that missions in Earth s neighborhood, such as to the Moon, can serve as stepping-stones toward further deep-space missions in terms of proving systems, technologies, and operational concepts. The material contained in this presentation was compiled to capture the work performed by the Mars Sub-Team of the DPT NEXT efforts in the late 1999-2001 timeframe.

Dynamics of axial torsional libration under the mantle-inner core gravitational interaction

NASA Astrophysics Data System (ADS)

Chao, B. F.

2017-01-01

The aims of this paper are (i) formulating the dynamics of the mantle-inner core gravitational (MICG) interaction in terms of the spherical-harmonic multipoles of mass density. The modeled MICG system is composed of two concentric rigid bodies (mantle and inner core) of near-spherical but otherwise heterogeneous configuration, with a fluid outer core in between playing a passive role. We derive the general equation of motion for the vector rotation but only focus on the polar component that describes the MICG axial torsional libration. The torsion constant and hence the square of the natural frequency of the libration is proportional to the product of the equatorial ellipticities of the mantle and inner-core geoid embodied in their multipoles (of two different types) of degree 2 and order 2 (such as the Large Low-Shear-Velocity Provinces above the core-mantle boundary) and (ii) studying the geophysical implications upon equating the said MICG libration to the steady 6 year oscillation that are observed in the Earth's spin rate or the length-of-day variation (ΔLOD). In particular, the MICG torsion constant is found to be Γ>˜z = CIC σz2 ≈ 6.5 × 1019 N m, while the inner core's (BIC - AIC) ≈ 1.08 × 1031 kg m2 gives the inner core triaxiality (BIC - AIC)/CIC ≈ 1.8 × 10-4, about 8 times the whole-Earth value. It is also asserted that the required inner-core ellipticity amounts to no more than 140 m in geoid height, much smaller than the sensitivity required for the seismic wave travel time to resolve the variation of the inner core.

The tidally-modulated plume of Enceladus: an update

NASA Astrophysics Data System (ADS)

Nimmo, F.; Porco, C.; Mitchell, C. J.; Van Hoolst, T.; Hedman, M. M.

2016-12-01

The brightness of the ice grain plume of Enceladus is observed to vary on a diurnal timescale [1,2], consistent with predictions that the plume's mass is modulated by normal tidal stresses, which open and close cracks that reach the ocean [3]. Here we extend our previous analysis [2] to a larger set of ISS plume observations, including images taken since 2010, extending the temporal baseline by more than a factor of two. The observations were reduced using the same approach as in [2]. Fits were performed as in [2] but now include two different assumptions of how plume brightness responds to stresses [4] plus an updated calculation of the effects of long-period librations [5]. An apparent phase lag of 30-60 degrees between the modelled and observed response is robustly present, irrespective of the data set and assumptions used. This phase lag may be the result of the viscosity structure of the ice shell [2,4], an eruptive delay caused by the hydrodynamics within tidally-pumped cracks [6], or other as yet unknown processes. An earlier suggestion [2], that the phase lag is caused by the additional stresses arising from an 0.8 degree 1:1 physical libration in the moon's ice shell, can be rejected now that this libration has been measured with an amplitude of 0.12 degrees [7]. We also find in ISS images a secular decrease in plume brightness over the ten years of Cassini observations; this decrease may be due to long-period (forced) librations of Enceladus. [1] Hedman et al., Nature 2013 [2] Nimmo et al., Astron. J. 2014 [3] Hurford et al., Nature 2007 [4] Behounkova et al., Nature Geosci. 2015 [5] Yseboodt & Van Hoolst, Fall AGU, 2015 [6] Kite & Rubin, PNAS 2016 [7] Thomas et al., Icarus 2016

Use of the Moon for spacecraft calibration over 350-2500 nm

USGS Publications Warehouse

Kieffer, H.H.; Anderson, J.M.

1998-01-01

The Moon is the only natural object outside the Earth's atmosphere that is within the dynamic range of most imaging instruments on Earth-orbiting spacecraft. The excellent photometric stability of the Lunar surface will allow its use as a long-term instrument calibration source once the dependence of Lunar spectral radiance on phase and libration angles are well characterized. A program to provide this characterization is underway. Observations are being made in 23 bands within 350-950 nm, 7 of which correspond closely with spacecraft instrument bands. Observations in nine bands within 950-2500 nm began recently. Although at this time the absolute Lunar radiance model is preliminary and uncertainties are larger than most instrument calibration goals, changes in spacecraft instrument sensitivity can be precisely monitored and absolute calibration can be applied retroactively as the accuracy of the Lunar spectral radiance model improves. Several space-based imaging systems have already begun using the Moon for calibration and the EOS AM-1 platform will make periodic attitude maneuvers for Lunar and space calibration.

Nature of the Kirkwood gaps in the asteroid belt

NASA Technical Reports Server (NTRS)

Dermott, S. F.; Murray, C. D.

1983-01-01

It is demonstrated that the Kirkwood gaps are not merely regions of low asteroidal number density, but are regions in a-e-sin 1/2 I space where libration of some argument is possible. It is argued that neither the statistical nor the cosmogonic hypothesis of gap formation can account for these new observations. It is shown that the present distribution of asteroidal semimajor axes can be used to deduce the present semimajor axis of Jupiter to an accuracy of one part in five thousand. Thus, there has been very little change in the orbital period of Jupiter since the time of formation of the present gaps. This observation eliminates the possibility that the observed gaps were formed by resonance sweeping at the time of the dispersal of the accretion disk. It is concluded that the gaps have been formed by the gravitational action of Jupiter on individual asteroids and that gap formation has probably continued throughout the lifetime of the solar system.

ARE THE KEPLER NEAR-RESONANCE PLANET PAIRS DUE TO TIDAL DISSIPATION?

DOE Office of Scientific and Technical Information (OSTI.GOV)

Lee, Man Hoi; Fabrycky, D.; Lin, D. N. C., E-mail: mhlee@hku.hk, E-mail: daniel.fabrycky@gmail.com, E-mail: lin@ucolick.org

The multiple-planet systems discovered by the Kepler mission show an excess of planet pairs with period ratios just wide of exact commensurability for first-order resonances like 2:1 and 3:2. In principle, these planet pairs could have both resonance angles associated with the resonance librating if the orbital eccentricities are sufficiently small, because the width of first-order resonances diverges in the limit of vanishingly small eccentricity. We consider a widely held scenario in which pairs of planets were captured into first-order resonances by migration due to planet-disk interactions, and subsequently became detached from the resonances, due to tidal dissipation in themore » planets. In the context of this scenario, we find a constraint on the ratio of the planet's tidal dissipation function and Love number that implies that some of the Kepler planets are likely solid. However, tides are not strong enough to move many of the planet pairs to the observed separations, suggesting that additional dissipative processes are at play.« less

Multiphysics elastodynamic finite element analysis of space debris deorbit stability and efficiency by electrodynamic tethers

NASA Astrophysics Data System (ADS)

Li, Gangqiang; Zhu, Zheng H.; Ruel, Stephane; Meguid, S. A.

2017-08-01

This paper developed a new multiphysics finite element method for the elastodynamic analysis of space debris deorbit by a bare flexible electrodynamic tether. Orbital motion limited theory and dynamics of flexible electrodynamic tethers are discretized by the finite element method, where the motional electric field is variant along the tether and coupled with tether deflection and motion. Accordingly, the electrical current and potential bias profiles of tether are solved together with the tether dynamics by the nodal position finite element method. The newly proposed multiphysics finite element method is applied to analyze the deorbit dynamics of space debris by electrodynamic tethers with a two-stage energy control strategy to ensure an efficient and stable deorbit process. Numerical simulations are conducted to study the coupled effect between the motional electric field and the tether dynamics. The results reveal that the coupling effect has a significant influence on the tether stability and the deorbit performance. It cannot be ignored when the libration and deflection of the tether are significant.

Collective excitations and ultrafast dipolar solvation dynamics in water-ethanol binary mixture

NASA Astrophysics Data System (ADS)

Hazra, Milan K.; Bagchi, Biman

2018-03-01

In order to understand the intermolecular vibrational spectrum and the collective excitations of water-ethanol binary mixture, we investigate the density of states and the power spectrum using computer simulations aided by theory. We investigate in particular the spectra at intermediate to low frequencies (a few hundreds to few tens of cm-1) by calculating (i) the density of states from quenched normal modes, (ii) the power spectrum from velocity time correlation function, and (iii) the far infrared and dielectric spectra (that is, the Cole-Cole plot) from the total dipole moment time correlation function. The different spectra are in broad agreement with each other and at the same time reveal unique characteristics of the water-ethanol mixture. Inverse participation ratio reveals several interesting features. Libration of pure ethanol is more localized than that of pure water. With increasing ethanol content, we observe localization of the collective libration mode as well as of the hindered translational and rotational mode. An interesting mixing between the libration of water and ethanol is observed. Solvation dynamics of tryptophan measured by equilibrium energy fluctuation time correlation function show surprisingly strong non-linear dependence on composition that can be tested against experiments.

Collective excitations and ultrafast dipolar solvation dynamics in water-ethanol binary mixture.

PubMed

Hazra, Milan K; Bagchi, Biman

2018-03-21

In order to understand the intermolecular vibrational spectrum and the collective excitations of water-ethanol binary mixture, we investigate the density of states and the power spectrum using computer simulations aided by theory. We investigate in particular the spectra at intermediate to low frequencies (a few hundreds to few tens of cm -1 ) by calculating (i) the density of states from quenched normal modes, (ii) the power spectrum from velocity time correlation function, and (iii) the far infrared and dielectric spectra (that is, the Cole-Cole plot) from the total dipole moment time correlation function. The different spectra are in broad agreement with each other and at the same time reveal unique characteristics of the water-ethanol mixture. Inverse participation ratio reveals several interesting features. Libration of pure ethanol is more localized than that of pure water. With increasing ethanol content, we observe localization of the collective libration mode as well as of the hindered translational and rotational mode. An interesting mixing between the libration of water and ethanol is observed. Solvation dynamics of tryptophan measured by equilibrium energy fluctuation time correlation function show surprisingly strong non-linear dependence on composition that can be tested against experiments.

What's the matter with Enceladus' gravity?

NASA Astrophysics Data System (ADS)

Rivoldini, A.; Beuthe, M.; Trinh, A.

2016-12-01

Isostasy is clearly at work on Enceladus: long-wavelength gravity is positively correlated with topography, but also well compensated. If the influence of Enceladus' fast spin is taken into account, Airy isostasy implies a very thick crust (50 km) above a very thin ocean, in flat contradiction of the thin crust (20 km) implied by librations. In a desperate attempt to solve the problem, it was recently proposed to substitute flexural isostasy to Airy isostasy, using librations as a constraint on the crust thickness. However the huge lithospheric stresses required to support the load result in complete lithospheric failure. Here we propose a new isostatic model based on the sound physical principle of minimum crustal stress. We demonstrate that gravity combined with topography predicts a 20 km thick crust agreeing with - but independent from - the libration constraint. A consistent picture finally emerges from gravity-topography analysis, confirming that the south polar crust is only a few kilometres thick. Enceladus' resonant companion, Dione, is in a similar state of minimum stress isostasy. Its gravity and topography can be explained in terms of a 100 km thick isostatic crust overlying a 60 km thick global ocean, thus providing the first clear evidence for a present-day ocean within Dione.

SMART-1 Technology and Science Experiments in Preparation of Future Missions and ESA Cornerstones

NASA Astrophysics Data System (ADS)

Marini, A. E.; Racca, G. D.; Foing, B. H.; SMART-1 Project

1999-12-01

SMART-1 is the first ESA Small Mission for Advanced Research in Technology, aimed at the demonstration of enabling technologies for future scientific missions. SMART-1's prime technology objective is the demonstration of the solar primary electric propulsion, a key for future interplanetary missions. SMART-1 will use a Stationary Plasma Thruster engine, cruising 15 months to capture a Moon polar orbit. A gallery of images of the spacecraft is available at the web site: http://www.estec.esa.nl/spdwww/smart1/html/11742.html SMART-1 payload aims at monitoring the electric propulsion and its spacecraft environment and to test novel instrument technologies. The Diagnostic Instruments include SPEDE, a spacecraft potential plasma and charged particles detector, to characterise both spacecraft and planetary environment, together with EPDP, a suite of sensors monitoring secondary thrust-ions, charging and deposition effects. Innovative spacecraft technologies will be tested on SMART-1 : Lithium batteries and KATE, an experimental X/Ka-band deep-space transponder, to support radio-science, to monitor the accelerations of the electric propulsion and to test turbo-code technique, enhancing the return of scientific data. The scientific instruments for imaging and spectrometry are: \\begin{itemize} D-CIXS, a compact X-ray spectrometer based on novel SCD detectors and micro-structure optics, to observe X-ray celectial objects and to perform lunar chemistry measurements. SIR, a miniaturised quasi-monolithic point-spectrometer, operating in the Near-IR (0.9 ÷ 2.4 micron), to survey the lunar crust in previously uncovered optical regions. AMIE, a miniature camera based on 3-D integrated electronics, imaging the Moon, and other bodies and supporting LASER-LINK and RSIS. RSIS and LASER-LINK are investigations performed with the SMART-1 Payload: \\begin{itemize} RSIS: A radio-science Experiment to validate in-orbit determination of the libration of the celestial target, based on high-accuracy tracking in Ka-band and imaging of a surface landmark LASER-LINK: a demonstration of acquisition of a deep-space laser-link from the ESA Optical Ground Station at Tenerife, validating also the novel sub-apertured telescope designed for the mitigation of atmospheric scintillation disturbances.

Absolute irradiance of the Moon for on-orbit calibration

USGS Publications Warehouse

Stone, T.C.; Kieffer, H.H.; ,

2002-01-01

The recognized need for on-orbit calibration of remote sensing imaging instruments drives the ROLO project effort to characterize the Moon for use as an absolute radiance source. For over 5 years the ground-based ROLO telescopes have acquired spatially-resolved lunar images in 23 VNIR (Moon diameter ???500 pixels) and 9 SWIR (???250 pixels) passbands at phase angles within ??90 degrees. A numerical model for lunar irradiance has been developed which fits hundreds of ROLO images in each band, corrected for atmospheric extinction and calibrated to absolute radiance, then integrated to irradiance. The band-coupled extinction algorithm uses absorption spectra of several gases and aerosols derived from MODTRAN to fit time-dependent component abundances to nightly observations of standard stars. The absolute radiance scale is based upon independent telescopic measurements of the star Vega. The fitting process yields uncertainties in lunar relative irradiance over small ranges of phase angle and the full range of lunar libration well under 0.5%. A larger source of uncertainty enters in the absolute solar spectral irradiance, especially in the SWIR, where solar models disagree by up to 6%. Results of ROLO model direct comparisons to spacecraft observations demonstrate the ability of the technique to track sensor responsivity drifts to sub-percent precision. Intercomparisons among instruments provide key insights into both calibration issues and the absolute scale for lunar irradiance.

Eccentricity Evolution of Extrasolar Multiple Planetary Systems Due to the Depletion of Nascent Protostellar Disks

NASA Astrophysics Data System (ADS)

Nagasawa, M.; Lin, D. N. C.; Ida, S.

2003-04-01

Most extrasolar planets are observed to have eccentricities much larger than those in the solar system. Some of these planets have sibling planets, with comparable masses, orbiting around the same host stars. In these multiple planetary systems, eccentricity is modulated by the planets' mutual secular interaction as a consequence of angular momentum exchange between them. For mature planets, the eigenfrequencies of this modulation are determined by their mass and semimajor axis ratios. However, prior to the disk depletion, self-gravity of the planets' nascent disks dominates the precession eigenfrequencies. We examine here the initial evolution of young planets' eccentricity due to the apsidal libration or circulation induced by both the secular interaction between them and the self-gravity of their nascent disks. We show that as the latter effect declines adiabatically with disk depletion, the modulation amplitude of the planets' relative phase of periapsis is approximately invariant despite the time-asymmetrical exchange of angular momentum between planets. However, as the young planets' orbits pass through a state of secular resonance, their mean eccentricities undergo systematic quantitative changes. For applications, we analyze the eccentricity evolution of planets around υ Andromedae and HD 168443 during the epoch of protostellar disk depletion. We find that the disk depletion can change the planets' eccentricity ratio. However, the relatively large amplitude of the planets' eccentricity cannot be excited if all the planets had small initial eccentricities.

Overstable librations can account for the paucity of mean motion resonances among exoplanet pairs

DOE Office of Scientific and Technical Information (OSTI.GOV)

Goldreich, Peter; Schlichting, Hilke E., E-mail: pmg@ias.edu, E-mail: hilke@mit.edu

2014-02-01

We assess the multi-planet systems discovered by the Kepler satellite in terms of current ideas about orbital migration and eccentricity damping due to planet-disk interactions. Our primary focus is on first order mean motion resonances, which we investigate analytically to lowest order in eccentricity. Only a few percent of planet pairs are in close proximity to a resonance. However, predicted migration rates (parameterized by τ{sub n}=n/| n-dot |) imply that during convergent migration most planets would have been captured into first order resonances. Eccentricity damping (parameterized by τ{sub e}=e/| e-dot |) offers a plausible resolution. Estimates suggest τ {sub e}/τmore » {sub n} ∼ (h/a){sup 2} ∼ 10{sup –2}, where h/a is the ratio of disk thickness to radius. Together, eccentricity damping and orbital migration give rise to an equilibrium eccentricity, e {sub eq} ∼ (τ {sub e}/τ {sub n}){sup 1/2}. Capture is permanent provided e {sub eq} ≲ μ{sup 1/3}, where μ denotes the planet to star mass ratio. But for e {sub eq} ≳ μ{sup 1/3}, capture is only temporary because librations around equilibrium are overstable and lead to passage through resonance on timescale τ {sub e}. Most Kepler planet pairs have e {sub eq} > μ{sup 1/3}. Since τ {sub n} >> τ {sub e} is the timescale for migration between neighboring resonances, only a modest percentage of pairs end up trapped in resonances after the disk disappears. Thus the paucity of resonances among Kepler pairs should not be taken as evidence for in situ planet formation or the disruptive effects of disk turbulence. Planet pairs close to a mean motion resonance typically exhibit period ratios 1%-2% larger than those for exact resonance. The direction of this shift undoubtedly reflects the same asymmetry that requires convergent migration for resonance capture. Permanent resonance capture at these separations from exact resonance would demand μ(τ {sub n}/τ {sub e}){sup 1/2} ≳ 0.01, a value that estimates of μ from transit data and (τ {sub e}/τ {sub n}){sup 1/2} from theory are insufficient to match. Plausible alternatives involve eccentricity damping during or after disk dispersal. The overstability referred to above has applications beyond those considered in this investigation. It was discovered numerically by Meyer and Wisdom in their study of the tidal evolution of Saturn's satellites.« less

Enceladus is not in Steady State

NASA Astrophysics Data System (ADS)

Cheunchitra, T.; Stevenson, D. J.

2016-12-01

Libration data tell us there is a global ocean. Topography and gravity tell us that there is substantial compensation at degree 2, meaning that the underside of the ice shell must have topography. This topography will decay, typically on a timescale of order a million years (fortuitously similar to thermal diffusion times through the ice shell), by viscous lateral flow of the ice. This could in principle be compensated in steady state by net melting beneath the poles and a compensating net freezing at the equator. In that model, the ice shell beneath the poles is partially melted with water being continuously produced and percolating to the base (or expelled if there are cracks, as at the South Pole). We have modeled this without an a priori assumption about the strength of tidal heating. We find that even if the tidal heating is zero on average around the equator, then the latent heat release from the required freezing can only be accommodated in steady state if the ice shell is 18km. The ice thickness must be even less at the poles in order to satisfy gravity and topography. Moreover, there must then be substantial tidal heating at the poles and it is physically unreasonable to have the volumetric tidal heating at the equator be enormously less than at the North Pole. For example, if the volumetric tidal heating at the equator is on average one quarter of that at the North Pole then marginal consistency with gravity and topography may be possible for a mean ice thickness at the equator of 12km. The global heat flow may exceed 40GW, much higher than the detectable IR excess (the observed south polar tiger stripe heat flow). Recent work (Fuller et al.) admits orbital evolutions with large heat flow at least for a recent part of the orbital history. However, this thin shell steady state model has difficulty reconciling observed gravity and topography as well as the libration data. We conclude that it is unlikely that Enceladus has no net melting or freezing. The ice shell can be thicker on average if there is net freezing at present but in that case it is difficult to explain the observed topography and gravity. A more likely scenario is that Enceladus has more melting beneath the poles than the current freezing (if any) beneath the equator. In that non-steady state model, the current ice thickness can be compatible with all current data.

New Model for Europa's Tidal Response Based after Laboratory Measurements

NASA Astrophysics Data System (ADS)

Castillo, J. C.; McCarthy, C.; Choukroun, M.; Rambaux, N.

2009-12-01

We explore the application of the Andrade model to the modeling of Europa’s tidal response at the orbital period and for different librations. Previous models have generally assumed that the satellite behaves as a Maxwell body. However, at the frequencies exciting Europa’s tides and librations, material anelasticity tends to dominate the satellite’s response for a wide range of temperatures, a feature that is not accounted for by the Maxwell model. Many experimental studies on the anelasticity of rocks, ice, and hydrates, suggest that the Andrade model usually provides a good fit to the dissipation spectra obtained for a wide range of frequencies, encompassing the tidal frequencies of most icy satellites. These data indicate that, at Europa’s orbital frequency, the Maxwell model overestimates water ice attenuation at temperature warmer than ~240 K, while it tends to significantly underestimate it at lower temperatures. Based on the available data we suggest an educated extrapolation of available data to Europa’s conditions. We compute the tidal response of a model of Europa differentiated in a rocky core and a water-rich shell. We assume various degrees of stratification of the core involving hydrated and anhydrous silicates, as well as an iron core. The water-rich shell of Europa is assumed to be fully frozen, or to have preserved a deep liquid layer. In both cases we consider a range of thermal structures, based on existing models. These structures take into account the presence of non-ice materials, especially hydrated salts. This new approach yields a greater tidal response (amplitude and phase lag) than previously expected. This is due to the fact that a greater volume of material dissipates tidal energy in comparison to models assuming a Maxwell body. Another feature of interest is that the tidal stress expected in Europa is at about the threshold between a linear and non-linear mechanical response of water ice as a function of stress. Increased stress at a time when Europa’s eccentricity was greater than its current value is likely to have resulted in significant dissipation increase. We will assess how this new approach affects our understanding of Europa, and we will quantify the tidal response of this satellite and the amount of tidal heating available to its evolution. Acknowledgements: Part of this work has been conducted at the Jet Propulsion Laboratory, California Institute of Technology, under contract with NASA. Government sponsorship acknowledged. Part of the experimental work was conducted at Brown University, funded by NASA. MC is supported by a NASA Postdoctoral Fellowship, administered by Oak Ridge Associated Universities.

Dust Trails of SP/Tuttle and the Unusual Outbursts of the Ursid Shower

NASA Technical Reports Server (NTRS)

Jenniskens, Peter; Lyytinen, E.; deLignie, M. C.; Johannink, C.; Jobse, K.; Schievink, R.; Langbroek, M.; Koop, M.; Gural, P.; Wilson, M.;

A Concept for Providing Warning of Chelyabinsk-like Meteors, including those approaching from the Sun

NASA Astrophysics Data System (ADS)

Dunham, D. W.; Reitsema, H.; Lu, E.; Arentz, R.; Linfield, R.; Chapman, C. R.; Farquhar, R. W.; Furfaro, R.; Eismont, N. A.; Ledkov, A.; Chumachenko, E.

2013-12-01

The detonation of a 20m-asteroid above Chelyabinsk, Russia on 2013 February 15 shows that even small asteroids can cause extensive damage. Earth-based telescopes have found smaller harmless objects, such as 2008 TC3, discovered 20h before it exploded over northern Sudan . 2008 TC3 remains the only asteroid discovered before it hit Earth because it approached Earth from the night side, where it was observed by large telescopes searching for near-Earth objects. The larger object that exploded over Chelyabinsk approached Earth from the day side, from too close to the Sun to be detected from Earth. A sizeable telescope in an orbit about the Sun-Earth L1 (SE-L1) libration point 1.5 million km from Earth towards the Sun (about 4 times the distance to the Moon) could find objects like the 'Chelyabinsk' asteroid approaching approximately from the line of sight to the Sun about a day before Earth closest approach; this would find the approximately 35% of asteroids that approach Earth from a direction too close to the Sun to be observed, or likely to be missed, from the ground. Our concept would give at least several hours, and often a day or more, to take protective measures, rather than the approximately two-minute interval between the flash and shock wave arrival that occurred in Chelyabinsk. An important reason for providing warning of these events, even smaller harmless ones that explode high in the atmosphere with the force of an atomic bomb, is to prevent mistaking such an event for a nuclear attack that could trigger a devastating nuclear war. This concept could also discover many small asteroids that would not impact Earth; some of them would likely be suitable for retrieval to move to a lunar orbit for study by astronauts in the next decade. A concept using a space telescope similar to that needed by our concept is already conceived by the B612 Foundation, whose planned Sentinel Space Telescope could find nearly all 140m and larger near-Earth objects (NEO's), including those in orbits mostly inside the Earth's orbit that are hard to find with Earth-based telescopes, from a Venus-like orbit. Few modifications would be needed to the 50cm aperture passively-cooled infrared-observing Sentinel Space Telescope to operate in a SE-L1 orbit, 0.01 AU from Earth towards the Sun, to find most asteroids larger than about 5 meters that approach the Earth from the solar direction. Many objects in the 25-50m range will not be found by current NEO surveys, while they would nearly always be seen by this possible mission. A dense metallic NEO as small as 5m across can rain destruction over an area of 1 or 2 square kilometers, as the Sikhote-Alin meteor showed in 1947 Other concepts are either ineffective at providing warning of asteroids approaching from the Sun, or are more expensive, involving three or more spacecraft. We should give better warning for future 'Bolts out of the blue'.

A Consideration of HALO Type Orbit Designation and Maintaining for KUAFU-A and WSO/UV Missions

NASA Astrophysics Data System (ADS)

Nianchuan, J.; Xian, S.; Jianguo, Y.; Guangli, W.; Jingsong, P.

In the new era of deep space exploration more and more explorations at special places or points in solar system are carried out and planned There are five equilibrium points in the Sun-Earth system and the orbits around these points have good dynamic attribute Due to this reason The areas vicinity equilibrium points have many advantages for space exploration In recent 20 years the NASA and ESA have successfully launched several spacecrafts orbiting the Sun-Earth collinear equilibrium points Following the developing steps of space and deep space exploration in China Chinese scientists and engineers are considering and suggesting two equilibrium points explorations One is named KUAFU-A mission whose craft will orbit L1 point and the scientific target is studying the evolution of space weather of solar-terrestrial area The other is WSO UV mission whose craft will orbit L2 point and the scientific target is studying the structure and evolution of galaxies This report is mainly about HALO type orbit designation and maintaining for these two missions Following points are included 1 Briefly reviewing the explorations at the equilibrium points launched by NASA and ESA 2 Simply introducing the exploration KUAFU-A and WSO UV 3 Discussing the designation and maintaining of HALO type orbits in some detail for KUAFU-A and WSO UV

Radiometric calibration stability and inter-calibration of solar-band instruments in orbit using the moon

USGS Publications Warehouse

Stone, T.C.

2008-01-01

With the increased emphasis on monitoring the Earth's climate from space, more stringent calibration requirements are being placed on the data products from remote sensing satellite instruments. Among these are stability over decade-length time scales and consistency across sensors and platforms. For radiometer instruments in the solar reflectance wavelength range (visible to shortwave infrared), maintaining calibration on orbit is difficult due to the lack of absolute radiometric standards suitable for flight use. The Moon presents a luminous source that can be viewed by all instruments in Earth orbit. Considered as a solar diffuser, the lunar surface is exceedingly stable. The chief difficulty with using the Moon is the strong variations in the Moon's brightness with illumination and viewing geometry. This mandates the use of a photometric model to compare lunar observations, either over time by the same instrument or between instruments. The U.S. Geological Survey in Flagstaff, Arizona, under NASA sponsorship, has developed a model for the lunar spectral irradiance that explicitly accounts for the effects of phase, the lunar librations, and the lunar surface reflectance properties. The model predicts variations in the Moon's brightness with precision ???1% over a continuous phase range from eclipse to the quarter lunar phases. Given a time series of Moon observations taken by an instrument, the geometric prediction capability of the lunar irradiance model enables sensor calibration stability with sub-percent per year precision. Cross-calibration of instruments with similar passbands can be achieved with precision comparable to the model precision. Although the Moon observations used for intercomparison can be widely separated in phase angle and/or time, SeaWiFS and MODIS have acquired lunar views closely spaced in time. These data provide an example to assess inter-calibration biases between these two instruments.

Mapping the stability region of the 3:2 Neptune-Pluto resonance

NASA Technical Reports Server (NTRS)

Levison, H. F.; Stern, S. A.

1993-01-01

Pluto and Charon are most likely the remnants of a large number of objects that existed in the Uranus-Neptune region at early epochs of the solar system. Numerical integrations have shown that, in general, such objects were ejected from the planetary region on timescales of approximately 10(exp 7) years after Neptune and Uranus reached their current masses. It is thought that the Pluto-Charon system survived to current times without being dynamically removed in this way because it is trapped in a set of secular and mean motion resonances with Neptune. The best-known Pluto-Neptune orbit coupling is the 3:2 mean motion resonance discovered almost 30 years ago by C. Cohen and E. Hubbard. These workers showed that the resonance angle, delta is equivalent to 3(lambda(sub P)) - 2(lambda(sub N)) - omega-bar(sub P) where omega-bar(sub P) is the longitude of perihelion of the Pluto-Charon system, and lambda(sub N) and lambda(sub P) are the mean longitude of Neptune and Pluto-Charon respectively, librates about 180 deg with an amplitude, A(sub delta), of 76 deg. A numerical simulation project to map out the stability region of the 3:2 resonance is reported. The results of these simulations are important to understanding whether Pluto's long-term heliocentric stability requires only the 3:2 resonance, or whether it instead requires one or more of the other Pluto-Neptune resonances. Our study also has another important application. By investigating stability timescales as a function of orbital elements, we gain insight into the fraction of orbital phase space which the stable 3:2 resonance occupies. This fraction is directly related to the probability that the Pluto-Charon system (and possibly other small bodies) could have been captured into this resonance.

The gravity field and orientation of Mercury after the MESSENGER mission

NASA Astrophysics Data System (ADS)

Mazarico, E.; Genova, A.; Goossens, S. J.; Lemoine, F. G.; Neumann, G. A.; Zuber, M. T.; Smith, D. E.; Solomon, S. C.

2015-12-01

After more than four years in orbit about Mercury, the MErcury Surface, Space ENvironment, GEochemistry, and Ranging (MESSENGER) spacecraft impacted the planet's surface north of Shakespeare crater (54.44° N, 210.12° E,) on 30 April 2015. One of the main goals of the mission was to determine the gravity field of Mercury in order to learn about Mercury's interior. Together with ground-based radar measurements of the obliquity and forced librations, MESSENGER-derived gravity models helped revise models of Mercury's interior. Nevertheless, the refinement of Mercury's orientation with the latest data from MESSENGER can further improve the interior modeling of the planet. The last eight months of the mission provided a special opportunity to conduct low-altitude measurements, with extensive radio tracking coverage below 200 km altitude north of ~30°N. MESSENGER's Mercury Laser Altimeter (MLA) mapped the topography of Mercury's northern hemisphere with a sub-meter vertical precision, an along-track sampling of ~500 m, and a longitudinal resolution (~0.1°) limited by the number of spacecraft orbits (~4,000). The combination of gravity and topography helps determine crustal thickness and interior properties. Altimetric ranges provide geodetic constraints to improve the spacecraft orbit determination, and thus the gravity field model. In particular, whereas the MESSENGER spacecraft was not tracked at each periapsis passage, MLA operated nearly continuously (outside of thermally challenging periods). From an analysis of the entire radiometric and altimetric datasets acquired by MESSENGER, a new gravity field to degree and order 100 has been obtained, resolving features down to ~75 km horizontal scale. The altimetric data help reduce the uncertainties in the determination of the pole position. A reanalysis of the Mercury flybys also constrains the spin rate over the longest available time span.

Orbital Evolution of Planetesimals by the Galactic Tide

NASA Astrophysics Data System (ADS)

Higuchi, A.; Kokubo, E.; Mukai, T.

2005-05-01

The Oort cloud is a spherical comet reservoir surrounding the solar system. There is general agreement that the Oort cloud comets are the residual planetesimals of planet formation. The standard scenario of the Oort cloud formation consists of two dynamical stages: (1) giant planets raise the aphelia of planetesimals to the outer region of the solar system and (2) the galactic tide, passing stars, and giant molecular clouds pull up their perihelia out of the planetary region. Here we show the orbital evolution of planetesimals by the galactic tide. Planetesimals with large aphelion distances change their perihelion distances toward the outside of the planetary region by the galactic tide and become members of the Oort cloud. The effect of the galactic tide on the planetesimals with semimajor axes of ˜ 104AU is about 10-3 of the solar gravity. The timescale of the orbital evolution is ˜ 108 years. We consider only the vertical component of the galactic tide. Under the axisymmetric potential, some planetesimals may show the librations around ω (argument of perihelion)=π /2 and 3π /2 (the Kozai mechanism). The alternate increases of eccentricity and inclination of the Kozai mechanism are effective to form the Oort cloud. The secular perturbation theory demonstrates the Kozai mechanism and we can understand the motion of the planetesimals analytically. We apply the Kozai mechanism to the galactic tide and discuss the property of the Oort cloud formed by the Kozai mechanizm. This work was supported by the 21st Century COE Program Origin and Evolution of Planetary Systems of the Ministry of Education, Culture, Sports, Science, and Technology, Japan, and JSPS Research Fellowship for Young Scientists.

Toward Understanding Astrophysical Phenomena

NASA Astrophysics Data System (ADS)

Luan, Jing

2015-06-01

I hope to resume working on fast radio bursts (FRBs) in the near future. But after we completed our FRB paper, I decided to pause this project because of the lack of observational constraints. The pulsar triple system, J0733+1715, has its orbital parameters fitted to high accuracy owing to the precise timing of the central ms pulsar. The two orbits are highly hierarchical, namely Porb,1 " Porb,2, where 1 and 2 label the inner and outer white dwarf (WD) companions respectively. Moreover, their orbital planes almost coincide, providing a unique opportunity to study secular interaction associated purely with eccentricity beyond the solar system. Secular interaction only involves effect averaged over many orbits. Thus each companion can be represented by an elliptical wire with its mass distributed inversely proportional to its local orbital speed. Generally there exists a mutual torque, which vanishes only when their apsidal lines are parallel or anti-parallel. To maintain either mode, the eccentricity ratio, e1/ e2, must be of the proper value, so that both apsidal lines precess together. For J0733+1715, e1 " e2 for the parallel mode, while e 1 " e2 for the anti-parallel one. We show that the former precesses ˜10 times slower than the latter. Currently the system is dominated by the parallel mode. Although only a little anti-parallel mode survives, both eccentricities especially e1 oscillate on ˜103yr timescale. Detectable changes would occur within ˜1y. We demonstrate that the anti-parallel mode gets damped ˜10 4 times faster than its parallel brother by any dissipative process diminishing e1. If it is the tidal damping in the inner WD, we proceed to estimate its tidal quantity parameter (Q) to be ˜106, which was poorly constrained by observations. However, tidal damping may also happen during the preceding low-mass X-ray binary (LMXB) phase or hydrogen thermal nuclear flashes. But, in both cases, the inner companion fills its Roche lobe and probably suffers mass/angular momentum loss, which might cause e1 to grow rather than decay. Several pairs of solar system satellites occupy mean motion resonances (MMRs). We divide these into two groups according to their proximity to exact resonance. Proximity is measured by the existence of a separatrix in phase space. MMRs between Io-Europa, Europa-Ganymede and Enceladus-Dione are too distant from exact resonance for a separatrix to appear. A separatrix is present only in the phase spaces of the Mimas-Tethys and Titan-Hyperion MMRs and their resonant arguments are the only ones to exhibit substantial librations. When a separatrix is present, tidal damping of eccentricity or inclination excites overstable librations that can lead to passage through resonance on the damping timescale. However, after investigation, we conclude that the librations in the Mimas-Tethys and Titan-Hyperion MMRs are fossils and do not result from overstability. Rubble piles are common in the solar system. Monolithic elements touch their neighbors in small localized areas. Voids occupy a significant fraction of the volume. In a fluid-free environment, heat cannot conduct through voids; only radiation can transfer energy across them. We model the effective thermal conductivity of a rubble pile and show that it is proportional the square root of the pressure, P, for P ≤ epsilon 3Ymu where epsilonY is the material's yield strain and mu its shear modulus. Our model provides an excellent fit to the depth dependence of the thermal conductivity in the top 140cm of the lunar regolith. It also offers an explanation for the low thermal inertias of rocky asteroids and icy satellites. Lastly, we discuss how rubble piles slow down the cooling of small bodies such as asteroids. In this paper, we propose a computationally efficient time-domain algorithm capable of detecting gravitational waves (GWs) from coalescing binaries of compact objects with nearly zero time delay. In case when the signal is strong enough, our algorithm also has the flexibility to trigger electromagnetic (EM) observation before the merger. The key to the efficiency of our algorithm arises from the use of chains of so-called Infinite Impulse Response (IIR) filters, which filter time-series data recursively. Computational cost is further reduced by a template interpolation technique that requires filtering to be done only for a much coarser template bank than otherwise required to sufficiently recover optimal signal-to-noise ratio. Towards future detectors with sensitivity extending to lower frequencies, our algorithm's computational cost is shown to increase rather insignificantly compared to the conventional time-domain correlation method. Moreover, at latencies of less than hundreds to thousands of seconds, this method is expected to be computationally more efficient than the straightforward frequency-domain method. (Abstract shortened by UMI.).

Density Waves in Saturn's Rings from Cassini Radio Occultations

NASA Astrophysics Data System (ADS)

French, R. G.; Rappaport, N. J.; Marouf, E. A.; McGhee, C. A.

2005-12-01

The Cassini Radio Science Team conducted a set of optimized diametric occultations by Saturn and its rings from May to September 2005, providing 11 separate probes of Saturn's ionosphere and atmosphere, and 12 optical depth profiles of the complete ring system. Each event was observed by the stations of the Deep Space Net (DSN) at three radio frequencies (S, X, Ka bands, with corresponding wavelengths of ? = 13, 3.6, and 0.9 cm). Very accurate pointing by the spacecraft and ground antennas resulted in stable baseline signal levels, and the relatively large ring opening angle (B=19-25°) permitted us to probe even quite dense ring regions with excellent SNR. The RSS occultation technique enables us to recover very fine detailed radial structure by correcting for diffraction effects. Multiple occultation chords, covering a variety of ring longitudes and ring opening angles, reveal the structure of the rings in remarkable detail, including density and bending waves, satellite wakes, and subtle variations at the 100-m radius scale. Janus and Epimetheus are responsible for a particularly rich set of density waves, and their coorbital interactions result in a complex interplay of time-variable ring structure over the 8-year libration period of the two satellites. We compare the first-order 2:1, 4:3, 5:4, and 6:5 coorbital density waves from multiple occultation chords to linear density wave models based on a dynamical model of the orbital exchange between the moons. From the observed dispersion relation of the wave crests, we infer the surface mass density and eccentricity gradient of particle streamlines, and match the detailed shapes of the wave crests using a non-linear analysis. Second-order coorbital features are also evident, and there are even hints of third-order density waves in the high SNR radio occultation data.

Technology Development for Human Exploration Beyond LEO in the New Millennium IAA-13-3 Strategies and Plans for Human Mars Missions

NASA Technical Reports Server (NTRS)

Larson, William E.; Lueck, Dale E.; Parrish, Clyde F.; Sanders, Gerald B.; Trevathan, Joseph R.; Baird, R. Scott; Simon, Tom; Peters, T.; Delgado, H. (Technical Monitor)

2001-01-01

As we look forward into the new millennium, the extension of human presence beyond Low-Earth Orbit (LEO) looms large in the plans of NASA. The Agency's Strategic Plan specifically calls out the need to identify and develop technologies for 100 and 1000-day class missions beyond LEO. To meet the challenge of these extended duration missions, it is important that we learn how to utilize the indigenous resources available to us on extraterrestrial bodies. This concept, known as In-Situ Resource Utilization (ISRU) can greatly reduce the launch mass & cost of human missions while reducing the risk. These technologies may also pave the way for the commercial development of space. While no specific target beyond LEO is identified in NASA's Strategic Plan, mission architecture studies have been on-going for the Moon, Mars, Near-Earth Asteroids and Earth/Moon & Earth/Sun Libration Points. As a result of these studies, the NASA Office of Space Flight (Code M) through the Johnson and Kennedy Space Centers, is leading the effort to develop ISRU technologies and systems to meet the current and future needs of human missions beyond LEO and on to Mars. This effort also receives support from the NASA Office of Biological and Physical Research (Code U), the Office of Space Science (Code S), and the Office of Aerospace Technology (Code R). This paper will present unique developments in the area of fuel and oxidizer production, breathing air production, water production, C02 collection, separation of atmospheric gases, and gas liquefaction and storage. A technology overview will be provided for each topic along with the results achieved to date, future development plans, and the mission architectures that these technologies support.

Quasi-Tangency Points on the Orbits of a Small Body and a Planet at the Low-Velocity Encounter

NASA Astrophysics Data System (ADS)

Emel'yanenko, N. Yu.

2018-03-01

We propose a method for selecting a low-velocity encounter of a small body with a planet from the evolution of the orbital elements. Polar orbital coordinates of the quasi-tangency point on the orbit of a small body are determined. Rectangular heliocentric coordinates of the quasi-tangency point on the orbit of a planet are determined. An algorithm to search for low-velocity encounters in the evolution of the orbital elements of small bodies is described. The low-velocity encounter of comet 39P/Oterma with Jupiter is considered as an example.

Homoclinic orbits and critical points of barrier functions

NASA Astrophysics Data System (ADS)

Cannarsa, Piermarco; Cheng, Wei

2015-06-01

We interpret the close link between the critical points of Mather's barrier functions and minimal homoclinic orbits with respect to the Aubry sets on {{T}}n . We also prove a critical point theorem for barrier functions and the existence of such homoclinic orbits on {{T}}2 as an application.

Heteroclinic, Homoclinic Connections Between the Sun-Earth Triangular Points and Quasi-Satellite Orbits for Solar Observations

NASA Technical Reports Server (NTRS)

Llanos, Pedro J.; Hintz, Gerald R.; Lo, Martin W.; Miller, James K.

2013-01-01

Investigation of new orbit geometries exhibits a very attractive behavior for a spacecraft to monitor space weather coming from the Sun. Several orbit transfer mechanisms are analyzed as potential alternatives to monitor solar activity such as a sub-solar orbit or quasi-satellite orbit and short and long heteroclinic and homoclinic connections between the triangular points L(sub 4) and L(sub 5) and the collinear point L(sub 3) of the Circular Restricted Three-Body Problem (CRTBP) in the Sun-Earth system.

Investigation of dynamic noise affecting geodynamics information in a tethered subsatellite

NASA Technical Reports Server (NTRS)

Gullahorn, G. E.

1984-01-01

The effects of a tethered satellite system's internal dynamics on the subsatellite were calculated including both overall motions (libration and attitude oscillations) and internal tether oscillations. The SKYHOOK tether simulation program was modified to operate with atmospheric density variations and to output quantities of interest. Techniques and software for analyzing the results were developed including noise spectral analysis. A program was begun for computing a stable configuration of a tether system subject to air drag. These configurations will be of use as initial conditions for SKYHOOK and, through linearized analysis, directly for stability and dynamical studies. A case study in which the subsatellite traverses an atmospheric density enhancement confirmed some theoretical calculations, and pointed out some aspects of the interaction with the tether system dynamics.

Laser Technology in Interplanetary Exploration: The Past and the Future

NASA Technical Reports Server (NTRS)

Smith, David E.

2000-01-01

Laser technology has been used in planetary exploration for many years but it has only been in the last decade that laser altimeters and ranging systems have been selected as flight instruments alongside cameras, spectrometers, magnetometers, etc. Today we have an active laser system operating at Mars and another destined for the asteroid Eros. A few years ago a laser ranging system on the Clementine mission changed much of our thinking about the moon and in a few years laser altimeters will be on their way to Mercury, and also to Europa. Along with the increased capabilities and reliability of laser systems has came the realization that precision ranging to the surface of planetary bodies from orbiting spacecraft enables more scientific problems to be addressed, including many associated with planetary rotation, librations, and tides. In addition, new Earth-based laser ranging systems working with similar systems on other planetary bodies in an asynchronous transponder mode will be able to make interplanetary ranging measurements at the few cm level and will advance our understanding of solar system dynamics and relativistic physics.

Peculiar Euphrosyne

NASA Astrophysics Data System (ADS)

Carruba, V.; Aljbaae, S.; Souami, D.

2014-09-01

The asteroid (31) Euphrosyne is the largest body of its namesake family, and it contains more than 99% of the family mass. Among large asteroid families, the Euphrosyne group is peculiar because of its quite steep size-frequency distribution (SFD), significantly depleted in large- and medium-sized asteroids (8 < D < 12 km). The current steep SFD of the Euphrosyne family has been suggested to be the result of a grazing impact in which only the farthest, smallest members failed to accrete. The Euphrosyne family is, however, also very peculiar because of its dynamics: near its center it is crossed by the ν6 = g - g 6 linear secular resonance, and it hosts the largest population (140 bodies) of asteroids in ν6 antialigned librating states (or Tina-like asteroids) in the main belt. In this work we investigated the orbital evolution of newly obtained members of the dynamical family, with an emphasis on its interaction with the ν6 resonance. Because of its unique resonant configuration, large- and medium-sized asteroids tend to migrate away from the family orbital region faster than small-sized objects, which were ejected farther away from the family center. As a consequence, the SFD of the Euphrosyne family becomes steeper in time with a growing depletion in the number of the largest family members. We estimate that the current SFD could be attained from a typical, initial SFD on timescales of 500 Myr, consistent with estimates of the family age obtained with other independent methods.

Peculiar Euphrosyne

NASA Astrophysics Data System (ADS)

Carruba, V.; Aljbaae, S.; Souami, D.

2014-07-01

(31) Euphrosyne is the largest body of its namesake family, and contains more the 99.35% of the family mass. Among asteroid families, the Euphosyne group is peculiar because of its quite steep size frequency distribution, significantly depleted in large and medium- sized asteroids (8 < D < 12~km). The current steep size frequency distribution of the Euphrosyne family has been suggested to be the result of a grazing impact in which only the farthest, smallest members failed to accrete. The Euphrosyne family is however also very peculiar because of its dynamics: near its center it is crossed by the ν_6 = g -g_6 linear secular resonance, and it hosts the largest population (140 bodies) of asteroids in ν_6 anti-aligned librating states (or Tina-like asteroids) in the main belt. In this work we investigated the orbital evolution of newly obtained members of the dynamical family, with an emphasis on its interaction with the ν_6 resonance. Because of its unique resonant configuration, large and medium sized asteroids tend to migrate away from the family orbital region faster than small-sized objects, that were ejected further away from the family center. As a consequence, the size-frequency distribution of the Euphrosyne family becomes steeper in time, with a growing depletion in the number of the largest family members. We estimate that the current size-frequency distribution could be attained from a typical, initial size-frequency distribution in time-scales of the order of 1~Byr, consistently with estimates of the family age obtained with other, independent, methods.

Variable character of O—O and M—O bonding in side-on (η2) 1:1 metal complexes of O2

PubMed Central

Cramer, Christopher J.; Tolman, William B.; Theopold, Klaus H.; Rheingold, Arnold L.

2003-01-01

The structures and the O—O and M—O bonding characters of a series of reported side-on (η2) 1:1 metal complexes of O2 are analyzed by using density functional theory calculations. Comparison of the calculated and experimental systems with respect to O—O bond distance, O—O stretching frequency, and O—O and M—O bond orders provides new insights into subtle influences relevant to O2 activation processes in biology and catalysis. The degree of charge transfer from the generally electron-rich metals to the dioxygen fragment is found to be variable, such that there are species well described as superoxides, others well described as peroxides, and several cases having intermediate character. Increased charge transfer to dioxygen takes place via overlap of the metal dxy orbital with the in-plane π* orbital of O2 and results in increased M—O bond orders and decreased O—O bond orders. Comparison of theory and experiment over the full range of compounds studied suggests that reevaluation of the O—O bond lengths determined from certain x-ray crystal structures is warranted; in one instance, an x-ray crystal structure redetermination was performed at low temperature, confirming the theoretical prediction. Librational motion of the coordinated O2 is identified as a basis for significant underestimation of the O—O distance at high temperature. PMID:12634422

Orbital stability analysis and chaotic dynamics of exoplanets in multi-stellar systems

NASA Astrophysics Data System (ADS)

Satyal, Suman

The advancement in detection technology has substantially increased the discovery rate of exoplanets in the last two decades. The confirmation of thousands of exoplanets orbiting the solar type stars has raised new astrophysical challenges, including the studies of orbital dynamics and long-term stability of such planets. Continuous orbital stability of the planet in stellar habitable zone is considered vital for life to develop. Hence, these studies furthers one self-evident aim of mankind to find an answer to the century old question: Are we alone?. This dissertation investigates the planetary orbits in single and binary star systems. Within binaries, a planet could orbit either one or both stars as S-type or P-type, respectively. I have considered S-type planets in two binaries, gamma Cephei and HD 196885, and compute their orbits by using various numerical techniques to assess their periodic, quasi-periodic or chaotic nature. The Hill stability (HS) function, which measures the orbital perturbation induced by the nearby companion, is calculated for each system and then its efficacy as a new chaos indicator is tested against Maximum Lyapunov Exponents (MLE) and Mean Exponential Growth factor of Nearby Orbits (MEGNO). The dynamics of HD 196885 AB is further explored with an emphasis on the planet's higher orbital inclination relative to the binary plane. I have quantitatively mapped out the chaotic and quasi-periodic regions of the system's phase space, which indicates a likely regime of the planet's inclination. In, addition, the resonant angle is inspected to determine whether alternation between libration and circulation occurs as a consequence of Kozai oscillations, a probable mechanism that can drive the planetary orbit to a large inclination. The studies of planetary system in GJ 832 shows potential of hosting multiple planets in close orbits. The phase space of GJ 832c (inner planet) and the Earth-mass test planet(s) are analyzed for periodic-aperiodic orbits. The stability of the system is defined in terms of its lifetime and maximum eccentricity during the integration period then a regime is established for the known and injected planet's orbital parameters. The de-stabilizing resonances due to the outer planet extend by 1.36 AU towards the star, nonetheless, existence of two Earth-mass planets seems plausible. The radial velocity (RV) curves generated for the test planets reveals a weak RV signal that cannot be measured by currently available instruments. A theory has been developed by extrapolating the radio emission processes in the Jupiter-Io system, which could reveal the presence of exomoons around the giant exoplanets. Based on this theory, maximum distance, radius and masses of exoplanets and exomoons are calculated that could be detected by the available radio telescopes. Observation time at the Low Frequency Array (LOFAR) radio telescope has been proposed to detect exomoon in five different stellar systems. Subjects of my future studies include analysis of the data from LOFAR, search for the additional transiting planets in Kepler 47 circumbinary system and observation at the Subaru telescope to verify the predicted planets in GJ 832 system by the method of direct imaging.

Development of non-bonded interaction parameters between graphene and water using particle swarm optimization.

PubMed

Bejagam, Karteek K; Singh, Samrendra; Deshmukh, Sanket A

2018-05-05

New Lennard-Jones parameters have been developed to describe the interactions between atomistic model of graphene, represented by REBO potential, and five commonly used all-atom water models, namely SPC, SPC/E, SPC/Fw, SPC/Fd, and TIP3P/Fs by employing particle swarm optimization (PSO) method. These new parameters were optimized to reproduce the macroscopic contact angle of water on a graphene sheet. The calculated line tension was in the order of 10 -11 J/m for the droplets of all water models. Our molecular dynamics simulations indicate the preferential orientation of water molecules near graphene-water interface with one OH bond pointing toward the graphene surface. Detailed analysis of simulation trajectories reveals the presence of water molecules with ≤∼1, ∼2, and ∼4 hydrogen bonds at the surface of air-water interface, graphene-water interface, and bulk region of the water droplet, respectively. Presence of water molecules with ≤∼1 and ∼2 hydrogen bonds suggest the existence of water clusters of different sizes at these interfaces. The trends observed in the libration, bending, and stretching bands of the vibrational spectra are closely associated with these structural features of water. The inhomogeneity in hydrogen bond network of water at the air-water and graphene-water interface is manifested by broadening of the peaks in the libration band for water present at these interfaces. The stretching band for the molecules in water droplet shows a blue shift as compared to the pure bulk water, which conjecture the presence of weaker hydrogen bond network in a droplet. © 2017 Wiley Periodicals, Inc. © 2017 Wiley Periodicals, Inc.

On geodynamo integrations conserving momentum flux

NASA Astrophysics Data System (ADS)

Wu, C.; Roberts, P. H.

2012-12-01

The equations governing the geodynamo are most often integrated by representing the magnetic field and fluid velocity by toroidal and poloidal scalars (for example, MAG code [1]). This procedure does not automatically conserve the momentum flux. The results can, particularly for flows with large shear, introduce significant errors, unless the viscosity is artificially increased. We describe a method that evades this difficulty, by solving the momentum equation directly while properly conserving momentum. It finds pressure by FFT and cyclic reduction, and integrates the governing equations on overlapping grids so avoiding the pole problem. The number of operations per time step is proportional to N3 where N is proportional to the number of grid points in each direction. This contrasts with the order N4 operations of standard spectral transform methods. The method is easily parallelized. It can also be easily adapted to schemes such as the Weighted Essentially Non-Oscillatory (WENO) method [2], a flux based procedure based on upwinding that is numerically stable even for zero explicit viscosity. The method has been successfully used to investigate the generation of magnetic fields by flows confined to spheroidal containers and driven by precessional and librational forcing [3, 4]. For spherical systems it satisfies dynamo benchmarks [5]. [1] MAG, http://www.geodynamics.org/cig/software/mag [2] Liu, XD, Osher, S and Chan, T, Weighted Essentially Nonoscillatory Schemes, J. Computational Physics, 115, 200-212, 1994. [3] Wu, CC and Roberts, PH, On a dynamo driven by topographic precession, Geophysical & Astrophysical Fluid Dynamics, 103, 467-501, (DOI: 10.1080/03091920903311788), 2009. [4] Wu, CC and Roberts, PH, On a dynamo driven topographically by longitudinal libration, Geophysical & Astrophysical Fluid Dynamics, DOI:10.1080/03091929.2012.682990, 2012. [5] Christensen, U, et al., A numerical dynamo benchmark, Phys. Earth Planet Int., 128, 25-34, 2001.

Void Points, Rosettes, and a Brief History of Planetary Astronomy

NASA Astrophysics Data System (ADS)

Kosso, Peter

2013-12-01

Almost all models of planetary orbits, from Aristotle through Newton, include void points, empty points in space that have an essential role in defining the orbit. By highlighting the role of these void points, as well as the rosette pattern of the orbit that often results, I bring out different features in the history of planetary astronomy and place a different emphasis on its revolutionary changes, different from those rendered in terms of epicycles or the location of the earth.

Chandra X-Ray Observatory Pointing Control System Performance During Transfer Orbit and Initial On-Orbit Operations

NASA Technical Reports Server (NTRS)

Quast, Peter; Tung, Frank; West, Mark; Wider, John

2000-01-01

The Chandra X-ray Observatory (CXO, formerly AXAF) is the third of the four NASA great observatories. It was launched from Kennedy Space Flight Center on 23 July 1999 aboard the Space Shuttle Columbia and was successfully inserted in a 330 x 72,000 km orbit by the Inertial Upper Stage (IUS). Through a series of five Integral Propulsion System burns, CXO was placed in a 10,000 x 139,000 km orbit. After initial on-orbit checkout, Chandra's first light images were unveiled to the public on 26 August, 1999. The CXO Pointing Control and Aspect Determination (PCAD) subsystem is designed to perform attitude control and determination functions in support of transfer orbit operations and on-orbit science mission. After a brief description of the PCAD subsystem, the paper highlights the PCAD activities during the transfer orbit and initial on-orbit operations. These activities include: CXO/IUS separation, attitude and gyro bias estimation with earth sensor and sun sensor, attitude control and disturbance torque estimation for delta-v burns, momentum build-up due to gravity gradient and solar pressure, momentum unloading with thrusters, attitude initialization with star measurements, gyro alignment calibration, maneuvering and transition to normal pointing, and PCAD pointing and stability performance.

Graphical techniques to assist in pointing and control studies of orbiting spacecraft

NASA Technical Reports Server (NTRS)

Howell, L. W.; Ruf, J. H.

1986-01-01

Computer generated graphics are developed to assist in the modeling and assessment of pointing and control systems of orbiting spacecraft. Three-dimensional diagrams are constructed of the Earth and of geometrical models which resemble the spacecraft of interest. Orbital positioning of the spacecraft model relative to the Earth and the orbital ground track are then displayed. A star data base is also available which may be used for telescope pointing and star tracker field-of-views to visually assist in spacecraft pointing and control studies. A geometrical model of the Hubble Space Telescope (HST) is constructed and placed in Earth orbit to demonstrate the use of these programs. Simulated star patterns are then displayed corresponding to the primary mirror's FOV and the telescope's star trackers for various telescope orientations with respect to the celestial sphere.

Closeup view of the Reinforced CarbonCarbon nose cap on the ...

Library of Congress Historic Buildings Survey, Historic Engineering Record, Historic Landscapes Survey

Close-up view of the Reinforced Carbon-Carbon nose cap on the front fuselage of the Orbiter Discovery. Note the 76-wheeled orbiter transfer system attached to the orbiter at the forward attach point, the same attach point used to mount the orbiter onto the External Tank. This view was taken at Kennedy Space Center. - Space Transportation System, Orbiter Discovery (OV-103), Lyndon B. Johnson Space Center, 2101 NASA Parkway, Houston, Harris County, TX

Evolution of NASA's Near-Earth Tracking and Data Relay Satellite System (TDRSS)

NASA Technical Reports Server (NTRS)

Flaherty, Roger; Stocklin, Frank; Weinberg, Aaron

2006-01-01

NASA's Tracking and Data Relay Satellite System (TDRSS) is now in its 23rd year of operations and its spacecraft fleet includes three second-generation spacecraft launched since the year 2000; a figure illustrates the first generation TDRSS spacecraft. During this time frame the TDRSS has provided communications relay support to a broad range of missions, with emphasis on low-earth-orbiting (LEO) spacecraft that include unmanned science spacecraft (e.g., Hubble Space Telescope), and human spaceflight (Space Shuttle and Space Station). Furthermore, the TDRSS has consistently demonstrated its uniqueness and adaptability in several ways. First, its S- and K-band services, combined with its multi-band/steerable single-access (SA) antennas and ground-based configuration flexibility, have permitted the mission set to expand to unique users such as scientific balloons and launch vehicles. Second, the bent-pipe nature of the system has enabled the introduction of new/improved services via technology insertion and upgrades at each of the ground terminals; a specific example here is the Demand Access Service (DAS), which, for example, is currently providing science-alert support to NASA science missions Third, the bent-pipe nature of the system, combined with the flexible ground-terminal signal processing architecture has permitted the demonstration/vaIidation of new techniques/services/technologies via a real satellite channel; over the past 10+ years these have, for example, included demonstrations/evaluations of emerging modulation/coding techniques. Given NASA's emerging Exploration plans, with missions beginning later this decade and expanding for decades to come, NASA is currently planning the development of a seamless, NASA-wide architecture that must accommodate missions from near-earth to deep space. Near-earth elements include Ground-Network (GN) and Near-Earth Relay (NER) components and both must efficiently and seamlessly support missions that encompass: earth orbit, including dedicated science missions and lunar support/cargo vehicles; earth/moon transit; lunar in-situ operations; and other missions within approximately 2 million km of earth (e.g., at the sun/earth libration points). Given that the NER is an evolution of TDRSS, one element of this NASA-wide architecture development activity is a trade study of future NER architecture candidates. The present paper focuses on trade study aspects associated with the NER, highlights study elements, and provides representative interim results.

The Space Shuttle orbiter payload retention systems

NASA Technical Reports Server (NTRS)

Hardee, J. H.

1982-01-01

Payloads are secured in the orbiter payload bay by the payload retention system or are equipped with their own unique retention systems. The orbiter payload retention mechanisms provide structural attachments for each payload by using four or five attachment points to secure the payload within the orbiter payload bay during all phases of the orbiter mission. The payload retention system (PRS) is an electromechanical system that provides standarized payload carrier attachment fittings to accommodate up to five payloads for each orbiter flight. The mechanisms are able to function under either l-g or zero-g conditions. Payload berthing or deberthing on orbit is accomplished by utilizing the remote manipulator system (RMS). The retention mechanisms provide the capability for either vertical or horizontal payload installation or removal. The payload support points are selected to minimize point torsional, bending, and radial loads imparted to the payloads. In addition to the remotely controlled latching system, the passive system used for nondeployable payloads performs the same function as the RMS except it provides fixed attachments to the orbiter.

Orbital stability close to asteroid 624 Hektor using the polyhedral model

NASA Astrophysics Data System (ADS)

Jiang, Yu; Baoyin, Hexi; Li, Hengnian

2018-03-01

We investigate the orbital stability close to the unique L4-point Jupiter binary Trojan asteroid 624 Hektor. The gravitational potential of 624 Hektor is calculated using the polyhedron model with observational data of 2038 faces and 1021 vertexes. Previous studies have presented three different density values for 624 Hektor. The equilibrium points in the gravitational potential of 624 Hektor with different density values have been studied in detail. There are five equilibrium points in the gravitational potential of 624 Hektor no matter the density value. The positions, Jacobian, eigenvalues, topological cases, stability, as well as the Hessian matrix of the equilibrium points are investigated. For the three different density values the number, topological cases, and the stability of the equilibrium points with different density values are the same. However, the positions of the equilibrium points vary with the density value of the asteroid 624 Hektor. The outer equilibrium points move away from the asteroid's mass center when the density increases, and the inner equilibrium point moves close to the asteroid's mass center when the density increases. There exist unstable periodic orbits near the surface of 624 Hektor. We calculated an orbit near the primary's equatorial plane of this binary Trojan asteroid; the results indicate that the orbit remains stable after 28.8375 d.

Photometric constraints on binary asteroid dynamics

NASA Astrophysics Data System (ADS)

Scheirich, Peter

2015-08-01

To date, about 50 binary NEAs, 20 Mars-crossing and 80 small MB asteroids are known. We observe also a population of about 200 unbound asteroid systems (asteroid pairs). I will review the photometric observational data we have for the best observed cases and compare them with theories of binary and paired asteroids evolution.The observed characteristics of asteroid systems suggest their formation by rotational fission of parent rubble-pile asteroids after being spun up by the YORP effect. The angular momentum content of binary asteroids is close to critical. The orientations of satellite orbits of observed binary systems are non-random; the orbital poles concentrate near the obliquities of 0 and 180 degrees, i.e., near the YORP asymptotic states.Recently, a significant excess of retrograde satellite orbits was detected, which is not yet explained characteristic.An evolution of binary system depend heavily on the BYORP effect. If BYORP is contractive, the primary and secondary could end in a tidal-BYORP equilibrium. Observations of mutual events between binary components in at least four apparitions are needed for BYORP to be revealed by detecting a quadratic drift in mean anomaly of the satellite. I will show the observational evidence of single-synchronous binary asteroid with tidally locked satellite (175706 1996 FG3), i.e, with the quadratic drift equal to zero, and binary asteroid with contracting orbit (88710 2001 SL9), with positive value of the quadratic drift (the solution for the quadratic drift is ambiguous so far, with possible values of 5 and 8 deg/yr2).The spin configuration of the satellite play a crucial role in the evolution of the system under the influence of the BYORP effect. I will show that the rotational lightcurves of the satellites show that most of them have small libration amplitudes (up to 20 deg.), with a few interesting exceptions.Acknowledgements: This work has been supported by the Grant Agency of the Czech Republic, Grant P209/12/0229, and by the Ministry of Education of the Czech Republic, Grant LG12001.

Low mass planet migration in magnetically torqued dead zones - I. Static migration torque

NASA Astrophysics Data System (ADS)

McNally, Colin P.; Nelson, Richard P.; Paardekooper, Sijme-Jan; Gressel, Oliver; Lyra, Wladimir

2017-12-01

Motivated by models suggesting that the inner planet forming regions of protoplanetary discs are predominantly lacking in viscosity-inducing turbulence, and are possibly threaded by Hall-effect generated large-scale horizontal magnetic fields, we examine the dynamics of the corotation region of a low-mass planet in such an environment. The corotation torque in an inviscid, isothermal, dead zone ought to saturate, with the libration region becoming both symmetrical and of a uniform vortensity, leading to fast inward migration driven by the Lindblad torques alone. However, in such a low viscosity situation, the material on librating streamlines essentially preserves its vortensity. If there is relative radial motion between the disc gas and the planet, the librating streamlines will no longer be symmetrical. Hence, if the gas is torqued by a large-scale magnetic field so that it undergoes a net inflow or outflow past the planet, driving evolution of the vortensity and inducing asymmetry of the corotation region, the corotation torque can grow, leading to a positive torque. In this paper, we treat this effect by applying a symmetry argument to the previously studied case of a migrating planet in an inviscid disc. Our results show that the corotation torque due to a laminar Hall-induced magnetic field in a dead zone behaves quite differently from that studied previously for a viscous disc. Furthermore, the magnetic field induced corotation torque and the dynamical corotation torque in a low viscosity disc can be regarded as one unified effect.

Practicality of Using a Tether for Electrodynamic Reboost of the International Space Station

NASA Technical Reports Server (NTRS)

Blumer, J. H.; Donahue, Benjamin B.; Bangham, Michal E.; Roth, A. (Technical Monitor)

2001-01-01

ElectroDynamic (ED) Tethers can generate continuous low thrust in a low Earth orbit. An induced current running through the length of the tether reacts with the geomagnetic field to produce thrust. The amount of thrust scales with tether lens!th and current. The International Space Station (ISS) requires periodic reboost to maintain an approximately circular orbit t above the Earth. The baseline reboost method is a traditional bi-propellant rocket thruster and tankage system which must to be refueled via Soyuz / Progress or other launch vehicle. The estimated propellant costs associated with keeping ISS in the designated orbit over a 10-year life have been extremely high. The ED Tether would draw energy from the renewable ISS Solar Array electrical power system. Propulsion requirements for ISS vary depending on solar wind and other conditions. It is projected that a ED Tether could provide the majority of the required reboost thrust for ISS for a nominal solar year. For above nominal solar wind years the ISS would have to use the rocket reboost system, but at a greatly reduced level. Thus resulting in substantial cost savings, via the reduction in the number of Earth-to-orbit launch vehicle flights to the ISS that must bring reboost propellant. However, the purposes of this paper is to further Previous research on an ISS ED Tether and examine the operational and technical issues working against using a ED Tether on ISS. Issues such as Shuttle rendezvous and flight path concerns raise serious safety concerns and restrictions on tether use. Tether issues such as tether librations and off angle thrust raise concerns about impacts to microgravity payloads and the long-term effect on ISS orbital path and inclination. Operational issues such as peak power available to an ED Tether and allowable duty cycle may impose severe restrictions on tether design and ultimately limit the practicality of an ED Tether on ISS. Thus while at first glance the cost numbers appear to be strongly in favor of an ED Tether the limitations imposed by safety, operations and technical concerns may severely undermine the economic model. Possible Solutions to these problems have been investigated and proposed, however some items like off angle thrust are still being actively investigated for an adequate solution.

In-Flight Guidance, Navigation, and Control Performance Results for the GOES-16 Spacecraft

NASA Technical Reports Server (NTRS)

Chapel, Jim; Stancliffe, Devin; Bevacqua, Tim; Winkler, Stephen; Clapp, Brian; Rood, Tim; Freesland, Doug; Reth, Alan; Early, Derrick; Walsh, Tim;

The Dynamics of Tightly-packed Planetary Systems in the Presence of an Outer Planet: Case Studies Using Kepler-11 and Kepler-90

NASA Astrophysics Data System (ADS)

Granados Contreras, A. P.; Boley, A. C.

2018-03-01

We explore the effects of an undetected outer giant planet on the dynamics, observability, and stability of Systems with Tightly-packed Inner Planets (STIPs). We use direct numerical simulations along with secular theory and synthetic secular frequency spectra to analyze how analogues of Kepler-11 and Kepler-90 behave in the presence of a nearly co-planar, Jupiter-like outer perturber with semimajor axes between 1 and 5.2 au. Most locations of the outer perturber do not affect the evolution of the inner planetary systems, apart from altering precession frequencies. However, there are locations at which an outer planet causes system instability due to, in part, secular eccentricity resonances. In Kepler-90, there is a range of orbital distances for which the outer perturber drives planets b and c, through secular interactions, onto orbits with inclinations that are ∼16° away from the rest of the planets. Kepler-90 is stable in this configuration. Such secular resonances can thus affect the observed multiplicity of transiting systems. We also compare the synthetic apsidal and nodal precession frequencies with the secular theory and find some misalignment between principal frequencies, indicative of strong interactions between the planets (consistent with the system showing TTVs). First-order libration angles are calculated to identify MMRs in the systems, for which two near-MMRs are shown in Kepler-90, with a 5:4 between b and c, as well as a 3:2 between g and h.

On a lunar space elevator

NASA Astrophysics Data System (ADS)

Lemke, E. H.

We consider a space elevator system for lunar surface access that consists of a space station in circumlunar orbit, a cable reaching down to some meters above the surface and a magnetically levitated vehicle driven by a linear motor. It accelerates the load to be lifted to the speed of the cable end. Loads to be delivered are either put on the vehicle and slowed down by it or they are slowed down by a sand braking technique in a mare terrain. It is technically possible to operate this transport system nearly without fuel supply from Earth. We calculate various steel cable dimensions for a static stress maximum of 1/5th of the tensile strength. The process of takeover is considered in detail. Five ways of eliminating the adverse large cable elongation due to the load are described. The touchdown process and behaviour of the cable after disconnection are analysed. The positive difference between the speed of the load at takeover and cable end can excite a large inplane swing motion. We propose to damp it by a dissipative pulley that hangs in a loop of wire leading to the ends of two beams mounted on the space station tangentially to the orbit, the pulley's core being connected with the load. Roll librations are damped by energy losses in the elastic beams; damping can be reinforced by viscous beam elements and/or controlled out-of-plane motions of the beams. We argue in favour of the possibility of fast deployment. The problems of vehicle vibrations and agglutination at sand braking blades are underlined and their combined experimental investigation is suggested.

Determining parameters of Moon's orbital and rotational motion from LLR observations using GRAIL and IERS-recommended models

NASA Astrophysics Data System (ADS)

Pavlov, Dmitry A.; Williams, James G.; Suvorkin, Vladimir V.

2016-11-01

The aim of this work is to combine the model of orbital and rotational motion of the Moon developed for DE430 with up-to-date astronomical, geodynamical, and geo- and selenophysical models. The parameters of the orbit and physical libration are determined in this work from lunar laser ranging (LLR) observations made at different observatories in 1970-2013. Parameters of other models are taken from solutions that were obtained independently from LLR. A new implementation of the DE430 lunar model, including the liquid core equations, was done within the EPM ephemeris. The postfit residuals of LLR observations make evident that the terrestrial models and solutions recommended by the IERS Conventions are compatible with the lunar theory. That includes: EGM2008 gravitational potential with conventional corrections and variations from solid and ocean tides; displacement of stations due to solid and ocean loading tides; and precession-nutation model. Usage of these models in the solution for LLR observations has allowed us to reduce the number of parameters to be fit. The fixed model of tidal variations of the geopotential has resulted in a lesser value of Moon's extra eccentricity rate, as compared to the original DE430 model with two fit parameters. A mixed model of lunar gravitational potential was used, with some coefficients determined from LLR observations, and other taken from the GL660b solution obtained from the GRAIL spacecraft mission. Solutions obtain accurate positions for the ranging stations and the five retroreflectors. Station motion is derived for sites with long data spans. Dissipation is detected at the lunar fluid core-solid mantle boundary demonstrating that a fluid core is present. Tidal dissipation is strong at both Earth and Moon. Consequently, the lunar semimajor axis is expanding by 38.20 mm/yr, the tidal acceleration in mean longitude is -25.90 {{}^' ' }}/cy^2, and the eccentricity is increasing by 1.48× 10^{-11} each year.

Communication: Photoionization of degenerate orbitals for randomly oriented molecules: The effect of time-reversal symmetry on recoil-ion momentum angular distributions

NASA Astrophysics Data System (ADS)

Suzuki, Yoshi-Ichi

2018-04-01

The photoelectron asymmetry parameter β, which characterizes the direction of electrons ejected from a randomly oriented molecular ensemble by linearly polarized light, is investigated for degenerate orbitals. We show that β is totally symmetric under the symmetry operation of the point group of a molecule, and it has mixed properties under time reversal. Therefore, all degenerate molecular orbitals, except for the case of degeneracy due to time reversal, have the same β (Wigner-Eckart theorem). The exceptions are e-type complex orbitals of the Cn, Sn, Cnh, T, and Th point groups, and calculations on boric acid (C3h symmetry) are performed as an example. However, including those point groups, all degenerate orbitals have the same β if those orbitals are real. We discuss the implications of this operator formalism for molecular alignment and photoelectron circular dichroism.

Evaluation of use of MPAD trajectory tape and number of orbit points for orbiter mission thermal predictions

NASA Technical Reports Server (NTRS)

Vogt, R. A.

1979-01-01

The application of using the mission planning and analysis division (MPAD) common format trajectory data tape to predict temperatures for preflight and post flight mission analysis is presented and evaluated. All of the analyses utilized the latest Space Transportation System 1 flight (STS-1) MPAD trajectory tape, and the simplified '136 note' midsection/payload bay thermal math model. For the first 6.7 hours of the STS-1 flight profile, transient temperatures are presented for selected nodal locations with the current standard method, and the trajectory tape method. Whether the differences are considered significant or not depends upon the view point. Other transient temperature predictions are also presented. These results were obtained to investigate an initial concern that perhaps the predicted temperature differences between the two methods would not only be caused by the inaccuracies of the current method's assumed nominal attitude profile but also be affected by a lack of a sufficient number of orbit points in the current method. Comparison between 6, 12, and 24 orbit point parameters showed a surprising insensitivity to the number of orbit points.

ASPS performance with large payloads onboard the Shuttle Orbiter. [Annular Suspension and Pointing System

NASA Technical Reports Server (NTRS)

Keckler, C. R.

1980-01-01

A high fidelity digital computer simulation was used to establish the viability of the Annular Suspension and Pointing System (ASPS) for satisfying the pointing and stability requirements of facility class payloads, such as the Solar Optical Telescope, when subjected to the Orbiter disturbance environment. The ASPS and its payload were subjected to disturbances resulting from crew motions in the Orbiter aft flight deck and VRCS thruster firings. Worst case pointing errors of 0.005 arc seconds were experienced under the disturbance environment simulated; this is well within the 0.08 arc seconds requirement specified by the payload.