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.

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.

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.

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.

Orbit Determination (OD) Error Analysis Results for the Triana Sun-Earth L1 Libration Point Mission and for the Fourier Kelvin Stellar Interferometer (FKSI) Sun-Earth L2 Libration Point Mission Concept

NASA Technical Reports Server (NTRS)

Marr, Greg C.

2003-01-01

The Triana spacecraft was designed to be launched by the Space Shuttle. The nominal Triana mission orbit will be a Sun-Earth L1 libration point orbit. Using the NASA Goddard Space Flight Center's Orbit Determination Error Analysis System (ODEAS), orbit determination (OD) error analysis results are presented for all phases of the Triana mission from the first correction maneuver through approximately launch plus 6 months. Results are also presented for the science data collection phase of the Fourier Kelvin Stellar Interferometer Sun-Earth L2 libration point mission concept with momentum unloading thrust perturbations during the tracking arc. The Triana analysis includes extensive analysis of an initial short arc orbit determination solution and results using both Deep Space Network (DSN) and commercial Universal Space Network (USN) statistics. These results could be utilized in support of future Sun-Earth libration point missions.

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.

ARTEMIS: The First Mission to the Lunar Libration Orbits

NASA Technical Reports Server (NTRS)

Woodward, Mark; Folta, David; Woodfork, Dennis

2009-01-01

The ARTEMIS mission will be the first to navigate to and perform stationkeeping operations around the Earth-Moon L1 and L2 Lagrangian points. The NASA Goddard Space Flight Center (GSFC) has previous mission experience flying in the Sun-Earth L1 (SOHO, ACE, WIND, ISEE-3) and L2 regimes (WMAP) and have maintained these spacecraft in libration point orbits by performing regular orbit stationkeeping maneuvers. The ARTEMIS mission will build on these experiences, but stationkeeping in Earth-Moon libration orbits presents new challenges since the libration point orbit period is on the order of two weeks rather than six months. As a result, stationkeeping maneuvers to maintain the Lissajous orbit will need to be performed frequently, and the orbit determination solutions between maneuvers will need to be quite accurate. The ARTEMIS mission is a collaborative effort between NASA GSFC, the University of California at Berkeley (UCB), and the Jet Propulsion Laboratory (JPL). The ARTEMIS mission is part of the THEMIS extended mission. ARTEMIS comprises two of the five THEMIS spacecraft that will be maneuvered from near-Earth orbits into lunar libration orbits using a sequence of designed orbital maneuvers and Moon & Earth gravity assists. In July 2009, a series of orbit-raising maneuvers began the proper orbit phasing of the two spacecraft for the first lunar flybys. Over subsequent months, additional propulsive maneuvers and gravity assists will be performed to move each spacecraft though the Sun-Earth weak stability regions and eventually into Earth-Moon libration point orbits. We will present the overall orbit designs for the two ARTEMIS spacecraft and provide analysis results of the 3/4-body dynamics, and the sensitivities of the trajectory design to both · maneuver errors and orbit determination errors. We will present results from the. initial orbit-raising maneuvers.

Optimization of Insertion Cost for Transfer Trajectories to Libration Point Orbits

NASA Technical Reports Server (NTRS)

Howell, K. C.; Wilson, R. S.; Lo, M. W.

1999-01-01

The objective of this work is the development of efficient techniques to optimize the cost associated with transfer trajectories to libration point orbits in the Sun-Earth-Moon four body problem, that may include lunar gravity assists. Initially, dynamical systems theory is used to determine invariant manifolds associated with the desired libration point orbit. These manifolds are employed to produce an initial approximation to the transfer trajectory. Specific trajectory requirements such as, transfer injection constraints, inclusion of phasing loops, and targeting of a specified state on the manifold are then incorporated into the design of the transfer trajectory. A two level differential corrections process is used to produce a fully continuous trajectory that satisfies the design constraints, and includes appropriate lunar and solar gravitational models. Based on this methodology, and using the manifold structure from dynamical systems theory, a technique is presented to optimize the cost associated with insertion onto a specified libration point orbit.

Time-free transfers between libration-point orbits in the elliptic restricted problem

NASA Astrophysics Data System (ADS)

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

This work is part of a larger research effort directed toward the formulation of a strategy to design optimal time-free impulsive transfers between three-dimensional libration-point orbits in the vicinity of the interior LI libration point of the Sun-Earth/Moon barycenter system. Inferior transfers that move a spacecraft from a large halo orbit to a smaller halo orbit are considered here. Primer vector theory is applied to non-optimal impulsive trajectories in the elliptic restricted three-body problem in order to establish whether 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 addition of interior impulses is also considered. Results indicate that a substantial savings in fuel can be achieved by the allowance for coastal periods on the specified libration-point orbits. The resulting time-free inferior transfers are compared to time-free superior transfers between halo orbits of equal z-amplitude separation.

Time-free transfers between libration-point orbits in the elliptic restricted problem

NASA Astrophysics Data System (ADS)

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

1992-08-01

This work is directed toward the formulation of a strategy to design optimal time-free impulsive transfers between 3D libration-point orbits in the vicinity of the interior L1 libration point of the sun-earth/moon barycenter system. Inferior transfers that move a spacecraft from a large halo orbit to a smaller halo orbit are considered here. Primer vector theory is applied to nonoptimal impulsive trajectories in the elliptic restricted three-body problem in order to establish whether 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 addition of interior impulses is also considered. Results indicate that a substantial savings in fuel can be achieved by the allowance for coastal periods on the specified libration-point orbits. The resulting time-free inferior transfers are compared to time-free superior transfers between halo orbits of equal z-amplitude separation.

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.

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.

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.

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.

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.

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.

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.

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.

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.

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

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.

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.

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.

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.

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.

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.

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.

Optimal trajectories from the Earth-Moon L1 and L3 points to deflect hazardous asteroids and comets.

PubMed

Maccone, Claudio

2004-05-01

Software code named asteroff was recently created by the author to simulate the deflection of hazardous asteroids off of their collision course with the Earth. This code was both copyrighted and patented to avoid unauthorized use of ideas that could possibly be vital to construct a planetary defense system in the vicinity of the Earth. Having so said, the basic ideas and equations underlying the asteroff simulation code are openly described in this paper. A system of two space bases housing missiles is proposed to achieve the planetary defense of the Earth against dangerous asteroids and comets, collectively called impactors herein. We show that the layout of the Earth-Moon system with the five relevant Lagrangian (or libration) points in space leads naturally to only one, unmistakable location of these two space bases within the sphere of influence of the Earth. These locations are at the two Lagrangian points L(1) (between the Earth and the Moon) and L(3) (in the direction opposite to the Moon from the Earth). We show that placing missile bases at L(1) and L(3) would enable those missiles to deflect the trajectory of impactors by hitting them orthogonally to their impact trajectory toward the Earth, so as to maximize their deflection. We show that confocal conics are the best class of trajectories fulfilling this orthogonal deflection requirement. One additional remark is that the theory developed in this paper is just a beginning for a wider set of future research. In fact, we only develop the Keplerian analytical theory for the optimal planetary defense achievable from the Earth-Moon Lagrangian points L(1) and L(3). Much more sophisticated analytical refinements would be needed to: (1) take into account many perturbation forces of all kinds acting on both the impactors and missiles shot from L(1) and L(3); (2) add more (non-optimal) trajectories of missiles shot from either the Lagrangian points L(4) and L(5) of the Earth-Moon System or from the surface of the

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.

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.

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

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.

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.

The end-of-life disposal of satellites in libration-point orbits using solar radiation pressure

NASA Astrophysics Data System (ADS)

Soldini, Stefania; Colombo, Camilla; Walker, Scott

2016-04-01

This paper proposes an end-of-life propellant-free disposal strategy for libration-point orbits which uses solar radiation pressure to restrict the evolution of the spacecraft motion. The spacecraft is initially disposed into the unstable manifold leaving the libration-point orbit, before a reflective sun-pointing surface is deployed to enhance the effect of solar radiation pressure. Therefore, the consequent increase in energy prevents the spacecraft's return to Earth. Three European Space Agency missions are selected as test case scenarios: Herschel, SOHO and Gaia. Guidelines for the end-of-life disposal of future libration-point orbit missions are proposed and a preliminary study on the effect of the Earth's orbital eccentricity on the disposal strategy is shown for the Gaia mission.

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

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

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

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.

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.

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

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.

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

NASA Technical Reports Server (NTRS)

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

1986-01-01

In order to test the accuracy of using magnetometer data from a spacecraft orbiting the sunward libration point to determine the orientation of the interplanetary magnetic field (IMF), the angle between the IMF at ISEE 3, when it was positioned around the libration point, and at ISEE 1, orbiting the earth, has been calculated for a data set of 1-hour periods covering four months. For each period, a 10-minute average of ISEE 1 data is compared with 10-minute averages of ISEE 3 data at successively lagged intervals. It is concluded that the IMF orientation at a libration-point-orbiting spacecraft, lagged by the time required for the solar wind to convect to the earth, is a convenient predictor of IMF orientation near the earth, to within about 20-degree accuracy.

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

Formation Flying in Earth, Libration, and Distant Retrograde Orbits

NASA Technical Reports Server (NTRS)

Folta, David C.

2004-01-01

This slide presentation examines the current and future state of formation flying, LEO formations, control strategies for flight in the vicinity of the libration points, and distant retrograde orbit formations. This discussion of LEO formations includes background on perturbation theory/accelerations and LEO formation flying. The discussion of strategies for formation flight in the vicinity of the libration points includes libration missions and natural and controlled libration orbit formations. A reference list is included.

Integration of Libration Point Orbit Dynamics into a Universal 3-D Autonomous Formation Flying Algorithm

NASA Technical Reports Server (NTRS)

Folta, David; Bauer, Frank H. (Technical Monitor)

2001-01-01

The autonomous formation flying control algorithm developed by the Goddard Space Flight Center (GSFC) for the New Millennium Program (NMP) Earth Observing-1 (EO-1) mission is investigated for applicability to libration point orbit formations. In the EO-1 formation-flying algorithm, control is accomplished via linearization about a reference transfer orbit with a state transition matrix (STM) computed from state inputs. The effect of libration point orbit dynamics on this algorithm architecture is explored via computation of STMs using the flight proven code, a monodromy matrix developed from a N-body model of a libration orbit, and a standard STM developed from the gravitational and coriolis effects as measured at the libration point. A comparison of formation flying Delta-Vs calculated from these methods is made to a standard linear quadratic regulator (LQR) method. The universal 3-D approach is optimal in the sense that it can be accommodated as an open-loop or closed-loop control using only state information.

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.

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..

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.

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.

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

Alternative Transfer to the Earth-Moon Lagrangian Points L4 and L5 Using Lunar Gravity assist

NASA Astrophysics Data System (ADS)

Salazar, Francisco; Winter, Othon; Macau, Elbert; Bertachini de Almeida Prado, Antonio Fernando

2012-07-01

Lagrangian points L4 and L5 lie at 60 degrees ahead of and behind Moon in its orbit with respect to the Earth. Each one of them is a third point of an equilateral triangle with the base of the line defined by those two bodies. These Lagrangian points are stable for the Earth-Moon mass ratio. Because of their distance electromagnetic radiations from the Earth arrive on them substantially attenuated. As so, these Lagrangian points represent remarkable positions to host astronomical observatories. However, this same distance characteristic may be a challenge for periodic servicing mission. This paper studies transfer orbits in the planar restricted three-body problem. To avoid solving a two-boundary problem, the patched-conic approximation is used to find initial conditions to transfer a spacecraft between an Earth circular parking orbit and the Lagrangian points L4, L5 (in the Earth-Moon system), such that a swing-by maneuver is applied using the lunar gravity. We also found orbits that can be used to make a tour to the Lagrangian points L4, L5 based on the theorem of image trajectories. Keywords: Stable Lagrangian points, L4, L5, Three-Body problem, Patched Conic, Swing-by

Chaotic Dynamics in a Low-Energy Transfer Strategy to the Equilateral Equilibrium Points in the Earth-Moon System

NASA Astrophysics Data System (ADS)

Salazar, F. J. T.; Macau, E. E. N.; Winter, O. C.

In the frame of the equilateral equilibrium points exploration, numerous future space missions will require maximization of payload mass, simultaneously achieving reasonable transfer times. To fulfill this request, low-energy non-Keplerian orbits could be used to reach L4 and L5 in the Earth-Moon system instead of high energetic transfers. Previous studies have shown that chaos in physical systems like the restricted three-body Earth-Moon-particle problem can be used to direct a chaotic trajectory to a target that has been previously considered. In this work, we propose to transfer a spacecraft from a circular Earth Orbit in the chaotic region to the equilateral equilibrium points L4 and L5 in the Earth-Moon system, exploiting the chaotic region that connects the Earth with the Moon and changing the trajectory of the spacecraft (relative to the Earth) by using a gravity assist maneuver with the Moon. Choosing a sequence of small perturbations, the time of flight is reduced and the spacecraft is guided to a proper trajectory so that it uses the Moon's gravitational force to finally arrive at a desired target. In this study, the desired target will be an orbit about the Lagrangian equilibrium points L4 or L5. This strategy is not only more efficient with respect to thrust requirement, but also its time transfer is comparable to other known transfer techniques based on time optimization.

Alternative transfer to the Earth-Moon Lagrangian points L4 and L5 using lunar gravity assist

NASA Astrophysics Data System (ADS)

Salazar, F. J. T.; Macau, E. E. N.; Winter, O. C.

2014-02-01

Lagrangian points L4 and L5 lie at 60° ahead of and behind the Moon in its orbit with respect to the Earth. Each one of them is a third point of an equilateral triangle with the base of the line defined by those two bodies. These Lagrangian points are stable for the Earth-Moon mass ratio. As so, these Lagrangian points represent remarkable positions to host astronomical observatories or space stations. However, this same distance characteristic may be a challenge for periodic servicing mission. This paper studies elliptic trajectories from an Earth circular parking orbit to reach the Moon's sphere of influence and apply a swing-by maneuver in order to re-direct the path of a spacecraft to a vicinity of the Lagrangian points L4 and L5. Once the geocentric transfer orbit and the initial impulsive thrust have been determined, the goal is to establish the angle at which the geocentric trajectory crosses the lunar sphere of influence in such a way that when the spacecraft leaves the Moon's gravitational field, its trajectory and velocity with respect to the Earth change in order to the spacecraft arrives at L4 and L5. In this work, the planar Circular Restricted Three Body Problem approximation is used and in order to avoid solving a two boundary problem, the patched-conic approximation is considered.

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

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.

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.

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 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.

Earth - Moon Conjunction

NASA Technical Reports Server (NTRS)

1992-01-01

On December 16, 1992, 8 days after its encounter with Earth, the Galileo spacecraft looked back from a distance of about 6.2 million kilometers (3.9 million miles) to capture this remarkable view of the Moon in orbit about Earth. The composite photograph was constructed from images taken through visible (violet, red) and near-infrared (1.0-micron) filters. The Moon is in the foreground; its orbital path is from left to right. Brightly colored Earth contrasts strongly with the Moon, which reacts only about one-third as much sunlight as our world. To improve the visibility of both bodies, contrast and color have been computer enhanced. At the bottom of Earth's disk, Antarctica is visible through clouds. The Moon's far side can also be seen. The shadowy indentation in the Moon's dawn terminator--the boundary between its dark and lit sides--is the South Pole-Aitken Basin, one of the largest and oldest lunar impact features. This feature was studied extensively by Galileo during the first Earth flyby in December 1990.

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.

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.

The Earth & Moon

NASA Image and Video Library

1998-06-04

During its flight, NASA’s Galileo spacecraft returned images of the Earth and Moon. Separate images of the Earth and Moon were combined to generate this view. http://photojournal.jpl.nasa.gov/catalog/PIA00342

Libration Orbit Mission Design: Applications of Numerical & Dynamical Methods

NASA Technical Reports Server (NTRS)

Bauer, Frank (Technical Monitor); Folta, David; Beckman, Mark

2002-01-01

Sun-Earth libration point orbits serve as excellent locations for scientific investigations. These orbits are often selected to minimize environmental disturbances and maximize observing efficiency. Trajectory design in support of libration orbits is ever more challenging as more complex missions are envisioned in the next decade. Trajectory design software must be further enabled to incorporate better understanding of the libration orbit solution space and thus improve the efficiency and expand the capabilities of current approaches. The Goddard Space Flight Center (GSFC) is currently supporting multiple libration missions. This end-to-end support consists of mission operations, trajectory design, and control. It also includes algorithm and software development. The recently launched Microwave Anisotropy Probe (MAP) and upcoming James Webb Space Telescope (JWST) and Constellation-X missions are examples of the use of improved numerical methods for attaining constrained orbital parameters and controlling their dynamical evolution at the collinear libration points. This paper presents a history of libration point missions, a brief description of the numerical and dynamical design techniques including software used, and a sample of future GSFC mission designs.

Motion of the Earth as viewed from the moon and the Y-suspended pendulum

NASA Astrophysics Data System (ADS)

Crowell, A. D.

1981-05-01

In the early nineteeth century, James Dean, the first Professor of Mathematics and Natural Philosophy at the University of Vermont, published a paper describing the effects of the librations of the moon on the apparent motion of the Earth in the sky of the moon. He noted that this motion could be simulated by the motion of a Y-suspended pendulum. Within a short time, Nathaniel Bowditch, the self-taught mathematician, navigator, and actuary, published a complete analysis of the two-dimensional oscillator, including derivations and drawings of the mathematical curves usually known as Lissajous figures, some forty years before their description by J. A. Lissajous. This paper gives an account of the contributions of Dean and Bowditch to this problem.

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.

Higher order approximation to the Hill problem dynamics about the libration points

NASA Astrophysics Data System (ADS)

Lara, Martin; Pérez, Iván L.; López, Rosario

2018-06-01

An analytical solution to the Hill problem Hamiltonian expanded about the libration points has been obtained by means of perturbation techniques. In order to compute the higher orders of the perturbation solution that are needed to capture all the relevant periodic orbits originated from the libration points within a reasonable accuracy, the normalization is approached in complex variables. The validity of the solution extends to energy values considerably far away from that of the libration points and, therefore, can be used in the computation of Halo orbits as an alternative to the classical Lindstedt-Poincaré approach. Furthermore, the theory correctly predicts the existence of the two-lane bridge of periodic orbits linking the families of planar and vertical Lyapunov orbits.

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.

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.

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

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

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.

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

Galileo's Earth-Moon portrait

NASA Astrophysics Data System (ADS)

Simarski, Lynn Teo

Research reported at an AGU session on Galileo's Earth/Moon flyby refined the spacecraft's distinctive portrait of the Earth-Moon system. The Galileo team presented dramatic new views of the Earth and Moon taken last December. Andrew P. Ingersoll showed a color movie of the rotating Earth, made through spectral filters with which Galileo viewed the Earth almost continuously for 25 hours.Galileo also made finely tuned observations of vegetation and clouds, using three very closely spaced spectral wavelengths in the near-infrared, explained W. Reid Thompson. In the resulting images, Argentinian grassland and Brazilian rain forest are clearly distinguished, demonstrating the applicability of this technique for routine monitoring of deforestation, shifts in vegetation due to climate, and other phenomena. Thompson suggested that this capability could be used on the Earth Observing System. One of the spectral bands may also have potential for monitoring cloud condensation, as it appears to differentiate actively condensing, vapor-heavy clouds from higher and drier clouds.

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.

Alkali element constraints on Earth-Moon relations

NASA Technical Reports Server (NTRS)

Norman, M. D.; Drake, M. J.; Jones, J. H.

1994-01-01

Given their range of volatilities, alkali elements are potential tracers of temperature-dependent processes during planetary accretion and formation of the Earth-Moon system. Under the giant impact hypothesis, no direct connection between the composition of the Moon and the Earth is required, and proto-lunar material does not necessarily experience high temperatures. Models calling for multiple collisions with smaller planetesimals derive proto-lunar materials mainly from the Earth's mantle and explicitly invoke vaporization, shock melting and volatility-related fractionation. Na/K, K/Rb, and Rb/Cs should all increase in response to thermal volatization, so theories which derive the Moon substantially from Earth's mantle predict these ratios will be higher in the Moon than in the primitive mantle of the Earth. Despite the overall depletion of volatile elements in the Moon, its Na/K and K/Rb are equal to or less than those of Earth. A new model presented here for the composition of Earth's continental crust, a major repository of the alkali elements, suggests the Rb/Cs of the Moon is also less than that of Earth. Fractionation of the alkali elements between Earth and Moon are in the opposite sense to predictions based on the relative volatilities of these elements, if the Moon formed by high-T processing of Earth's mantle. Earth, rather than the Moon, appears to carry a signature of volatility-related fractionation in the alkali elements. This may reflect an early episode of intense heating on Earth with the Moon's alkali budget accreting from cooler material.

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

Crescent Earth and Moon

NASA Technical Reports Server (NTRS)

1977-01-01

This picture of a crescent-shaped Earth and Moon -- the first of its kind ever taken by a spacecraft -- was recorded Sept. 18, 1977, by NASA's Voyager 1 when it was 7.25 million miles (11.66 million kilometers) from Earth. The Moon is at the top of the picture and beyond the Earth as viewed by Voyager. In the picture are eastern Asia, the western Pacific Ocean and part of the Arctic. Voyager 1 was directly above Mt. Everest (on the night side of the planet at 25 degrees north latitude) when the picture was taken. The photo was made from three images taken through color filters, then processed by the Jet Propulsion Laboratory's Image Processing Lab. Because the Earth is many times brighter than the Moon, the Moon was artificially brightened by a factor of three relative to the Earth by computer enhancement so that both bodies would show clearly in the print. Voyager 2 was launched Aug. 20, 1977, followed by Voyager 1 on Sept. 5, 1977, en route to encounters at Jupiter in 1979 and Saturn in 1980 and 1981. JPL manages the Voyager mission for NASA's Office of Space Science.

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.

A Perspective On The Earth From The Moon

NASA Astrophysics Data System (ADS)

Scott, David R.

``What was most significant about the lunar voyage was not that men set foot on the Moon, but that they set eye on the Earth''. This statement, by Mr. Norman Cousins, Editor of the Saturday Review, summarizes the most significant aspect of the first departure of humans from the environment in which they were born, and in which they must survive. Looking back at the Earth from the Moon, the view is both splendid and overwhelming. This small blue ball in the vastness of black space, dotted with millions of marvellous stars, is an oasis that we must understand and protect. For, if one searches the heavens, one will find no other island for life as we understand it. If we humans do not protect and nurture this environment, it will disappear - just as quickly as the Earth will disappear from behind an outstretched thumb of a man on the Moon. Everything that has meaning disappears: science, history, music, poetry, art, literature, all of it on this small, fragile, and precious little spot out there in the vastness of the universe. From the Moon, we see many new and fascinating visions of the Earth. These views change not only our perspective of the Earth but our value system as well. As an example, from the Earth, we see the Moon track across the sky from horizon to horizon, always the same face, always the same features. But from the Moon, we see the Earth at the same point in the sky, day after day, but always turning, showing us new faces and changing features as the hours pass. We become aware of how much the physical features of the Earth are interrelated. And in a sense, we can ``see the future'' as the Earth turns in our view. From the Moon we see the Earth as a ``whole'' - we see no borders, we see no boundaries, we see all humankind together and interrelated on this single small sphere. This perspective from the Moon makes us realize that the Earth is dynamic and alive and evolving for the human presence - and we realize that if we care not for the life of the

Clementine Images of Earth and Moon

NASA Technical Reports Server (NTRS)

1997-01-01

During its flight and lunar orbit, the Clementine spacecraft returned images of the planet Earth and the Moon. This collection of UVVIS camera Clementine images shows the Earth from the Moon and 3 images of the Earth.

The image on the left shows the Earth as seen across the lunar north pole; the large crater in the foreground is Plaskett. The Earth actually appeared about twice as far above the lunar horizon as shown. The top right image shows the Earth as viewed by the UVVIS camera while Clementine was in transit to the Moon; swirling white cloud patterns indicate storms. The two views of southeastern Africa were acquired by the UVVIS camera while Clementine was in low Earth orbit early in the mission

Moon-based Earth Observation for Large Scale Geoscience Phenomena

NASA Astrophysics Data System (ADS)

Guo, Huadong; Liu, Guang; Ding, Yixing

2016-07-01

The capability of Earth observation for large-global-scale natural phenomena needs to be improved and new observing platform are expected. We have studied the concept of Moon as an Earth observation in these years. Comparing with manmade satellite platform, Moon-based Earth observation can obtain multi-spherical, full-band, active and passive information,which is of following advantages: large observation range, variable view angle, long-term continuous observation, extra-long life cycle, with the characteristics of longevity ,consistency, integrity, stability and uniqueness. Moon-based Earth observation is suitable for monitoring the large scale geoscience phenomena including large scale atmosphere change, large scale ocean change,large scale land surface dynamic change,solid earth dynamic change,etc. For the purpose of establishing a Moon-based Earth observation platform, we already have a plan to study the five aspects as follows: mechanism and models of moon-based observing earth sciences macroscopic phenomena; sensors' parameters optimization and methods of moon-based Earth observation; site selection and environment of moon-based Earth observation; Moon-based Earth observation platform; and Moon-based Earth observation fundamental scientific framework.

Trajectory Design Strategies for the NGST L2 Libration Point Mission

NASA Technical Reports Server (NTRS)

Folta, David; Cooley, Steven; Howell, Kathleen; Bauer, Frank H.

2001-01-01

The Origins' Next Generation Space Telescope (NGST) trajectory design is addressed in light of improved methods for attaining constrained orbit parameters and their control at the exterior collinear libration point, L2. The use of a dynamical systems approach, state-space equations for initial libration orbit control, and optimization to achieve constrained orbit parameters are emphasized. The NGST trajectory design encompasses a direct transfer and orbit maintenance under a constant acceleration. A dynamical systems approach can be used to provide a biased orbit and stationkeeping maintenance method that incorporates the constraint of a single axis correction scheme.

Earth-moon system: Dynamics and parameter estimation

NASA Technical Reports Server (NTRS)

Breedlove, W. J., Jr.

1975-01-01

A theoretical development of the equations of motion governing the earth-moon system is presented. The earth and moon were treated as finite rigid bodies and a mutual potential was utilized. The sun and remaining planets were treated as particles. Relativistic, non-rigid, and dissipative effects were not included. The translational and rotational motion of the earth and moon were derived in a fully coupled set of equations. Euler parameters were used to model the rotational motions. The mathematical model is intended for use with data analysis software to estimate physical parameters of the earth-moon system using primarily LURE type data. Two program listings are included. Program ANEAMO computes the translational/rotational motion of the earth and moon from analytical solutions. Program RIGEM numerically integrates the fully coupled motions as described above.

Crescent-shaped Earth and Moon

NASA Technical Reports Server (NTRS)

1978-01-01

This picture of a crescent-shaped Earth and Moon -- the first of its kind ever taken by a spacecraft -- was recorded Sept. 18, 1977, by NASA's Voyager 1 when it was 7.25 million miles (11.66 million kilometers) from Earth. The Moon is at the top of the picture and beyond the Earth as viewed by Voyager. In the picture are eastern Asia, the western Pacific Ocean and part of the Arctic. Voyager 1 was directly above Mt. Everest (on the night side of the planet at 25 degrees north latitude) when the picture was taken. The photo was made from three images taken through color filters, then processed by the Jet Propulsion Laboratory's Image Processing Lab. Because the Earth is many times brighter than the Moon, the Moon was artificially brightened by a factor of three relative to the Earth by computer enhancement so that both bodies would show clearly in the print. Voyager 2 was launched Aug. 20, 1977, followed by Voyager 1 on Sept. 5, 1977, en route to encounters at Jupiter in 1979 and Saturn in 1980 and 1981. JPL manages the Voyager mission for NASA.

Dynamics of tethered satellites in the vicinity of the Lagrangian point L2 of the Earth-Moon system

NASA Astrophysics Data System (ADS)

Baião, M. F.; Stuchi, T. J.

2017-08-01

This paper analyzes the dynamical evolution of satellites formed by two masses connected by a cable— tethered satellites. We derive the Lagrangian equations of motion in the neighborhood of the collinear equilibrium points, especially for the L2 , of the restricted problem of three bodies. The rigid body configuration is expanded in Legendre polynomials up to fourth degree. We present some numerical simulations of the influence of the parameters such as cable length, mass ratio and initial conditions in the behavior of the tethered satellites. The equation for the collinear equilibrium point is derived and numerically solved. The evolution of the equilibria with the variation of the cable length as a parameter is studied. We also present a discussion of the linear stability around these equilibria. Based on this analysis calculate some unstable Lyapunov orbits associated to these equilibrium points. We found periodic orbits in which the tether travels parallel to itself without involving the angular motion. The numerical applications are focused on the Earth-Moon system. However, the general character of the equations allows applications to the L1 equilibrium and obviously to systems other than the Earth-Moon.

Modeling low-thrust transfers between periodic orbits about five libration points: Manifolds and hierarchical design

NASA Astrophysics Data System (ADS)

Zeng, Hao; Zhang, Jingrui

2018-04-01

The low-thrust version of the fuel-optimal transfers between periodic orbits with different energies in the vicinity of five libration points is exploited deeply in the Circular Restricted Three-Body Problem. Indirect optimization technique incorporated with constraint gradients is employed to further improve the computational efficiency and accuracy of the algorithm. The required optimal thrust magnitude and direction can be determined to create the bridging trajectory that connects the invariant manifolds. A hierarchical design strategy dividing the constraint set is proposed to seek the optimal solution when the problem cannot be solved directly. Meanwhile, the solution procedure and the value ranges of used variables are summarized. To highlight the effectivity of the transfer scheme and aim at different types of libration point orbits, transfer trajectories between some sample orbits, including Lyapunov orbits, planar orbits, halo orbits, axial orbits, vertical orbits and butterfly orbits for collinear and triangular libration points, are investigated with various time of flight. Numerical results show that the fuel consumption varies from a few kilograms to tens of kilograms, related to the locations and the types of mission orbits as well as the corresponding invariant manifold structures, and indicates that the low-thrust transfers may be a beneficial option for the extended science missions around different libration points.

Clementine Images of Earth and Moon

NASA Image and Video Library

1999-06-12

During its flight and lunar orbit, NASA’s Clementine spacecraft returned images of the planet Earth and the Moon. This collection of UVVIS camera Clementine images shows the Earth from the Moon and 3 images of the Earth. The image on the left shows the Earth as seen across the lunar north pole; the large crater in the foreground is Plaskett. The Earth actually appeared about twice as far above the lunar horizon as shown. The top right image shows the Earth as viewed by the UVVIS camera while Clementine was in transit to the Moon; swirling white cloud patterns indicate storms. The two views of southeastern Africa were acquired by the UVVIS camera while Clementine was in low Earth orbit early in the mission. http://photojournal.jpl.nasa.gov/catalog/PIA00432

Earth and Moon as viewed from Mars

NASA Technical Reports Server (NTRS)

2003-01-01

MGS MOC Release No. MOC2-368, 22 May 2003

[figure removed for brevity, see original site] Globe diagram illustrates the Earth's orientation as viewed from Mars (North and South America were in view).

Earth/Moon: This is the first image of Earth ever taken from another planet that actually shows our home as a planetary disk. Because Earth and the Moon are closer to the Sun than Mars, they exhibit phases, just as the Moon, Venus, and Mercury do when viewed from Earth. As seen from Mars by MGS on 8 May 2003 at 13:00 GMT (6:00 AM PDT), Earth and the Moon appeared in the evening sky. The MOC Earth/Moon image has been specially processed to allow both Earth (with an apparent magnitude of -2.5) and the much darker Moon (with an apparent magnitude of +0.9) to be visible together. The bright area at the top of the image of Earth is cloud cover over central and eastern North America. Below that, a darker area includes Central America and the Gulf of Mexico. The bright feature near the center-right of the crescent Earth consists of clouds over northern South America. The image also shows the Earth-facing hemisphere of the Moon, since the Moon was on the far side of Earth as viewed from Mars. The slightly lighter tone of the lower portion of the image of the Moon results from the large and conspicuous ray system associated with the crater Tycho.

A note about the coloring process: The MGS MOC high resolution camera only takes grayscale (black-and-white) images. To 'colorize' the image, a Mariner 10 Earth/Moon image taken in 1973 was used to color the MOC Earth and Moon picture. The procedure used was as follows: the Mariner 10 image was converted from 24-bit color to 8-bit color using a JPEG to GIF conversion program. The 8-bit color image was converted to 8-bit grayscale and an associated lookup table mapping each gray value of the image to a red-green-blue color triplet (RGB). Each color triplet was root-sum-squared (RSS), and sorted in increasing RSS

A Free-Return Earth-Moon Cycler Orbit for an Interplanetary Cruise Ship

NASA Technical Reports Server (NTRS)

Genova, Anthony L.; Aldrin, Buzz

2015-01-01

A periodic circumlunar orbit is presented that can be used by an interplanetary cruise ship for regular travel between Earth and the Moon. This Earth-Moon cycler orbit was revealed by introducing solar gravity and modest phasing maneuvers (average of 39 m/s per month) which yields close-Earth encounters every 7 or 10 days. Lunar encounters occur every 26 days and offer the chance for a smaller craft to depart the cycler and enter lunar orbit, or head for a Lagrange point (e.g., EM-L2 halo orbit), distant retrograde orbit (DRO), or interplanetary destination such as a near-Earth object (NEO) or Mars. Additionally, return-to-Earth abort options are available from many points along the cycling trajectory.

Tidal Friction in the Earth-Moon System and Laplace Planes: Darwin Redux

NASA Technical Reports Server (NTRS)

Rubincam, David P.

2015-01-01

The dynamical evolution of the Earth-Moon system due to tidal friction is treated here. George H. Darwin used Laplace planes (also called proper planes) in his study of tidal evolution. The Laplace plane approach is adapted here to the formalisms of W.M. Kaula and P. Goldreich. Like Darwin, the approach assumes a three-body problem: Earth, Moon, and Sun, where the Moon and Sun are point-masses. The tidal potential is written in terms of the Laplace plane angles. The resulting secular equations of motion can be easily integrated numerically assuming the Moon is in a circular orbit about the Earth and the Earth is in a circular orbit about the Sun. For Earth-Moon distances greater than 10 Earth radii, the Earth's approximate tidal response can be characterized with a single parameter, which is a ratio: a Love number times the sine of a lag angle divided by another such product. For low parameter values it can be shown that Darwin's low-viscosity molten Earth, M. Ross's and G. Schubert's model of an Earth near melting, and Goldreich's equal tidal lag angles must all give similar histories. For higher parameter values, as perhaps has been the case at times with the ocean tides, the Earth's obliquity may have decreased slightly instead of increased once the Moon's orbit evolved further than 50 Earth radii from the Earth, with possible implications for climate. This is contrast to the other tidal friction models mentioned, which have the obliquity always increasing with time. As for the Moon, its orbit is presently tilted to its Laplace plane by 5.2deg. The equations do not allow the Moon to evolve out of its Laplace plane by tidal friction alone, so that if it was originally in its Laplace plane, the tilt arose with the addition of other mechanisms, such as resonance passages.

Calibration View of Earth and the Moon by Mars Color Imager

NASA Technical Reports Server (NTRS)

2005-01-01

Three days after the Mars Reconnaissance Orbiter's Aug. 12, 2005, launch, the spacecraft was pointed toward Earth and the Mars Color Imager camera was powered up to acquire a suite of images of Earth and the Moon. When it gets to Mars, the Mars Color Imager's main objective will be to obtain daily global color and ultraviolet images of the planet to observe martian meteorology by documenting the occurrence of dust storms, clouds, and ozone. This camera will also observe how the martian surface changes over time, including changes in frost patterns and surface brightness caused by dust storms and dust devils.

The purpose of acquiring an image of Earth and the Moon just three days after launch was to help the Mars Color Imager science team obtain a measure, in space, of the instrument's sensitivity, as well as to check that no contamination occurred on the camera during launch. Prior to launch, the team determined that, three days out from Earth, the planet would only be about 4.77 pixels across, and the Moon would be less than one pixel in size, as seen from the Mars Color Imager's wide-angle perspective. If the team waited any longer than three days to test the camera's performance in space, Earth would be too small to obtain meaningful results.

The Earth and Moon images were acquired by turning Mars Reconnaissance Orbiter toward Earth, then slewing the spacecraft so that the Earth and Moon would pass before each of the five color and two ultraviolet filters of the Mars Color Imager. The distance to the Moon was about 1,440,000 kilometers (about 895,000 miles); the range to Earth was about 1,170,000 kilometers (about 727,000 miles).

This view combines a sequence of frames showing the passage of Earth and the Moon across the field of view of a single color band of the Mars Color Imager. As the spacecraft slewed to view the two objects, they passed through the camera's field of view. Earth has been saturated white in this image so that both Earth

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.

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

Optimal ballistically captured Earth-Moon transfers

NASA Astrophysics Data System (ADS)

Ricord Griesemer, Paul; Ocampo, Cesar; Cooley, D. S.

2012-07-01

The optimality of a low-energy Earth-Moon transfer terminating in ballistic capture is examined for the first time using primer vector theory. An optimal control problem is formed with the following free variables: the location, time, and magnitude of the transfer insertion burn, and the transfer time. A constraint is placed on the initial state of the spacecraft to bind it to a given initial orbit around a first body, and on the final state of the spacecraft to limit its Keplerian energy with respect to a second body. Optimal transfers in the system are shown to meet certain conditions placed on the primer vector and its time derivative. A two point boundary value problem containing these necessary conditions is created for use in targeting optimal transfers. The two point boundary value problem is then applied to the ballistic lunar capture problem, and an optimal trajectory is shown. Additionally, the problem is then modified to fix the time of transfer, allowing for optimal multi-impulse transfers. The tradeoff between transfer time and fuel cost is shown for Earth-Moon ballistic lunar capture transfers.

Calibration View of Earth and the Moon by Mars Color Imager

NASA Image and Video Library

2005-08-22

Three days after the Mars Reconnaissance Orbiter Aug. 12, 2005, launch, the spacecraft was pointed toward Earth and the Mars Color Imager camera was powered up to acquire a suite of images of Earth and the Moon.

Earth Moon

NASA Image and Video Library

1998-06-08

NASA Galileo spacecraft took this image of Earth moon on December 7, 1992 on its way to explore the Jupiter system in 1995-97. The distinct bright ray crater at the bottom of the image is the Tycho impact basin. http://photojournal.jpl.nasa.gov/catalog/PIA00405

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.

Mission design for a halo orbiter of the earth

NASA Technical Reports Server (NTRS)

Farquhar, R. W.; Muhonen, D. P.; Richardson, D. L.

1976-01-01

The International Sun-Earth Explorer (ISEE) scientific satellite to be stationed in 1978 in the vicinity of the sun-earth interior libration point to continuously monitor the space between the sun and the earth, including the distant geomagnetic tail is described. Orbit selection considerations for the ISEE-C are discussed along with stationkeeping requirements and fuel-optimal trajectories. Due to the alignment of the interior libration point with the sun as viewed from the earth, it will be necessary to place the satellite into a 'halo orbit' around the libration point, in order to eliminate solar interference with down-link telemetry. Parametric data for transfer trajectories between an earth parking orbit (altitude about 185 km) and a libration-point orbit are presented. It is shown that the insertion magnitude required for placing a satellite into an acceptable halo orbit is rather modest.

Earth and Moon as viewed from Mars

NASA Image and Video Library

2003-05-22

This is the first image of Earth ever taken from another planet that actually shows our home as a planetary disk. Because Earth and the Moon are closer to the Sun than Mars, they exhibit phases, just as the Moon, Venus, & Mercury do when viewed from Earth

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

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.

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.

Lunar Flight Study Series: Volume 6. A Study of Geometrical and Terminal Characteristics of Earth-Moon Transits Embedded in the Earth-Moon Plane

NASA Technical Reports Server (NTRS)

Lisle, B. J.

1963-01-01

This report represents the results of a study of coplanar earth-moon transits. The study was initiated to provide information concerning coplanar geometrical characteristics of earth-moon trnasits. The geometrical aspects of transit behavior are related to variations injection conditions. The model of the earth-moon system used in this investigation is the Jacobian model of the restricted three body problem. All transits considered in this study are restricted to the moon-earth plane (MEP).

The earth and the moon /Harold Jeffreys Lecture/.

NASA Technical Reports Server (NTRS)

Press, F.

1971-01-01

The internal structures of the earth and the moon are compared in the light of the latest extensive data on the earth structure, mobility of the earth outer layers, and the properties of lunar crust. The Monte Carlo method is applied to develop an earth model by a stepwise process beginning with a random distribution of two elastic velocities and the density as a function of de pth. Lunar seismic, magnetic, and rock analysis data are used to infer the properties of the moon. The marked planetological contrast between the earth and the moon is shown to consist in that the earth is highly differentiated and still undergoes a large-scale differentiation, while the moon has lost its volatiles in its early history and has a cold dynamically inactive shell which has been without basic changes for three billion years.

Crescent Earth and Moon

NASA Image and Video Library

1996-08-29

This picture of a crescent-shaped Earth and Moon, the first of its kind ever taken by a spacecraft, was recorded Sept. 18, 1977, by NASA Voyager 1 when it was 7.25 million miles 11.66 million kilometers from Earth. http://photojournal.jpl.nasa.gov/catalog/PIA00013

Water: Communicator In Moon-Earth Relationships

NASA Astrophysics Data System (ADS)

Davis, Joan S.

The Moon's myriad effects upon Earth have been objects of fascination, and subjects for literary works and scientific speculation throughout history. Although many of Moon's influences upon Earth involve water, tidal movement is clearly the most readily associated effect. While very obvious, it however represents only one of a multitude of ways in which lunar forces effect this planet, and all life upon it. Much less apparent, though essential for all of life, is the wide spectrum of subtle fluctuating influences upon the water in the cells of living systems. Water's capacity to respond to extremely subtle changes in physical influences (such as gravitational fields), as associated with Moon phases (N.B. also with planetary constellations and sunspot activity), enables it to communicate such inputs to living systems. The periodicity of changes in natural systems has been of interest to man throughout history. However, only in more recent times has insight into water's behaviour led to its being recognised as a link between the periodicities seen in abiotic (Moon and other planetary) systems and biotic systems. Particular attention has long been paid to systematic fluctuations in agriculture and forestry: Different growth patterns are observed in connection with the Moon phases (and zodiac constellations) at planting time; different characteristics (e.g., fire resistance, pliability, firmness, etc.) of wood are seen in trees harvested at different phases and constellations. . The usefulness of such correlations has influenced planting and harvesting patterns in more traditional-oriented agriculture and forestry. Its acceptance by science has, however, been long in coming. The case similar, as regards physiological fluctuations observed in the medical field. A documented case in point is the correlation between the Moon-phase and risk of hemorrhage during surgery: This is one of many observations on periodicity in body functions, which deserve more research attention

Non-rocket Earth-Moon transport system

NASA Astrophysics Data System (ADS)

Bolonkin, Alexander

2003-06-01

This paper proposes a new transportation system for travel between Earth and Moon. This transportation system uses mechanical energy transfer and requires only minimal energy, using an engine located on Earth. A cable directly connects a pole of the Earth through a drive station to the lunar surface_ The equation for an optimal equal stress cable for complex gravitational field of Earth-Moon has been derived that allows significantly lower cable masses. The required strength could be provided by cables constructed of carbon nanotubes or carbon whiskers. Some of the constraints on such a system are discussed.

Unique Moon Formation Model: Two Impacts of Earth and After Moon's Birth

NASA Astrophysics Data System (ADS)

Miura, Y.

2018-04-01

The Moon rocks are mixed with two impact-processes of Earth's impact breccias and airless Moon's impact breccias; discussed voids-rich texture and crust-like composition. The present model might be explained as cave-rich interior on the airless-and waterless Moon.

An Exploration Of Fuel Optimal Two-impulse Transfers To Cyclers in the Earth-Moon System

NASA Astrophysics Data System (ADS)

Hosseinisianaki, Saghar

2011-12-01

This research explores the optimum two-impulse transfers between a low Earth orbit and cycler orbits in the Earth-Moon circular restricted three-body framework, emphasizing the optimization strategy. Cyclers are those types of periodic orbits that meet both the Earth and the Moon periodically. A spacecraft on such trajectories are under the influence of both the Earth and the Moon gravitational fields. Cyclers have gained recent interest as baseline orbits for several Earth-Moon mission concepts, notably in relation to human exploration. In this thesis it is shown that a direct optimization starting from the classic lambert initial guess may not be adequate for these problems and propose a three-step optimization solver to improve the domain of convergence toward an optimal solution. The first step consists of finding feasible trajectories with a given transfer time. I employ Lambert's problem to provide initial guess to optimize the error in arrival position. This includes the analysis of the liability of Lambert's solution as an initial guess. Once a feasible trajectory is found, the velocity impulse is only a function of transfer time, departure, and arrival points' phases. The second step consists of the optimization of impulse over transfer time which results in the minimum impulse transfer for fixed end points. Finally, the third step is mapping the optimal solutions as the end points are varied.

An Exploration Of Fuel Optimal Two-impulse Transfers To Cyclers in the Earth-Moon System

NASA Astrophysics Data System (ADS)

Hosseinisianaki, Saghar

This research explores the optimum two-impulse transfers between a low Earth orbit and cycler orbits in the Earth-Moon circular restricted three-body framework, emphasizing the optimization strategy. Cyclers are those types of periodic orbits that meet both the Earth and the Moon periodically. A spacecraft on such trajectories are under the influence of both the Earth and the Moon gravitational fields. Cyclers have gained recent interest as baseline orbits for several Earth-Moon mission concepts, notably in relation to human exploration. In this thesis it is shown that a direct optimization starting from the classic lambert initial guess may not be adequate for these problems and propose a three-step optimization solver to improve the domain of convergence toward an optimal solution. The first step consists of finding feasible trajectories with a given transfer time. I employ Lambert's problem to provide initial guess to optimize the error in arrival position. This includes the analysis of the liability of Lambert's solution as an initial guess. Once a feasible trajectory is found, the velocity impulse is only a function of transfer time, departure, and arrival points' phases. The second step consists of the optimization of impulse over transfer time which results in the minimum impulse transfer for fixed end points. Finally, the third step is mapping the optimal solutions as the end points are varied.

The Geolocation model for lunar-based Earth observation

NASA Astrophysics Data System (ADS)

Ding, Yixing; Liu, Guang; Ren, Yuanzhen; Ye, Hanlin; Guo, Huadong; Lv, Mingyang

2016-07-01

In recent years, people are more and more aware of that the earth need to treated as an entirety, and consequently to be observed in a holistic, systematic and multi-scale view. However, the interaction mechanism between the Earth's inner layers and outer layers is still unclear. Therefore, we propose to observe the Earth's inner layers and outer layers instantaneously on the Moon which may be helpful to the studies in climatology, meteorology, seismology, etc. At present, the Moon has been proved to be an irreplaceable platform for Earth's outer layers observation. Meanwhile, some discussions have been made in lunar-based observation of the Earth's inner layers, but the geolocation model of lunar-based observation has not been specified yet. In this paper, we present a geolocation model based on transformation matrix. The model includes six coordinate systems: The telescope coordinate system, the lunar local coordinate system, the lunar-reference coordinate system, the selenocentric inertial coordinate system, the geocentric inertial coordinate system and the geo-reference coordinate system. The parameters, lncluding the position of the Sun, the Earth, the Moon, the libration and the attitude of the Earth, can be acquired from the Ephemeris. By giving an elevation angle and an azimuth angle of the lunar-based telescope, this model links the image pixel to the ground point uniquely.

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

Crescent-shaped Earth and Moon

NASA Image and Video Library

1999-05-15

This picture of a crescent-shaped Earth and Moon -- the first of its kind ever taken by a spacecraft -- was recorded Sept. 18, 1977, by NASA Voyager 1 when it was 7.25 million miles 11.66 million kilometers from Earth.

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

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.

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.

Relationship between seismic status of Earth and relative position of bodies in sun-earth-moon system

NASA Astrophysics Data System (ADS)

Kulanin, N. V.

1985-03-01

The time spectrum of variations in seismicity is quite broad. There are seismic seasons, as well as multiannual variations. The range of characteristic times of variation from days to about one year is studied. Seismic activity as a function of the position of the moon relative to the Earth and the direction toward the Sun is studied. The moments of strong earthquakes, over 5.8 on the Richter scale, between 1968 and June 1980 are plotted in time coordinates relating them to the relative positions of the three bodies in the sun-earth-moon system. Methods of mathematical statistics are applied to the points produced, indicating at least 99% probability that the distribution was not random. a periodicity of the earth's seismic state of 413 days is observed.

Non-rocket Earth-Moon transportation system

NASA Astrophysics Data System (ADS)

Bolonkin, A.

Author suggests and researches one of his methods of flights to outer Space, described in book "Non Rocket Flights in Space", which is prepared and offered for publication. In given report the method and facilities named "Bolonkin Transport System" (BTS) for delivering of payload and people to Moon and back is presented. BTS can be used also for free trip to outer Space up at altitude 60,000 km and more. BTS can be applying as a trust system for atmospheric supersonic aircrafts, and as a free energy source. This method uses, in general, the rotary and kinetic energy of the Moon. The manuscript contains the theory and results of computation of special Project. This project uses three cables (main and two for driving of loads) from artificial material: fiber, whiskers, nanotubes, with the specific tensile strength (ratio the tensile stress to density) k=/=4*10^7 or more. The nanotubes with same and better parameters are received in scientific laboratories. Theoretical limit of nanotubes SWNT is about k=100*10^7. The upper end of the cable is connected to the Moon. The lower end of the cable is connected to an aircraft (or buoy), which flies (i.e. glides or slides) in Earth atmosphere along the planet's surface. The aircraft (and Moon) has devices, which allows the length of cables to be changed. The device would consists of a spool, motor, brake, transmission, and controller. The facility could have devices for delivering people and payloads t o the Moon and back using the suggested Transport System. The delivery devices include: containers, cables, motors, brakes, and controllers. If the aircraft is small and the cable is strong the motion of the Moon can be used to move the airplane. For example (see enclosed project), if the airplane weighs 15 tons and has an aerodynamic ratio (the lift force to the drag force) equal 5, a thrust of 3000 kg would be enough for the aircraft to fly for infinity without requiring any fuel. The aircraft could use a small turbine engine

Earth and Its Moon, as Seen From Mars

NASA Image and Video Library

2017-01-06

This composite image of Earth and its moon, as seen from Mars, combines the best Earth image with the best moon image from four sets of images acquired on Nov. 20, 2016, by the High Resolution Imaging Science Experiment (HiRISE) camera on NASA's Mars Reconnaissance Orbiter. Each was separately processed prior to combining them so that the moon is bright enough to see. The moon is much darker than Earth and would barely be visible at the same brightness scale as Earth. The combined view retains the correct sizes and positions of the two bodies relative to each other. HiRISE takes images in three wavelength bands: infrared, red, and blue-green. These are displayed here as red, green, and blue, respectively. This is similar to Landsat images in which vegetation appears red. The reddish feature in the middle of the Earth image is Australia. Southeast Asia appears as the reddish area (due to vegetation) near the top; Antarctica is the bright blob at bottom-left. Other bright areas are clouds. These images were acquired for calibration of HiRISE data, since the spectral reflectance of the Moon's near side is very well known. When the component images were taken, Mars was about 127 million miles (205 million kilometers) from Earth. http://photojournal.jpl.nasa.gov/catalog/PIA21260

Earth and Moon as viewed by Mariner 10

NASA Technical Reports Server (NTRS)

1973-01-01

Mariner 10 was launched on November 3, 1973, 12:45 am PST, from Cape Canaveral on an Atlas/Centaur rocket (a reconditioned Intercontinental Ballistic Missile - ICBM). Within 12 hours of launch the twin cameras were turned on and several hundred pictures of both the Earth and the Moon were acquired over the following days.

The Earth and Moon were imaged by Mariner 10 from 2.6 million km while completing the first ever Earth-Moon encounter by a spacecraft capable of returning high resolution digital color image data. These images have been combined at right to illustrate the relative sizes of the two bodies. From this particular viewpoint the Earth appears to be a water planet!

The Mariner 10 mission is managed by the Jet Propulsion Laboratory for NASA's Office of Space Science, explored Venus in February 1974 on the way to three encounters with Mercury-in March and September 1974 and in March 1975. The spacecraft took more than 7,000 photos of Mercury, Venus, the Earth and the Moon.

Image Credit: NASA/JPL/Northwestern University

Simulating the Liaison Navigation Concept in a Geo + Earth-Moon Halo Constellation

NASA Technical Reports Server (NTRS)

Fujimoto, K.; Leonard, J. M.; McGranaghan, R. M.; Parker, J. S.; Anderson, R. L.; Born, G. H.

2012-01-01

Linked Autonomous Interplanetary Satellite Orbit Navigation, or LiAISON, is a novel satellite navigation technique where relative radiometric measurements between two or more spacecraft in a constellation are processed to obtain the absolute state of all spacecraft. The method leverages the asymmetry of the gravity field that the constellation exists in. This paper takes a step forward in developing a high fidelity navigation simulation for the LiAISON concept in an Earth-Moon constellation. In particular, we aim to process two-way Doppler measurements between a satellite in GEO orbit and another in a halo orbit about the Earth-Moon L1 point.

Using Cassini UVIS Data to Constrain Enceladus' Libration State

NASA Technical Reports Server (NTRS)

Hurford, Terry A.; Helfenstein, P.; Hansen, C.

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, stall 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 and a previous study has explored possible libration states that provided better matches to Cassini CIRS observations of heat along the tiger stripes. Cassini UVIS stellar occultations provided measurements of the column density of the Enceladus plume at two different points in Enceladus' orbit and find comparable column density values. This column density may be a reflection of the amount of the tiger stripe rifts in tension and able to vent volatiles and a physical libration will also affect the fraction of tiger stripe in tension at different points in the orbit. We have modeled the expected fraction of tiger stripes in tension under different libration conditions. Without libration the amount of tiger stripe rifts in tension at both paints in the orbit would not be comparable and therefore may not allow comparable amounts of volatiles to escape. However, we identify libration conditions that do allow comparable amounts of the tiger stripes to be in tension at each point in the orbit, which might lead to comparable column densities. The librations identified coincide with possible librations states identified in the earlier study, which used Cassini CIRS observations.

Evidence for magma oceans on asteroids, the moon, and Earth

NASA Technical Reports Server (NTRS)

Taylor, G. Jeffrey; Norman, Marc D.

1992-01-01

There are sound theoretical reasons to suspect that the terrestrial planets melted when they formed. For Earth, the reasons stem largely from the hypothesis that the moon formed as a result of the impact of a Mars-sized planetesimal with the still accreting Earth. Such a monumental event would have led to widespread heating of the Earth and the materials from which the moon was made. In addition, formation of a dense atmosphere on the Earth (and possibly the Moon) would have led to retention of accretional heat and, thus, widespread melting. In other words, contemporary theory suggests that the primitive Moon and terrestrial planets had magma oceans.

Visualizing Moon Data and Imagery with Google Earth

NASA Astrophysics Data System (ADS)

Weiss-Malik, M.; Scharff, T.; Nefian, A.; Moratto, Z.; Kolb, E.; Lundy, M.; Hancher, M.; Gorelick, N.; Broxton, M.; Beyer, R. A.

2009-12-01

There is a vast store of planetary geospatial data that has been collected by NASA but is difficult to access and visualize. Virtual globes have revolutionized the way we visualize and understand the Earth, but other planetary bodies including Mars and the Moon can be visualized in similar ways. Extraterrestrial virtual globes are poised to revolutionize planetary science, bring an exciting new dimension to science education, and allow ordinary users to explore imagery being sent back to Earth by planetary science satellites. The original Google Moon Web site was a limited series of maps and Apollo content. The new Moon in Google Earth feature provides a similar virtual planet experience for the Moon as we have for the Earth and Mars. We incorporated existing Clementine and Lunar Orbiter imagery for the basemaps and a combination of Kaguya LALT topography and some terrain created from Apollo Metric and Panoramic images. We also have information about the Apollo landings and other robotic landers on the surface, as well as historic maps and charts, and guided tours. Some of the first-released LROC imagery of the Apollo landing sites has been put in place, and we look forward to incorporating more data as it is released from LRO, Chandraayan-1, and Kaguya. These capabilities have obvious public outreach and education benefits, but the potential benefits of allowing planetary scientists to rapidly explore these large and varied data collections — in geological context and within a single user interface — are also becoming evident. Because anyone can produce additional KML content for use in Google Earth, scientists can customize the environment to their needs as well as publish their own processed data and results for others to use. Many scientists and organizations have begun to do this already, resulting in a useful and growing collection of planetary-science-oriented Google Earth layers. Screen shot of Moon in Google Earth, a freely downloadable application for

Not So Rare Earth? New Developments in Understanding the Origin of the Earth and Moon

NASA Technical Reports Server (NTRS)

Righter, Kevin

2007-01-01

A widely accepted model for the origin of the Earth and Moon has been a somewhat specific giant impact scenario involving an impactor to proto-Earth mass ratio of 3:7, occurring 50-60 Ma after T(sub 0), when the Earth was only half accreted, with the majority of Earth's water then accreted after the main stage of growth, perhaps from comets. There have been many changes to this specific scenario, due to advances in isotopic and trace element geochemistry, more detailed, improved, and realistic giant impact and terrestrial planet accretion modeling, and consideration of terrestrial water sources other than high D/H comets. The current scenario is that the Earth accreted faster and differentiated quickly, the Moon-forming impact could have been mid to late in the accretion process, and water may have been present during accretion. These new developments have broadened the range of conditions required to make an Earth-Moon system, and suggests there may be many new fruitful avenues of research. There are also some classic and unresolved problems such as the significance of the identical O isotopic composition of the Earth and Moon, the depletion of volatiles on the lunar mantle relative to Earth's, the relative contribution of the impactor and proto-Earth to the Moon's mass, and the timing of Earth's possible atmospheric loss relative to the giant impact.

Tectonomagmatic evolution of the Earth and Moon

NASA Astrophysics Data System (ADS)

Sharkov, E. V.; Bogatikov, O. A.

2010-03-01

The Earth and Moon evolved following a similar scenario. The formation of their protocrusts started with upward crystallization of global magmatic oceans. As a result of this process, easily fusible components accumulated in the course of fractional crystallization of melt migrating toward the surface. The protocrusts (granitic in the Earth and anorthositic in the Moon) are retained in ancient continents. The tectonomagmatic activity at the early stage of planet evolution was related to the ascent of mantle plume of the first generation composed of mantle material depleted due to the formation of protocrusts. The regions of extension, rise, and denudation were formed in the Earth above the diffluent heads of such superplumes (Archean granite-greenstone domains and Paleoproterozoic cratons), whereas granulite belts as regions of compression, subsidence, and sedimentation arose above descending mantle flows. The situation may be described in terms of plume tectonics. Gentle uplifts and basins ( thalassoids) in lunar continents are probable analogues of these structural elements in the Moon. The period of 2.3-2.0 Ga ago was a turning point in the tectonomagmatic evolution of the Earth, when geochemically enriched Fe-Ti picrites and basalts typical of Phanerozoic within-plate magmatism became widespread. The environmental setting on the Earth’s surface changed at that time, as well. Plate tectonics, currently operating on a global scale, started to develop about ˜2 Ga ago. This turn was related to the origination of thermochemical mantle plumes of the second generation at the interface of the liquid Fe-Ni core and silicate mantle. A similar turning point in the lunar evolution probably occurred 4.2-3.9 Ga ago and completed with the formation of large depressions ( seas) with thinned crust and vigorous basaltic magmatism. Such a sequence of events suggests that qualitatively new material previously retained in the planets’ cores was involved in tectonomagmatic

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.

Earth radiation balance and climate: Why the Moon is the wrong place to observe the Earth

NASA Astrophysics Data System (ADS)

Kandel, Robert S.

1994-06-01

Increasing 'greenhouse' gases in the Earth's atmosphere will perturb the Earth's radiation balance, forcing climate change over coming decades. Climate sensitivity depends critically on cloud-radiation feedback: its evaluation requires continual observation of changing patterns of Earth radiation balance and cloud cover. The Moon is the wrong place for such observations, with many disadvantages compared to an observation system combining platforms in low polar, intermediate-inclination and geostationary orbits. From the Moon, active observations are infeasible; thermal infrared observations require very large instruments to reach spatial resolutions obtained at much lower cost from geostationary or lower orbits. The Earth's polar zones are never well observed from the Moon; other zones are invisible more than half the time. The monthly illumination cycle leads to further bias in radiation budget determinations. The Earth will be a pretty sight from the Earth-side of the Moon, but serious Earth observations will be made elsewhere.

Curiosity Mars Rover First Image of Earth and Earth Moon

NASA Image and Video Library

2014-02-06

The two bodies in this portion of an evening-sky view by NASA Mars rover Curiosity are Earth and Earth moon. The rover Mast Camera Mastcam imaged them in the twilight sky of Curiosity 529th Martian day, or sol Jan. 31, 2014.

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.

Formation and growth of embryos of the Earth-Moon system

NASA Astrophysics Data System (ADS)

Ipatov, Sergei I.

2016-07-01

Galimov and Krivtsov [1] made computer simulations of the formation of the embryos of the Earth and the Moon as a result of contraction of a rarefied condensation. The angular momentum needed for such contraction could not be acquired during formation of the condensation from a protoplanetary disk. Using the formulas presented in [2], we obtained that the angular momentum of the present Earth-Moon system could be acquired at a collision of two rarefied condensations with a total mass not smaller than 0.1M_{e}, where M_{e} is the Earth mass. In principle, the angular momentum of the condensation needed for formation of the Earth-Moon system could be acquired by accumulation only of small objects, but for such model, the parental condensations of Venus and Mars could also get the angular momentum that was enough for formation of large satellites. Probably, the condensations that contracted and formed the embryos of the terrestrial planets other than the Earth did not collide with massive condensations, and therefore they did not get a large enough angular momentum needed to form massive satellites. The embryos formed as a result of contraction of the condensation grew by accumulation of solid planetesimals. The mass of the rarefied condensation that was a parent for the embryos of the Earth and the Moon could be relatively small (0.02M_{e} or even less), if we take into account the growth of the angular momentum of the embryos at the time when they accumulated planetesimals. There could be also the second main collision of the parental rarefied condensation with another condensation, at which the radius of the Earth's embryo condensation was smaller than the semi-major axis of the orbit of the Moon's embryo. The second main collision (or a series of similar collisions) could change the tilt of the Earth to its present value. For large enough eccentricities of planetesimals, the effective radii of proto-Earth and proto-Moon were proportional to r (where r is the

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.

Early differentiation of the Earth and the Moon.

PubMed

Bourdon, Bernard; Touboul, Mathieu; Caro, Guillaume; Kleine, Thorsten

2008-11-28

We examine the implications of new 182W and 142Nd data for Mars and the Moon for the early evolution of the Earth. The similarity of 182W in the terrestrial and lunar mantles and their apparently differing Hf/W ratios indicate that the Moon-forming giant impact most probably took place more than 60Ma after the formation of calcium-aluminium-rich inclusions (4.568Gyr). This is not inconsistent with the apparent U-Pb age of the Earth. The new 142Nd data for Martian meteorites show that Mars probably has a super-chondritic Sm/Nd that could coincide with that of the Earth and the Moon. If this is interpreted by an early mantle differentiation event, this requires a buried enriched reservoir for the three objects. This is highly unlikely. For the Earth, we show, based on new mass-balance calculations for Nd isotopes, that the presence of a hidden reservoir is difficult to reconcile with the combined 142Nd-143Nd systematics of the Earth's mantle. We argue that a likely possibility is that the missing component was lost during or prior to accretion. Furthermore, the 142Nd data for the Moon that were used to argue for the solidification of the magma ocean at ca 200Myr are reinterpreted. Cumulate overturn, magma mixing and melting following lunar magma ocean crystallization at 50-100Myr could have yielded the 200Myr model age.

Visualizing Sun-Earth-Moon Relationships through Hands-On Modeling

NASA Astrophysics Data System (ADS)

Morton, Abby

2013-04-01

"Tell me and I forget, teach me and I may remember, involve me and I learn." -Benjamin Franklin Understanding the spatial relationships between the sun, Earth and Moon is fundamental to any basic earth science education. Since both of the following concepts involve shadows on three-dimensional spheres, seeing them on paper is not often conducive to understanding. In the first activity, students use five Styrofoam balls painted to look like the sun and the four positions of the earth in each season. Students position the Earth-balls in their correct order around the sun and translate what they are seeing onto paper. In the second activity, students hold up a Styrofoam ball painted half white, half black. A picture of the sun is projected at the front of the classroom. They move the ball around their heads as if they were the Earth, keeping the lit side of the moon always facing the sun. They then draw the phases of the moon as they see them.

Forming a Moon with an Earth-like composition via a giant impact.

PubMed

Canup, Robin M

2012-11-23

In the giant impact theory, the Moon formed from debris ejected into an Earth-orbiting disk by the collision of a large planet with the early Earth. Prior impact simulations predict that much of the disk material originates from the colliding planet. However, Earth and the Moon have essentially identical oxygen isotope compositions. This has been a challenge for the impact theory, because the impactor's composition would have likely differed from that of Earth. We simulated impacts involving larger impactors than previously considered. We show that these can produce a disk with the same composition as the planet's mantle, consistent with Earth-Moon compositional similarities. Such impacts require subsequent removal of angular momentum from the Earth-Moon system through a resonance with the Sun as recently proposed.

Supporting a Deep Space Gateway with Free-Return Earth-Moon Periodic Orbits

NASA Astrophysics Data System (ADS)

Genova, A. L.; Dunham, D. W.; Hardgrove, C.

2018-02-01

Earth-Moon periodic orbits travel between the Earth and Moon via free-return circumlunar segments and can host a station that can provide architecture support to other nodes near the Moon and Mars while enabling science return from cislunar space.

The Dynamical Evolution of the Earth-Moon Progenitors. 1; Motivation and Methodology

NASA Technical Reports Server (NTRS)

Lissuer, Jack; Rivera, E.; Duncan, M. J.; Levison, H. F.; DeVincenzi, Donald (Technical Monitor)

1999-01-01

The Giant Impact Hypothesis was introduced in the mid-1970's after consideration of results from the Apollo Moon missions. This hypothesis best explains the similarity in elemental proportions in lunar and terrestrial rocks, the depletion of lunar volatiles, the lack of lunar iron. and the large angular momentum in the Earth-Moon system. Comparison between the radiometric ages of inclusions in the most primitive meteorites and those of inclusions in the oldest lunar rocks and the differentiation age of Earth suggests that the Earth-Moon system formed about 100 Myr after the oldest meteorites. In addition, the age of the famous Martian meteorite ALH84001 and an early solidification time estimated from the Martian crust, suggest that the inner Solar System was fairly clear of large bodies about 10 Myr after the oldest meteorites formed. Thus, the 'standard model' suggests that for a period of several tens of millions of years the terrestrial planet region had few. if any, lunar-sized bodies and there were five terrestrial planets, Mercury, Venus, the two progenitors of the Earth-Moon system, and Mars. To simulate the dynamics of the Solar System before the hypothesized Moon-forming impact, we are integrating the Solar System with the Earth-Moon system replaced by two bodies in heliocentric orbits between Venus and Mars. The total (orbital) angular momentum of the Earth-Moon progenitors is that of the present Earth-Moon system, and their total mass is that of the Earth-Moon system. We are looking at ranges in mass ratio and initial values for eccentricity, inclination. and semi-major axis. We are using the SYMBA integrator to integrate these systems until a collision occurs or a time of 200 Myr elapses. Results are presented in a companion paper.

Tube dynamics and low energy Earth-Moon transfers in the 4-body system

NASA Astrophysics Data System (ADS)

Onozaki, Kaori; Yoshimura, Hiroaki; Ross, Shane D.

2017-11-01

In this paper, we show a low energy Earth-Moon transfer in the context of the Sun-Earth-Moon-spacecraft 4-body system. We consider the 4-body system as the coupled system of the Sun-Earth-spacecraft 3-body system perturbed by the Moon (which we call the Moon-perturbed system) and the Earth-Moon-spacecraft 3-body system perturbed by the Sun (which we call the Sun-perturbed system). In both perturbed systems, analogs of the stable and unstable manifolds are computed numerically by using the notion of Lagrangian coherent structures, wherein the stable and unstable manifolds play the role of separating orbits into transit and non-transit orbits. We obtain a family of non-transit orbits departing from a low Earth orbit in the Moon-perturbed system, and a family of transit orbits arriving into a low lunar orbit in the Sun-perturbed system. Finally, we show that we can construct a low energy transfer from the Earth to the Moon by choosing appropriate trajectories from both families and patching these trajectories with a maneuver.

Earth after the Moon-forming Impact

NASA Technical Reports Server (NTRS)

Zahnle, K. J.

2006-01-01

The Hadean Earth is widely and enduringly pictured as a world of exuberant volcanism, exploding meteors, huge craters, infernal heat, and billowing sulfurous steams; i.e., a world of fire and brimstone punctuated with blows to the head. In the background the Moon looms gigantic in the sky. The popular image has given it a name that celebrates our mythic roots. A hot early Earth is an inevitable consequence of accretion. The Moon-forming impact ensured that Earth as we know it emerged from a fog of silicate vapor. The impact separated the volatiles from the silicates. It took approx. 100 years to condense and rain out the bulk of the vaporized silicates, although relatively volatile elements may have remained present in the atmosphere throughout the magma ocena stage. The magma ocean lasted approx. 2 Myr, its lifetime prolonged by tidal heating and thermal blanketing by a thick CO2-rich steam atmosphere. Water oceans condensed quickly after the mantle solidified, but for some 10-100 Myr the surface would have stayed warm (approx. 500 K) until the CO2 was removed into the mantle. Thereafter the faint young Sun suggests that a lifeless Earth would always have been evolving toward a bitterly cold ice world, but the cooling trend was fiequently interrupted by volcanic or impact induced thaws. A cartoon history of water, temperature, and carbon dioxide in the aftermath of the moon-formining-impact is shown. How long it stays hot depends on how long it takes to scrub the C02 out of the atmosphere.

STS-32 view of the moon setting over the Earth's limb

NASA Image and Video Library

1990-01-20

STS-32 crew took this view of the moon setting over the Earth's limb. Near the center is a semi-vortex in the clouds - a storm system in the early stages of formation. The moon's image is distorted due to refraction through the Earth's atmosphere. The near side of the moon is visible showing the vast area of the moon's western seas (Mare Occidental), Apollo landing sites: Apollo 14 at Fra Mauro and Apollo 16 at Central Highlands near Descartes.

STS-32 view of the moon setting over the Earth's limb

NASA Technical Reports Server (NTRS)

1990-01-01

STS-32 crew took this view of the moon setting over the Earth's limb. Near the center is a semi-vortex in the clouds - a storm system in the early stages of formation. The moon's image is distorted due to refraction through the Earth's atmosphere. The near side of the moon is visible showing the vast area of the moon's western seas (Mare Occidental), Apollo landing sites: Apollo 14 at Fra Mauro and Apollo 16 at Central Highlands near Descartes.

Comments on 'The origin of the earth-moon system'

NASA Astrophysics Data System (ADS)

Savic, P.; Teleki, G.

1986-10-01

A new hypothesis for the origin of the earth-moon system is developed on the basis of Savic's (1961) theory of the origin of rotation of celestial bodies. According to the theory, the cooling off and contraction due to gravitational attraction on vast particle systems, with the pushing out of electrons from atom shells, results in the continually increasing density of a planet; the expulsion of electrons causes formation of a magnetic field by which a rotational motion is brought about. It is argued that these conditions are consistent with the formation of the earth and the moon from a unique protoplanet which, in course of the rotation, has taken shape of a large Jacobi ellipsoid. New condensation forming along the edge of the ellipsoid led to the creation of the dual earth-moon system.

Topography of Earth's moon

NASA Image and Video Library

2014-10-07

Topography of Earth's moon generated from data collected by the Lunar Orbiter Laser Altimeter, aboard NASA's Lunar Reconnaissance Orbiter, with the gravity anomalies bordering the Procellarum region superimposed in blue. The border structures are shown using gravity gradients calculated with data from NASA's Gravity Recovery and Interior Laboratory (GRAIL) mission. These gravity anomalies are interpreted as ancient lava-flooded rift zones buried beneath the volcanic plains (or maria) on the nearside of the Moon. Launched as GRAIL A and GRAIL B in September 2011, the probes, renamed Ebb and Flow, operated in a nearly circular orbit near the poles of the moon at an altitude of about 34 miles (55 kilometers) until their mission ended in December 2012. The distance between the twin probes changed slightly as they flew over areas of greater and lesser gravity caused by visible features, such as mountains and craters, and by masses hidden beneath the lunar surface. The twin spacecraft flew in a nearly circular orbit until the end of the mission on Dec. 17, 2012, when the probes intentionally were sent into the moon's surface. NASA later named the impact site in honor of late astronaut Sally K. Ride, who was America's first woman in space and a member of the GRAIL mission team. GRAIL's prime and extended science missions generated the highest-resolution gravity field map of any celestial body. The map will provide a better understanding of how Earth and other rocky planets in the solar system formed and evolved. The GRAIL mission was managed by NASA's Jet Propulsion Laboratory (JPL) in Pasadena, California, for NASA's Science Mission Directorate in Washington. The mission was part of the Discovery Program managed at NASA's Marshall Space Flight Center in Huntsville, Alabama. GRAIL was built by Lockheed Martin Space Systems in Denver. For more information about GRAIL, please visit grail.nasa.gov. Credit: NASA/Colorado School of Mines/MIT/GSFC/Scientific Visualization

The Dynamical Evolution of the Earth-Moon Progenitors. 1; Motivation and Methodology

NASA Technical Reports Server (NTRS)

Lissauer, J. J.; Rivera, E.; Duncan, M. J.; Levison, H. F.

1998-01-01

The giant impact hypothesis was introduced in the mid-1970s after consideration of results from the Apollo missions. This hypothesis best explains the similarity in elemental proportions in lunar and terrestrial rocks, the depletion of lunar volatiles, the lack of lunar Fe, and the large angular momentum in the Earth-Moon system. Comparison between the radiometric ages of inclusions in the most primitive meteorites and in the oldest lunar rocks and the differentiation age of Earth suggests that the Earth-Moon system formed about100 m.y. after the oldest meteorites. In addition, the age of the famous martian meteorite ALH 84001 and an early Martian solidification time obtained by Lee and Halliday suggest that the inner solar system was fairly clear of large bodies about 10 m.y. after the oldest meteorites formed. Thus, the "standard model" suggests that for several tens of millions of years, the terrestrial planet region had few, if any, lunar-sized bodies, and there were five terrestrial planets: Mercury, Venus, the two progenitors of the Earth-Moon system, and Mars. To simulate the dynamics of the solar system before the hypothesized Moon-forming impact, we are integrating the solar system with the Earth-Moon system replaced by two bodies in heliocentric orbits between Venus and Mars. The total (orbital) angular momentum of the Earth-Moon progenitors is that of the present Earth-Moon system, and their total mass is that of the Earth-Moon System. We are looking at ranges in mass ratio and initial values for eccentricity, inclination, and semimajor axis. We are using the SYMBA integrator to integrate these systems until a collision occurs or a time of 200 m.y. elapses. Results are presented in a companion abstract, (also presented at this meeting).

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.

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.

The Tethered Moon

NASA Technical Reports Server (NTRS)

Zahnle, Kevin; Lupu, Roxana Elena; Dubrovolskis, A. R.

2014-01-01

A reasonable initial condition on Earth after the Moonforming impact is that it begins as a hot global magma ocean1,2. We therefore begin our study with the mantle as a liquid ocean with a surface temperature on the order of 3000- 4000 K at a time some 100-1000 years after the impact, by which point we can hope that early transients have settled down. A 2nd initial condition is a substantial atmosphere, 100-1000 bars of H2O and CO2, supplemented by smaller amounts of CO, H2, N2, various sulfur-containing gases, and a suite of geochemical volatiles evaporated from the magma. Third, we start the Moon with its current mass at the relevant Roche limit. The 4th initial condition is the angular momentum of the Earth-Moon system. Canonical models hold this constant, whilst some recent models begin with considerably more angular momentum than is present today. Here we present a ruthlessly simplified model of Earth's cooling magmasphere based on a full-featured atmosphere and including tidal heating by the newborn Moon. Thermal blanketing by H2O-CO2 atmospheres slows cooling of a magma ocean. Geochemical volatiles - chiefly S, Na, and Cl - raise the opacity of the magma ocean's atmosphere and slow cooling still more. We assume a uniform mantle with a single internal (potential) temperature and a global viscosity. The important "freezing point" is the sharp rheological transition between a fluid carrying suspended crystals and a solid matrix through which fluids percolate. Most tidal heating takes place at this "freezing point" in a gel that is both pliable and viscous. Parameterized convection links the cooling rate to the temperature and heat generation inside the Earth. Tidal heating is a major effect. Tidal dissipation in the magma ocean is described by viscosity. The Moon is entwined with Earth by the negative feedback between thermal blanketing and tidal heating that comes from the temperature-dependent viscosity of the magma ocean. Because of this feedback, the rate

Development of the earth-moon system with implications for the geology of the early earth

NASA Technical Reports Server (NTRS)

Smith, J. V.

1976-01-01

Established facts regarding the basic features of the earth and the moon are reviewed, and some important problems involving the moon are discussed (extent of melting, time of crustal differentiation and nature of bombardment, bulk chemical composition, and nature and source of mare basins), with attention given to the various existing theories concerning these problems. Models of the development of the earth-moon system from the solar nebula are examined, with particular attention focused on those that use the concept of capture with disintegration. Impact processes in the early crust of the earth are briefly considered, with attention paid to Green's (1972) suggestion that Archaean greenstone belts may be the terrestrial equivalent of lunar maria.

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.

Circumlunar Free-Return Cycler Orbits for a Manned Earth-Moon Space Station

NASA Technical Reports Server (NTRS)

Genova, Anthony L.; Aldrin, Buzz

2015-01-01

Multiple free-return circumlunar cycler orbits were designed to allow regular travel between the Earth and Moon by a manned space station. The presented cycler orbits contain circumlunar free-return "figure-8" segments and yield lunar encounters every month. Smaller space "taxi" vehicles can rendezvous with (and depart from) the cycling Earth-Moon space station to enter lunar orbit (and/or land on the lunar surface), return to Earth, or reach destinations including Earth-Moon L1 and L2 halo orbits, near-Earth objects (NEOs), Venus, and Mars. To assess the practicality of the selected orbits, relevant cycler characteristics (including (Delta)V maintenance requirements) are presented and compared.

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.

Small asteroids temporarily captured in the Earth-Moon system

NASA Astrophysics Data System (ADS)

Jedicke, Robert; Bolin, Bryce; Bottke, William F.; Chyba, Monique; Fedorets, Grigori; Granvik, Mikael; Patterson, Geoff

2016-01-01

We present an update on our work on understanding the population of natural objects that are temporarily captured in the Earth-Moon system like the 2-3 meter diameter, 2006 RH120, that was discovered by the Catalina Sky Survey. We use the term `minimoon' to refer to objects that are gravitationally bound to the Earth-Moon system, make at least one revolution around the barycenter in a co-rotating frame relative to the Earth-Sun axis, and are within 3 Earth Hill-sphere radii. There are one or two 1 to 2 meter diameter minimoons in the steady state population at any time, and about a dozen larger than 50 cm diameter. `Drifters' are also bound to the Earth-Moon system but make less than one revolution about the barycenter. The combined population of minimoons and drifters provide a new opportunity for scientific exploration of small asteroids and testing concepts for in-situ resource utilization. These objects provide interesting challenges for rendezvous missions because of their limited lifetime and complicated trajectories. Furthermore, they are difficult to detect because they are small, available for a limited time period, and move quickly across the sky.

Small asteroids temporarily captured in the Earth-Moon system

NASA Astrophysics Data System (ADS)

Jedicke, Robert; Bolin, Bryce; Bottke, William F.; Chyba, Monique; Fedorets, Grigori; Granvik, Mikael; Patterson, Geoff

2015-08-01

We will present an update on our work on understanding the population of natural objects that are temporarily captured in the Earth-Moon system, such as the 2-3 meter diameter 2006 RH120 that was discovered by the Catalina Sky Survey. We use the term 'minimoon' to refer to objects that are gravitationally bound to the Earth-Moon system, make at least one revolution around the barycenter in a co-rotating frame relative to the Earth-Sun axis, and are within 3 Earth Hill-sphere radii. There are one or two 1 to 2 meter diameter minimoons in the steady state population at any time, and about a dozen larger than 50 cm diameter. `Drifters' are also bound to the Earth-Moon system but make less than one revolution about the barycenter. The combined population of minimoons and drifters provide a new opportunity for scientific exploration of small asteroids and testing concepts for in-situ resource utilization. These objects provide interesting challenges for rendezvous missions because of their limited lifetime and complicated trajectories. Furthermore, they are difficult to detect because they are small, available for a limited time period, and move quickly across the sky.

V, Cr, and Mn in the Earth, Moon, EPB, and SPB and the origin of the Moon: Experimental studies

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

Drake, M.J.; Capobianco, C.J.; Newsom, H.E.

1989-08-01

The abundances of V, Cr, and Mn inferred for the mantles of the Earth and Moon decrease in that order and are similar, but are distinct from those inferred for the mantles of the Eucrite Parent Body (EPB) and Shergottite Parent Body (SPB). This similarity between Earth and Moon has been used to suggest that the Moon is derived substantially or entirely from Earth mantle material following terrestrial core formation. To test this hypothesis, the authors have determined the partitioning of V, Cr, and Mn between solid iron metal, S-rich metallic liquid, and synthetic basaltic silicate liquid at 1,260{degree}C andmore » one bar pressure. The sequence of compatibility in the metallic phases is Cr > V > Mn at high oxygen fugacity and V > Cr > Mn at low oxygen fugacities. Solubilities in liquid metal always exceed solubilities in solid metal. These partition coefficients suggest that the abundances of V, Cr, and Mn do not reflect core formation in the Earth. Rather, they are consistent with the relative volatilities of these elements. The similarity in the depletion patterns of V, Cr, and Mn inferred for the mantles of the Earth and Moon is a necessary, but not sufficient, condition for the Moon to have been derived wholly or in part from the Earth's mantle.« less

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.

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.

Geochemical arguments for an Earth-like Moon-forming impactor.

PubMed

Dauphas, Nicolas; Burkhardt, Christoph; Warren, Paul H; Fang-Zhen, Teng

2014-09-13

Geochemical evidence suggests that the material accreted by the Earth did not change in nature during Earth's accretion, presumably because the inner protoplanetary disc had uniform isotopic composition similar to enstatite chondrites, aubrites and ungrouped achondrite NWA 5363/5400. Enstatite meteorites and the Earth were derived from the same nebular reservoir but diverged in their chemical evolutions, so no chondrite sample in meteorite collections is representative of the Earth's building blocks. The similarity in isotopic composition (Δ(17)O, ε(50)Ti and ε(54)Cr) between lunar and terrestrial rocks is explained by the fact that the Moon-forming impactor came from the same region of the disc as other Earth-forming embryos, and therefore was similar in isotopic composition to the Earth. The heavy δ(30)Si values of the silicate Earth and the Moon relative to known chondrites may be due to fractionation in the solar nebula/protoplanetary disc rather than partitioning of silicon in Earth's core. An inversion method is presented to calculate the Hf/W ratios and ε(182)W values of the proto-Earth and impactor mantles for a given Moon-forming impact scenario. The similarity in tungsten isotopic composition between lunar and terrestrial rocks is a coincidence that can be explained in a canonical giant impact scenario if an early formed embryo (two-stage model age of 10-20 Myr) collided with the proto-Earth formed over a more protracted accretion history (two-stage model age of 30-40 Myr). © 2014 The Author(s) Published by the Royal Society. All rights reserved.

Geochemical arguments for an Earth-like Moon-forming impactor

PubMed Central

Dauphas, Nicolas; Burkhardt, Christoph; Warren, Paul H.; Fang-Zhen, Teng

2014-01-01

Geochemical evidence suggests that the material accreted by the Earth did not change in nature during Earth's accretion, presumably because the inner protoplanetary disc had uniform isotopic composition similar to enstatite chondrites, aubrites and ungrouped achondrite NWA 5363/5400. Enstatite meteorites and the Earth were derived from the same nebular reservoir but diverged in their chemical evolutions, so no chondrite sample in meteorite collections is representative of the Earth's building blocks. The similarity in isotopic composition (Δ17O, ε50Ti and ε54Cr) between lunar and terrestrial rocks is explained by the fact that the Moon-forming impactor came from the same region of the disc as other Earth-forming embryos, and therefore was similar in isotopic composition to the Earth. The heavy δ30Si values of the silicate Earth and the Moon relative to known chondrites may be due to fractionation in the solar nebula/protoplanetary disc rather than partitioning of silicon in Earth's core. An inversion method is presented to calculate the Hf/W ratios and ε182W values of the proto-Earth and impactor mantles for a given Moon-forming impact scenario. The similarity in tungsten isotopic composition between lunar and terrestrial rocks is a coincidence that can be explained in a canonical giant impact scenario if an early formed embryo (two-stage model age of 10–20 Myr) collided with the proto-Earth formed over a more protracted accretion history (two-stage model age of 30–40 Myr). PMID:25114316

Tungsten isotope evidence for post-giant impact equilibration of the Earth and Moon

NASA Astrophysics Data System (ADS)

Kruijer, T.; Kleine, T.; Fischer-Gödde, M.

2015-12-01

The Moon is thought to have formed by re-accretion of material ejected by a giant impact on Earth [e.g., 1]. This model, at least in its classical form, predicts an isotopic difference between the Earth and Moon, because the Moon would largely consist of impactor material. Yet Earth and Moon show an unexpected isotopic similarity for many elements [e.g., 2]. Here we use variations in 182W—the decay-product of short-lived 182Hf (t1/2~9 Myr)—between the Moon and the bulk silicate Earth (BSE) to shed new light on this issue. We precisely determined the lunar 182W value by analysing KREEP-rich samples with MC-ICPMS and a new approach for quantifying cosmogenic 182W variations using Hf isotopes [6]. We find that the Moon shows a 27±4 ppm 182W excess over the modern BSE, in excellent agreement with [7]. This excess agrees with the predicted 182W change resulting from disproportional late accretion to the Earth and Moon after Earth's core had fully formed [6,7]. Thus, the pre-late-veneer BSE and the Moon were indistinguishable in 182W. However, the giant impact itself should have caused a notable Earth-Moon 182W difference by (1) changing the ɛ182W of the proto-Earth mantle by adding impactor mantle and core material, both carrying distinct 182W anomalies, and (2) by supplying W-rich but 182W-depleted impactor core material into the lunar accretion disk [6]. Thus, the Earth-Moon 182W homogeneity is an unexpected outcome of the giant impact. Unlike for Ti and O isotopes, the 182W homogeneity cannot be explained by accretion of impactor and proto-Earth from a homogeneous inner disk reservoir [3] or by making the Moon fully from proto-Earth mantle [4,5]. Thus, the 182W results require an efficient post-impact isotopic equilibration of the BSE and the Moon, but the mechanism for this has yet to be explored. One option is that Earth's mantle and its vapour atmosphere remained connected with the lunar accretion disk just after the giant impact [8]. [1] Canup R

Tidal evolution of the Moon from a high-obliquity, high-angular-momentum Earth.

PubMed

Ćuk, Matija; Hamilton, Douglas P; Lock, Simon J; Stewart, Sarah T

2016-11-17

In the giant-impact hypothesis for lunar origin, the Moon accreted from an equatorial circum-terrestrial disk; however, the current lunar orbital inclination of five degrees requires a subsequent dynamical process that is still unclear. In addition, the giant-impact theory has been challenged by the Moon's unexpectedly Earth-like isotopic composition. Here we show that tidal dissipation due to lunar obliquity was an important effect during the Moon's tidal evolution, and the lunar inclination in the past must have been very large, defying theoretical explanations. We present a tidal evolution model starting with the Moon in an equatorial orbit around an initially fast-spinning, high-obliquity Earth, which is a probable outcome of giant impacts. Using numerical modelling, we show that the solar perturbations on the Moon's orbit naturally induce a large lunar inclination and remove angular momentum from the Earth-Moon system. Our tidal evolution model supports recent high-angular-momentum, giant-impact scenarios to explain the Moon's isotopic composition and provides a new pathway to reach Earth's climatically favourable low obliquity.

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.

Properties of the moon, Mars, Martian satellites, and near-earth asteroids

NASA Technical Reports Server (NTRS)

Taylor, Jeffrey G.

1989-01-01

Environments and surface properties of the moon, Mars, Martian satellites, and near-earth asteroids are discussed. Topics include gravity, atmospheres, surface properties, surface compositions, seismicity, radiation environment, degradation, use of robotics, and environmental impacts. Gravity fields vary from large fractions of the earth's field such as 1/3 on Mars and 1/6 on the moon to smaller fractions of 0.0004 g on an asteroid 1 km in diameter. Spectral data and the analogy with meteor compositions suggest that near-earth asteroids may contain many resources such as water-rich carbonaceous materials and iron-rich metallic bodies. It is concluded that future mining and materials processing operations from extraterrestrial bodies require an investment now in both (1) missions to the moon, Mars, Phobos, Deimos, and near-earth asteroids and (2) earth-based laboratory research in materials and processing.

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.

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.

Observation duration analysis for Earth surface features from a Moon-based platform

NASA Astrophysics Data System (ADS)

Ye, Hanlin; Guo, Huadong; Liu, Guang; Ren, Yuanzhen

2018-07-01

Earth System Science is a discipline that performs holistic and comprehensive research on various components of the Earth. One of a key issue for the Earth monitoring and observation is to enhance the observation duration, the time intervals during which the Earth surface features can be observed by sensors. In this work, we propose to utilise the Moon as an Earth observation platform. Thanks to the long distance between the Earth and the Moon, and the vast space on the lunar surface which is suitable for sensor installation, this Earth observation platform could have large spatial coverage, long temporal duration, and could perform multi-layer detection of the Earth. The line of sight between a proposed Moon-based platform and the Earth will change with different lunar surface positions; therefore, in this work, the position of the lunar surface was divided into four regions, including one full observation region and three incomplete observation regions. As existing methods are not able to perform global-scale observations, a Boolean matrix method was established to calculate the necessary observation durations from a Moon-based platform. Based on Jet Propulsion Laboratory (JPL) ephemerides and Earth Orientation Parameters (EOP), a formula was developed to describe the geometrical relationship between the Moon-based platform and Earth surface features in the unified spatial coordinate system and the unified time system. In addition, we compared the observation geometries at different positions on the lunar surface and two parameters that are vital to observation duration calculations were considered. Finally, an analysis method was developed. We found that the observation duration of a given Earth surface feature shows little difference regardless of sensor position within the full observation region. However, the observation duration for sensors in the incomplete observation regions is reduced by at least half. In summary, our results demonstrate the suitability

Making the Moon from a fast-spinning Earth: a giant impact followed by resonant despinning.

PubMed

Ćuk, Matija; Stewart, Sarah T

2012-11-23

A common origin for the Moon and Earth is required by their identical isotopic composition. However, simulations of the current giant impact hypothesis for Moon formation find that most lunar material originated from the impactor, which should have had a different isotopic signature. Previous Moon-formation studies assumed that the angular momentum after the impact was similar to that of the present day; however, Earth-mass planets are expected to have higher spin rates at the end of accretion. Here, we show that typical last giant impacts onto a fast-spinning proto-Earth can produce a Moon-forming disk derived primarily from Earth's mantle. Furthermore, we find that a faster-spinning early Earth-Moon system can lose angular momentum and reach the present state through an orbital resonance between the Sun and Moon.

An Earth-Moon System Trajectory Design Reference Catalog

NASA Technical Reports Server (NTRS)

Folta, David; Bosanac, Natasha; Guzzetti, Davide; Howell, Kathleen C.

2014-01-01

As demonstrated by ongoing concept designs and the recent ARTEMIS mission, there is, currently, significant interest in exploiting three-body dynamics in the design of trajectories for both robotic and human missions within the Earth-Moon system. The concept of an interactive and 'dynamic' catalog of potential solutions in the Earth-Moon system is explored within this paper and analyzed as a framework to guide trajectory design. Characterizing and compiling periodic and quasi-periodic solutions that exist in the circular restricted three-body problem may offer faster and more efficient strategies for orbit design, while also delivering innovative mission design parameters for further examination.

Tidal-friction theory of the earth-moon system

NASA Technical Reports Server (NTRS)

Lyttleton, R. A.

1980-01-01

Serious errors contained in Jeffreys' (1952, 1959, 1970, 1976) discussion of tidal friction in the earth-moon system are identified and their consequences are discussed. A direct solution of the dynamical tidal equations for the couple from the earth acting upon the moon and the couple from the earth acting upon the sun, which were left unsolved by Jeffreys, is found to be incompatible with observations and the predictions of linear or quadratic friction theory, due to his failure to take into account the possible change of the moment of inertia of the earth with time in the derivation of the dynamical equations. Consideration of this factor leads to the conclusion that the earth must be contracting at a rate of 14.7 x 10 to the -11th/year, which can be accounted for only by the Ramsey theory, in which the terrestrial core is considered as a phase change rather than a change in chemical composition. Implications of this value for the rates of changes in day length and lunar distance are also indicated.

Earth After the Moon Forming Impact

NASA Technical Reports Server (NTRS)

Zahnle, Kevin

2006-01-01

The Hadean Earth is widely and enduringly pictured as a world of exuberant volcanism, exploding meteors, huge craters, infernal heat, and billowing sulfurous steams; i.e., a world of fire and brimstone punctuated with blows to the head. In the background the Moon looms gigantic in the sky. The popular image has given it a name that celebrates our mythic roots. A hot early Earth is an inevitable consequence of accretion. The Moon-forming impact ensured that Earth as we know it emerged from a fog of silicate vapor. The impact separated the volatiles from the silicates. It took -100 years to condense and rain out the bulk of the vaporized silicates, although relatively volatile elements may have remained present in the atmosphere throughout the magma ocena stage. The magma ocean lasted approx. 2 Myr, its lifetime prolonged by tidal heating and thermal blanketing by a thick (CO2-rich steam atmosphere. Water oceans condensed quickly after the mantle solidified, but for some 10-100 Myr the surface would have stayed warm (approx. 500 K) until the CO2 was removed into the mantle. Thereafter the faint young Sun suggests that a lifeless Earth would always have been evolving toward a bitterly cold ice world, but the cooling trend was frequently interrupted by volcanic or impact induced thaws.

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

Optimal Low Energy Earth-Moon Transfers

NASA Technical Reports Server (NTRS)

Griesemer, Paul Ricord; Ocampo, Cesar; Cooley, D. S.

2010-01-01

The optimality of a low-energy Earth-Moon transfer is examined for the first time using primer vector theory. An optimal control problem is formed with the following free variables: the location, time, and magnitude of the transfer insertion burn, and the transfer time. A constraint is placed on the initial state of the spacecraft to bind it to a given initial orbit around a first body, and on the final state of the spacecraft to limit its Keplerian energy with respect to a second body. Optimal transfers in the system are shown to meet certain conditions placed on the primer vector and its time derivative. A two point boundary value problem containing these necessary conditions is created for use in targeting optimal transfers. The two point boundary value problem is then applied to the ballistic lunar capture problem, and an optimal trajectory is shown. Additionally, the ballistic lunar capture trajectory is examined to determine whether one or more additional impulses may improve on the cost of the transfer.

A primordial origin for the compositional similarity between the Earth and the Moon.

PubMed

Mastrobuono-Battisti, Alessandra; Perets, Hagai B; Raymond, Sean N

2015-04-09

Most of the properties of the Earth-Moon system can be explained by a collision between a planetary embryo (giant impactor) and the growing Earth late in the accretion process. Simulations show that most of the material that eventually aggregates to form the Moon originates from the impactor. However, analysis of the terrestrial and lunar isotopic compositions show them to be highly similar. In contrast, the compositions of other Solar System bodies are significantly different from those of the Earth and Moon, suggesting that different Solar System bodies have distinct compositions. This challenges the giant impact scenario, because the Moon-forming impactor must then also be thought to have a composition different from that of the proto-Earth. Here we track the feeding zones of growing planets in a suite of simulations of planetary accretion, to measure the composition of Moon-forming impactors. We find that different planets formed in the same simulation have distinct compositions, but the compositions of giant impactors are statistically more similar to the planets they impact. A large fraction of planet-impactor pairs have almost identical compositions. Thus, the similarity in composition between the Earth and Moon could be a natural consequence of a late giant impact.

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.

Main Difference with Formed Process of the Moon and Earth Minerals and Fluids

NASA Astrophysics Data System (ADS)

Kato, T.; Miura, Y.

2018-04-01

Minerals show large and global distribution on Earth system, but small and local formation on the Moon. Fluid water is formed as same size and distribution on Earth and the Moon based on their body-systems.

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

Cosmic acceleration of Earth and the Moon by dark matter

NASA Technical Reports Server (NTRS)

Nordtvedt, Kenneth L.

1994-01-01

In order to test the hypothesis that the gravitational interaction between our Galaxy's dark matter and the ordinary matter in Earth and the Moon might not fulfill the equivalence principle (universality of free fall), we consider the pertinent perturbation of the lunar orbit -- a sidereal month period range oscillation resulting from a spatially fixed polarization of the orbit. Lunar laser ranging (LLR) data can measure this sidereal perturbation to an accuracy equal to or better than its existing measurement of the synodic month period range oscillation amplitude (+/- 3 cm) which has been used for testing whether Earth and the Moon accelerate at equal rates toward the Sun. Because of the slow precession rate of the Moon's perigree (8.9 yr period), the lunar orbit is particularly sensitive to a cosmic acceleration; the LLR fit of the orbit places an upper limit of 10(exp -13) cm/sq. s for any cosmic differential acceleration between Earth (Fe) and the Moon (silicates). This is 10(exp -5) of the total galactic acceleration of the solar system, of which, it has been suggested, a large portion is produced by dark matter.

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.

Galileo Earth/Moon News Conference. Part 1

NASA Technical Reports Server (NTRS)

1992-01-01

This NASA Kennedy Space Center (KSC) video release (Part 1 of 2) begins with a presentation given by William J. O'Neil (Galileo Project Manager) describing the status and position of the Galileo spacecraft 7 days prior to the Galileo Earth-2 flyby. Slides are presented including diagrams of the Galileo spacecraft trajectory, trajectory correction maneuvers, and the Venus and asteroid flybys. Torrence Johnson (Galileo Project Scientist) follows Mr. O'Neil with an explanation of the Earth/Moon science activities that will be undertaken during the second Galileo/Earth encounter. These activities include remote sensing, magnetospheric and plasma measurements, and images taken directly from Galileo of the Earth and Moon. Dr. Joseph Veverka (Galileo Imaging Team, Cornell University) then gives a brief presentation of the data collected by the first Galileo/Gaspra asteroid flyby. Images sampled from the 57 photographs taken of Gaspra are presented along with discussions of Gaspra's morphology, shape and size, and surface features. These presentations are followed by a question and answer period given for the benefit of scientific journalists whose subjects include overall Galileo spacecraft health, verification of the Gaspra images timeframe, and the condition of certain scientific spacecraft instruments. Part 2 of this video can be retrieved by using Report No. NONP-NASA-VT-2000001078.

Tidal effects on Earth, Planets, Sun by far visiting moons

NASA Astrophysics Data System (ADS)

Fargion, Daniele

2016-07-01

The Earth has been formed by a huge mini-planet collision forming our Earth surface and our Moon today. Such a central collision hit was statistically rare. A much probable skimming or nearby encounter by other moons or planets had to occur. Indeed Recent observations suggest that many planetary-mass objects may be present in the outer solar system between the Kuiper belt and the Oort cloud. Gravitational perturbations may occasionally bring them into the inner solar system. Their passage near Earth could have generated gigantic tidal waves, large volcanic eruptions, sea regressions, large meteoritic impacts and drastic changes in global climate. They could have caused the major biological mass extinctions in the past in the geological records. For instance a ten times a terrestrial radius nearby impact scattering by a peripherical encounter by a small moon-like object will force huge tidal waves (hundred meter height), able to lead to huge tsunami and Earth-quake. Moreover the historical cumulative planet hits in larger and wider planets as Juppiter, Saturn, Uranus will leave a trace, as observed, in their tilted spin axis. Finally a large fraction of counter rotating moons in our solar system probe and test such a visiting mini-planet captur origination. In addition the Earth day duration variability in the early past did show a rare discountinuity, very probably indebt to such a visiting planet crossing event. These far planets in rare trajectory to our Sun may, in thousands event capture, also explain sudden historical and recent temperature changes.

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

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

Precession of the Earth-Moon System

ERIC Educational Resources Information Center

Urbassek, Herbert M.

2009-01-01

The precession rate of the Earth-Moon system by the gravitational influence of the Sun is derived. Attention is focussed on a physically transparent but complete presentation accessible to first- or second-year physics students. Both a shortcut and a full analysis are given, which allows the inclusion of this material as an example of the physics…

Stochastic late accretion to Earth, the Moon, and Mars.

PubMed

Bottke, William F; Walker, Richard J; Day, James M D; Nesvorny, David; Elkins-Tanton, Linda

2010-12-10

Core formation should have stripped the terrestrial, lunar, and martian mantles of highly siderophile elements (HSEs). Instead, each world has disparate, yet elevated HSE abundances. Late accretion may offer a solution, provided that ≥0.5% Earth masses of broadly chondritic planetesimals reach Earth's mantle and that ~10 and ~1200 times less mass goes to Mars and the Moon, respectively. We show that leftover planetesimal populations dominated by massive projectiles can explain these additions, with our inferred size distribution matching those derived from the inner asteroid belt, ancient martian impact basins, and planetary accretion models. The largest late terrestrial impactors, at 2500 to 3000 kilometers in diameter, potentially modified Earth's obliquity by ~10°, whereas those for the Moon, at ~250 to 300 kilometers, may have delivered water to its mantle.

From a Million Miles Away, NASA Camera Shows Moon Crossing Face of Earth

NASA Image and Video Library

2015-08-05

This animation still image shows the far side of the moon, illuminated by the sun, as it crosses between the DISCOVR spacecraft's Earth Polychromatic Imaging Camera (EPIC) camera and telescope, and the Earth - one million miles away. Credits: NASA/NOAA A NASA camera aboard the Deep Space Climate Observatory (DSCOVR) satellite captured a unique view of the moon as it moved in front of the sunlit side of Earth last month. The series of test images shows the fully illuminated “dark side” of the moon that is never visible from Earth. The images were captured by NASA’s Earth Polychromatic Imaging Camera (EPIC), a four megapixel CCD camera and telescope on the DSCOVR satellite orbiting 1 million miles from Earth. From its position between the sun and Earth, DSCOVR conducts its primary mission of real-time solar wind monitoring for the National Oceanic and Atmospheric Administration (NOAA).

Galileo view of Moon orbiting the Earth taken from 3.9 million miles

NASA Technical Reports Server (NTRS)

1992-01-01

Eight days after its encounter with the Earth, the Galileo spacecraft was able to look back and capture this remarkable view of the Moon in orbit about the Earth, taken from a distance of about 6.2 million kilometers (3.9 million miles). The picture was constructed from images taken through the violet, red, and 1.0-micron infrared filters. The Moon is in the foreground, moving from left to right. The brightly-colored Earth contrasts strongly with the Moon, which reflects only about one-third as much sunlight as the Earth. Contrast and color have been computer-enhanced for both objects to improve visibility. Antarctica is visible through clouds (bottom). The Moon's far side is seen; the shadowy indentation in the dawn terminator is the south-Pole/Aitken Basin, one of the largest and oldest lunar impact features. Alternate Jet Propulsion Laboratory (JPL) number is P-41508.

Earthlike planets: Surfaces of Mercury, Venus, earth, moon, Mars

NASA Technical Reports Server (NTRS)

Murray, B.; Malin, M. C.; Greeley, R.

1981-01-01

The surfaces of the earth and the other terrestrial planets of the inner solar system are reviewed in light of the results of recent planetary explorations. Past and current views of the origin of the earth, moon, Mercury, Venus and Mars are discussed, and the surface features characteristic of the moon, Mercury, Mars and Venus are outlined. Mechanisms for the modification of planetary surfaces by external factors and from within the planet are examined, including surface cycles, meteoritic impact, gravity, wind, plate tectonics, volcanism and crustal deformation. The origin and evolution of the moon are discussed on the basis of the Apollo results, and current knowledge of Mercury and Mars is examined in detail. Finally, the middle periods in the history of the terrestrial planets are compared, and future prospects for the exploration of the inner planets as well as other rocky bodies in the solar system are discussed.

Earth and Moon as Seen from Mars

NASA Image and Video Library

2008-03-03

The High Resolution Imaging Science Experiment HiRISE camera would make a great backyard telescope for viewing Mars, and we can also use it at Mars to view other planets. This is an image of Earth and the moon, acquired on October 3, 2007.

Accretion of Moon and Earth and the emergence of life.

PubMed

Arrhenius, G; Lepland, A

2000-08-15

The discrepancy between the impact records on the Earth and Moon in the time period, 4.0-3.5 Ga calls for a re-evaluation of the cause and localization of the late lunar bombardment. As one possible explanation, we propose that the time coverage in the ancient rock record is sufficiently fragmentary, so that the effects of giant, sterilizing impacts throughout the inner solar system, caused by marauding asteroids, could have escaped detection in terrestrial and Martian records. Alternatively, the lunar impact record may reflect collisions of the receding Moon with a series of small, original satellites of the Earth and their debris in the time period about 4.0-3.5 Ga. The effects on Earth of such encounters could have been comparatively small. The location of these tellurian moonlets has been estimated to have been in the region around 40 Earth radii. Calculations presented here, indicate that this is the region that the Moon would traverse at 4.0-3.5 Ga, when the heavy and declining lunar bombardment took place. The ultimate time limit for the emergence of life on Earth is determined by the effects of planetary accretion--existing models offer a variety of scenarios, ranging from low average surface temperature at slow accretion of the mantle, to complete melting of the planet followed by protracted cooling. The choice of accretion model affects the habitability of the planet by dictating the early evolution of the atmosphere and hydrosphere. Further exploration of the sedimentary record on Earth and Mars, and of the chemical composition of impact-generated ejecta on the Moon, may determine the choice between the different interpretations of the late lunar bombardment and cast additional light on the time and conditions for the emergence of life.

Accretion of Moon and Earth and the emergence of life

NASA Technical Reports Server (NTRS)

Arrhenius, G.; Lepland, A.

2000-01-01

The discrepancy between the impact records on the Earth and Moon in the time period, 4.0-3.5 Ga calls for a re-evaluation of the cause and localization of the late lunar bombardment. As one possible explanation, we propose that the time coverage in the ancient rock record is sufficiently fragmentary, so that the effects of giant, sterilizing impacts throughout the inner solar system, caused by marauding asteroids, could have escaped detection in terrestrial and Martian records. Alternatively, the lunar impact record may reflect collisions of the receding Moon with a series of small, original satellites of the Earth and their debris in the time period about 4.0-3.5 Ga. The effects on Earth of such encounters could have been comparatively small. The location of these tellurian moonlets has been estimated to have been in the region around 40 Earth radii. Calculations presented here, indicate that this is the region that the Moon would traverse at 4.0-3.5 Ga, when the heavy and declining lunar bombardment took place. The ultimate time limit for the emergence of life on Earth is determined by the effects of planetary accretion--existing models offer a variety of scenarios, ranging from low average surface temperature at slow accretion of the mantle, to complete melting of the planet followed by protracted cooling. The choice of accretion model affects the habitability of the planet by dictating the early evolution of the atmosphere and hydrosphere. Further exploration of the sedimentary record on Earth and Mars, and of the chemical composition of impact-generated ejecta on the Moon, may determine the choice between the different interpretations of the late lunar bombardment and cast additional light on the time and conditions for the emergence of life.

Galileo view of Moon orbiting the Earth taken from 3.9 million miles

NASA Image and Video Library

1992-12-16

Eight days after its encounter with the Earth, the Galileo spacecraft was able to look back and capture this remarkable view of the Moon in orbit about the Earth, taken from a distance of about 6.2 million kilometers (3.9 million miles). The picture was constructed from images taken through the violet, red, and 1.0-micron infrared filters. The Moon is in the foreground, moving from left to right. The brightly-colored Earth contrasts strongly with the Moon, which reflects only about one-third as much sunlight as the Earth. Contrast and color have been computer-enhanced for both objects to improve visibility. Antarctica is visible through clouds (bottom). The Moon's far side is seen; the shadowy indentation in the dawn terminator is the south-Pole/Aitken Basin, one of the largest and oldest lunar impact features. Alternate Jet Propulsion Laboratory (JPL) number is P-41508. View appears in the Space News Roundup v32 n1 p1, 01-11-93.

Short-term capture of the Earth-Moon system

NASA Astrophysics Data System (ADS)

Qi, Yi; de Ruiter, Anton

2018-06-01

In this paper, the short-term capture (STC) of an asteroid in the Earth-Moon system is proposed and investigated. First, the space condition of STC is analysed and five subsets of the feasible region are defined and discussed. Then, the time condition of STC is studied by parameter scanning in the Sun-Earth-Moon-asteroid restricted four-body problem. Numerical results indicate that there is a clear association between the distributions of the time probability of STC and the five subsets. Next, the influence of the Jacobi constant on STC is examined using the space and time probabilities of STC. Combining the space and time probabilities of STC, we propose a STC index to evaluate the probability of STC comprehensively. Finally, three potential STC asteroids are found and analysed.

Chromium isotopic homogeneity between the Moon, the Earth, and enstatite chondrites

NASA Astrophysics Data System (ADS)

Mougel, Bérengère; Moynier, Frédéric; Göpel, Christa

2018-01-01

Among the elements exhibiting non-mass dependent isotopic variations in meteorites, chromium (Cr) has been central in arguing for an isotopic homogeneity between the Earth and the Moon, thus questioning physical models of Moon formation. However, the Cr isotopic composition of the Moon relies on two samples only, which define an average value that is slightly different from the terrestrial standard. Here, by determining the Cr isotopic composition of 17 lunar, 9 terrestrial and 5 enstatite chondrite samples, we re-assess the isotopic similarity between these different planetary bodies, and provide the first robust estimate for the Moon. In average, terrestrial and enstatite samples show similar ε54Cr. On the other hand, lunar samples show variables excesses of 53Cr and 54Cr compared to terrestrial and enstatite chondrites samples with correlated ε53Cr and ε54Cr (per 10,000 deviation of the 53Cr/52Cr and 54Cr/52Cr ratios normalized to the 50Cr/52Cr ratio from the NIST SRM 3112a Cr standard). Unlike previous suggestions, we show for the first time that cosmic irradiation can affect significantly the Cr isotopic composition of lunar materials. Moreover, we also suggest that rather than spallation reactions, neutron capture effects are the dominant process controlling the Cr isotope composition of lunar igneous rocks. This is supported by the correlation between ε53Cr and ε54Cr, and 150Sm/152Sm ratios. After correction of these effects, the average ε54Cr of the Moon is indistinguishable from the terrestrial and enstatite chondrite materials reinforcing the idea of an Earth-Moon-enstatite chondrite system homogeneity. This is compatible with the most recent scenarios of Moon formation suggesting an efficient physical homogenization after a high-energy impact on a fast spinning Earth, and/or with an impactor originating from the same reservoir in the inner proto-planetary disk as the Earth and enstatite chondrites and having similar composition.

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 Earth, the Moon and Conservation of Momentum

ERIC Educational Resources Information Center

Brunt, Marjorie; Brunt, Geoff

2013-01-01

We consider the application of both conservation of momentum and Newton's laws to the Moon in an assumed circular orbit about the Earth. The inadequacy of some texts in applying Newton's laws is considered.

Time-optimal control of the spacecraft trajectories in the Earth-Moon system

NASA Astrophysics Data System (ADS)

Starinova, O. L.; Fain, M. K.; Materova, I. L.

2017-01-01

This paper outlines the multiparametric optimization of the L1-L2 and L2-L1 missions in the Earth-Moon system using electric propulsion. The optimal control laws are obtained using the Fedorenko successful linearization method to estimate the derivatives and the gradient method to optimize the control laws. The study of the transfers is based on the restricted circular three-body problem. The mathematical model of the missions is described within the barycentric system of coordinates. The optimization criterion is the total flight time. The perturbation from the Earth, the Moon and the Sun are taking into account. The impact of the shaded areas, induced by the Earth and the Moon, is also accounted. As the results of the optimization we obtained optimal control laws, corresponding trajectories and minimal total flight times.

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.

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.

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.

Fast accretion of the earth with a late moon-forming giant impact.

PubMed

Yu, Gang; Jacobsen, Stein B

2011-10-25

Constraints on the formation history of the Earth are critical for understanding of planet formation processes. (182)Hf-(182)W chronometry of terrestrial rocks points to accretion of Earth in approximately 30 Myr after the formation of the solar system, immediately followed by the Moon-forming giant impact (MGI). Nevertheless, some N-body simulations and (182)Hf-(182)W and (87)Rb-(87)Sr chronology of some lunar rocks have been used to argue for a later formation of the Moon at 52 to > 100 Myr. This discrepancy is often explained by metal-silicate disequilibrium during giant impacts. Here we describe a model of the (182)W isotopic evolution of the accreting Earth, including constraints from partitioning of refractory siderophile elements (Ni, Co, W, V, and Nb) during core formation, which can explain the discrepancy. Our modeling shows that the concentrations of the siderophile elements of the mantle are consistent with high-pressure metal-silicate equilibration in a terrestrial magma ocean. Our analysis shows that the timing of the MGI is inversely correlated with the time scale of the main accretion stage of the Earth. Specifically, the earliest time the MGI could have taken place right at approximately 30 Myr, corresponds to the end of main-stage accretion at approximately 30 Myr. A late MGI (> 52 Myr) requires the main stage of the Earth's accretion to be completed rapidly in < 10.7 ± 2.5 Myr. These are the two end member solutions and a continuum of solutions exists in between these extremes.

Lagrange Point Missions: the Key to Next-Generation Integrated Earth Observations. DSCOVR Innovation

NASA Astrophysics Data System (ADS)

Valero, F. P. J.

2016-12-01

From L-1 DSCOVR is capable of new, unique observations potentially conducive to a deeper scientific understanding of the Earth sciences. At L-1 and L-2 the net gravitational pull of the Earth and Sun equals the centripetal force required to orbit the Sun with the same period as the Earth. Satellites at or near L-1 and L-2 keep the same position relative to the Sun and the Earth. DSCOVR does not orbit the Earth but the Sun in synchronism with Earth, acts like a planetoid (orbits the Sun in the ecliptic plane) while acquiring integrated plus spatially and time resolved scientific data as Earth rotates around its axis. Because of the planet's axial tilt relative to the ecliptic plane, the Polar Regions are visible during local summer from L-1 and local winter from L-2 (Fig. 1). DSCOVR's synoptic and continuous observations solve most of the temporal and spatial limitations associated with low Earth (LEO) and Geostationary (GEO) orbits. Two observatories, one at L-1 (daytime) and one at L-2 (nighttime), would acquire minute-by-minute climate quality data for essentially every point on Earth. The integration of L-1, L-2, LEO, and GEO satellites plus the Moon offers new scientific tools and enriched data sets for Earth sciences. Lagrange points observatories are key to next-generation integrated Earth observations. For example, DSCOVR at L-1 views the Earth plus the Moon (a reference) and simultaneously, at one time or another, all LEO and GEO satellites. The L-1 and L-2 satellites would be the link between the Moon, LEO and GEO satellites while providing the data needed to build an integrated Earth observational system. The above properties are the bases for DSCOVR's innovation and scientific approach that systematically observes climate drivers (radiation, aerosols, ozone, clouds, water vapor, vegetation) from L-1 in a way not possible but synergistic with other satellites. Next step: more capable L-1 plus L-2 satellites. The way of the future.

Examples of the nonlinear dynamics of ballistic capture and escape in the earth-moon system

NASA Technical Reports Server (NTRS)

Belbruno, Edward A.

1990-01-01

An example of a trajectory is given which is initially captured in an elliptic resonant orbit about the earth and then ballistically escapes the earth-moon system. This is demonstrated by a numerical example in three-dimensions using a planetary ephemeris. Another example shows a mechanism of how an elliptic orbit about the earth can increase its energy by performing a complex nonlinear transition to an elliptic orbit of a larger semi-major axis. Capture is also considered. An application of ballistic capture at the moon via an unstable periodic orbit using the four-body sun-earth-moon-S/C interaction is described.

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.

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.

Science in Exploration: From the Moon to Mars and Back Home to Earth

NASA Technical Reports Server (NTRS)

Garvin, James B.

2007-01-01

NASA is embarking on a grand journey of exploration that naturally integrates the past successes of the Apollo missions to the Moon, as well as robotic science missions to Mars, to Planet Earth, and to the broader Universe. The US Vision for Space Exporation (VSE) boldly lays out a plan for human and robotic reconnaissance of the accessible Universe, starting with the surface of the Moon, and later embracing the surface of Mars. Sustained human and robotic access to the Moon and Mars will enable a new era of scientific investigation of our planetary neighbors, tied to driving scientific questions that pertain to the evolution and destiny of our home planet, but which also can be related to the search habitable worlds across the nearby Universe. The Apollo missions provide a vital legacy for what can be learned from the Moon, and NASA is now poised to recapture the lunar frontier starting with the flight of the Lunar Reconnaissance Orbiter (LRO) in late 2008. LRO will provide a new scientific context from which joint human and robotic exploration will ensue, guided by objectives some of which are focused on the grandest scientific challenges imaginable : Where did we come from? Are we alone? and Where are we going? The Moon will serve as an essential stepping stone for sustained human access and exploration of deep space and as a training ground while robotic missions with ever increasing complexity probe the wonders of Mars. As we speak, an armada of spacecraft are actively investigating the red planet both from orbit (NASA's Mars Reconnaissance Orbiter and Mars Odyssey Orbiter, plus ESA's Mars Express) and from the surface (NASA's twin Mars Exploration Rovers, and in 2008 NASA's Phoenix polar lander). The dramatically changing views of Mars as a potentially habitable world, with its own flavor of global climate change and unique climate records, provides a new vantage point from which to observe and question the workings of our own planet Earth. By 2010 NASA will

Americas from the Moon

NASA Image and Video Library

2010-09-15

The western hemisphere of our home planet Earth. North (upper left), Central, and South America (lower right) were nicely free of clouds when LRO pointed home on 9 August 2010 to acquire this beautiful view. LROC NAC E136013771. As LRO orbits the Moon every two hours sending down a stream of science data, it is easy to forget how close the Moon is to the Earth. The average distance between the two heavenly bodies is just 384,399 km (238,854 miles). Check your airline frequent flyer totals, perhaps you have already flown the distance to the Moon and back on a single airline. http://photojournal.jpl.nasa.gov/catalog/PIA13519

The Dynamical Evolution of the Earth-Moon Progenitors. 2; Results and Interpretation

NASA Technical Reports Server (NTRS)

Rivera, E.; Lissauer, J. J.; Duncan, M. J.; Levison, H. F.

1998-01-01

Substantial evidence indicates that the Earth-Moon system formed about 100 m.y. after the oldest meteorites and that the inner solar system had five terrestrial planets for several tens of millions of years before the hypothesized Moon-forming impact. We present and discuss some results from a series of N-body integrations in which the mass ratio of the Earth-Moon progenitors is 8:1 or 1:1. We want to know if it is plausible to have the Earth-Moon progenitors collide between 8 m.y. and 200 m.y. after the other planets had formed and to have the resulting system look "similar" to the solar system. If a collision occurs, the integrations tell us which two bodies collide and the time of the collision. We also determine the angular momentum deficit (AMD) of the resulting terrestrial planets. Additionally, we calculate several parameters of the collision. We use the AMD of the terrestrial planets to compare the resulting system to our own. The AMD or a planet is the difference between its orbital angular momentum and its orbital angular momentum if it were in a circular orbit with zero inclination.

Designating Earth's Moon as a United Nations World Heritage Site - Permanently Protected from Commercial or Military Uses

NASA Astrophysics Data System (ADS)

Steiner, R. G.

2002-01-01

paradigm that has characterized 19th and 20th century western civilization on Earth. The World Heritage process, and how Earth's Moon clearly satisfies necessary criteria, is described, as are the political challenges this proposal presents, including the 'national sovereignty' issue. The 1972 United Nations World Heritage Convention (signed by 167 countries), provides for the protection of cultural and natural properties deemed to be of "outstanding universal value", including value "from the point of view of science, conservation, or natural beauty" and places them under "a collective responsibility." The Moon clearly meets several criteria for WHS designation, as follow: a. "be outstanding examples representing major stages of Earth's history...significant on-going geological processes in the development of landforms, or significant geomorphic or physiographic features"; b. "contain superlative natural phenomena or areas of exceptional natural beauty and aesthetic importance"; and c. the Moon qualifies within the Convention as an "associative cultural landscape" which designates areas "by virtue of their powerful religious, artistic or cultural associations of the natural element." To facilitate WHS site designation for the Moon, it is proposed that the 1979 "Moon Treaty" (Agreement Governing the Activities of States on the Moon and Other Celestial Bodies, entered into force 7/11/84) be amended and broadly ratified internationally. Specifically, Article 11 - which presently provides for 'the establishment of an international regime to govern the exploitation of the natural resources of the moon, encourage the development of the natural resources of the moon, the management and expansion of opportunities in the use of those resources' - should be amended to provide a clear and unequivocal declaration of the extraordinary, irreplaceable cultural and natural value of the Moon, and designation of the Moon in its entirety as an inviolate World Heritage Site reserved

Tidal dissipation in the Earth and Moon from lunar laser ranging

NASA Technical Reports Server (NTRS)

Yoder, C. F.; Williams, J. G.; Dickey, J. O.; Newhall, X. X.

1984-01-01

The evolution of the Moon's orbit which is governed by tidal dissipation in the Earth while the evolution of its spin is controlled by its own internal dissipation is discussed. Lunar laser ranging data from August 1969 through May 1982 yields the values of both of these parameters. It is suggested that if the Moon was orbited the Earth since its formation, this must be an anomalously high value presumably due to changes in dissipation in the oceans due to continental drift. The explanation that the dissipation occurs at the interface between the mantle and a liquid core of shell is preferred.

Earth-moon system: Dynamics and parameter estimation; numerical considerations and program documentation

NASA Technical Reports Server (NTRS)

Breedlove, W. J., Jr.

1976-01-01

Major activities included coding and verifying equations of motion for the earth-moon system. Some attention was also given to numerical integration methods and parameter estimation methods. Existing analytical theories such as Brown's lunar theory, Eckhardt's theory for lunar rotation, and Newcomb's theory for the rotation of the earth were coded and verified. These theories serve as checks for the numerical integration. Laser ranging data for the period January 1969 - December 1975 was collected and stored on tape. The main goal of this research is the development of software to enable physical parameters of the earth-moon system to be estimated making use of data available from the Lunar Laser Ranging Experiment and the Very Long Base Interferometry experiment of project Apollo. A more specific goal is to develop software for the estimation of certain physical parameters of the moon such as inertia ratios, and the third and fourth harmonic gravity coefficients.

The moon-Earth system...As a vacuum gravity energy machine? A Hint about the Nature of Universal Gravity that May Have Been Overlooked

NASA Astrophysics Data System (ADS)

Masters, Roy

2011-10-01

We revisit the theories describing the moon raising the tides by virtue of pull gravity combined with the moon's centripetal angular momentum. We show that if gravity is considered as the attractive interaction between individual bodies, then a laboring moon doing work would have fallen to earth eons ago. Isaac Newton's laws of motion cannot work with pull gravity, but they do with Einstein's gravity as a property of the universe, which produces a continuous infusion of energy. In other words, the moon-Earth system becomes the first observable vacuum gravity energy machine. In other words the dynamics of what appears to be a closed system has been producing energy that continues raising the tides into perpetuity along with the force needed for the moon to escape the Earth's gravitational pull 4cm per year. All this is in defiance of Newton's first law which says ``If no force is added to a body it cannot accelerate.'' In this theory, a flowing space-time curves with three dimensions of force. A (flowing) spatial fabric bends around mass and displaces the inverse square field vanishing point property of matter with the appearance of a push-force square of the distance. In other words, the immeasurable universal gravity field appears as measurable local gravitation, concentrating universal gravitational pressure with the square of the distance from the very point was supposed to have disappeared. Needless to say such ``gravity'' necessitates a different beginning.

Fuel optimization for low-thrust Earth-Moon transfer via indirect optimal control

NASA Astrophysics Data System (ADS)

Pérez-Palau, Daniel; Epenoy, Richard

2018-02-01

The problem of designing low-energy transfers between the Earth and the Moon has attracted recently a major interest from the scientific community. In this paper, an indirect optimal control approach is used to determine minimum-fuel low-thrust transfers between a low Earth orbit and a Lunar orbit in the Sun-Earth-Moon Bicircular Restricted Four-Body Problem. First, the optimal control problem is formulated and its necessary optimality conditions are derived from Pontryagin's Maximum Principle. Then, two different solution methods are proposed to overcome the numerical difficulties arising from the huge sensitivity of the problem's state and costate equations. The first one consists in the use of continuation techniques. The second one is based on a massive exploration of the set of unknown variables appearing in the optimality conditions. The dimension of the search space is reduced by considering adapted variables leading to a reduction of the computational time. The trajectories found are classified in several families according to their shape, transfer duration and fuel expenditure. Finally, an analysis based on the dynamical structure provided by the invariant manifolds of the two underlying Circular Restricted Three-Body Problems, Earth-Moon and Sun-Earth is presented leading to a physical interpretation of the different families of trajectories.

Long term evolution of distant retrograde orbits in the Earth-Moon system

NASA Astrophysics Data System (ADS)

Bezrouk, Collin; Parker, Jeffrey S.

2017-09-01

This work studies the evolution of several Distant Retrograde Orbits (DROs) of varying size in the Earth-Moon system over durations up to tens of millennia. This analysis is relevant for missions requiring a completely hands off, long duration quarantine orbit, such as a Mars Sample Return mission or the Asteroid Redirect Mission. Four DROs are selected from four stable size regions and are propagated for up to 30,000 years with an integrator that uses extended precision arithmetic techniques and a high fidelity dynamical model. The evolution of the orbit's size, shape, orientation, period, out-of-plane amplitude, and Jacobi constant are tracked. It has been found that small DROs, with minor axis amplitudes of approximately 45,000 km or less decay in size and period largely due to the Moon's solid tides. Larger DROs (62,000 km and up) are more influenced by the gravity of bodies external to the Earth-Moon system, and remain bound to the Moon for significantly less time.

Optimal design of near-Earth asteroid sample-return trajectories in the Sun-Earth-Moon system

NASA Astrophysics Data System (ADS)

He, Shengmao; Zhu, Zhengfan; Peng, Chao; Ma, Jian; Zhu, Xiaolong; Gao, Yang

2016-08-01

In the 6th edition of the Chinese Space Trajectory Design Competition held in 2014, a near-Earth asteroid sample-return trajectory design problem was released, in which the motion of the spacecraft is modeled in multi-body dynamics, considering the gravitational forces of the Sun, Earth, and Moon. It is proposed that an electric-propulsion spacecraft initially parking in a circular 200-km-altitude low Earth orbit is expected to rendezvous with an asteroid and carry as much sample as possible back to the Earth in a 10-year time frame. The team from the Technology and Engineering Center for Space Utilization, Chinese Academy of Sciences has reported a solution with an asteroid sample mass of 328 tons, which is ranked first in the competition. In this article, we will present our design and optimization methods, primarily including overall analysis, target selection, escape from and capture by the Earth-Moon system, and optimization of impulsive and low-thrust trajectories that are modeled in multi-body dynamics. The orbital resonance concept and lunar gravity assists are considered key techniques employed for trajectory design. The reported solution, preliminarily revealing the feasibility of returning a hundreds-of-tons asteroid or asteroid sample, envisions future space missions relating to near-Earth asteroid exploration.

The Earth-Moon system as a typical binary in the Solar System

NASA Astrophysics Data System (ADS)

Ipatov, S.

2014-07-01

primaries with d<100 km can be explained by other models (not by contraction of RPPs). [5] noted that the giant impact concept, which is a popular model of the Moon formation, has several weaknesses. In particular, they calculated formation of the Earth-Moon system from a rarefied protoplanet which mass equaled to the mass of the Earth-Moon system. Using the formulas presented in [2], we obtained that the ratio r_K=K_{EM}/K_{s2} of the angular momentum K_{EM} of the Earth-Moon system to the angular momentum K_{s2} at a typical collision of two identical RPPs - Hill spheres, which masses m_2 are equal to 0.5\\cdot1.0123M_E and heliocentric orbits are circular, is about 0.0335. As K_{s2} ∝ (m_2)^{3/5} [2], then K_{s2}=K_{EM} at 2 m_2=0.0335^{3/5}\\cdot 1.0123M_E=0.13M_E. For circular heliocentric orbits, the maximum value of K_{s2} is greater by a factor of 0.6^{-1} than the above typical value. In this case, r_K=0.02 and 0.02^{3/5}=0.096. Therefore, the angular momentum of the Earth-Moon system can be acquired at a collision of two RPPs with a total mass not smaller than the mass of Mars. We suppose that solid proto-Earth and proto-Moon (with masses m_{Eo} and m_{Mo}) could be formed from a RPP (e.g., according to the models of contraction of a RPP [3,5]). Let us consider the model of the growth of proto-Earth and proto-Moon to the present masses of the Earth and the Moon (M_E and 0.0123M_E, respectively) by accumulation of smaller planetesimals for the case when the effective radii of proto-Earth and proto-Moon are proportional to r (where r is a radius of a considered object). Such proportionality can be considered for large enough eccentricities of planetesimals. In this case, r_{Mo}=m_{Mo}/M_E = [ (0.0123)^{-2/3} - k + k \\cdot (m_{Eo}/M_E)^{-2/3})]^{-3/2}, where k=(k_d)^{-2/3}, and k_d is the ratio of the density of the growing Moon to that of the growing Earth (k_d=0.6 for the present Earth and Moon). For r_{Eo}=m_{Eo}/M_E=0.1, we have r_{Mo}=0.0094 at k=1 and r

From a Million Miles Away, NASA Camera Shows Moon Crossing Face of Earth

NASA Image and Video Library

2015-08-05

This animation shows images of the far side of the moon, illuminated by the sun, as it crosses between the DISCOVR spacecraft's Earth Polychromatic Imaging Camera (EPIC) camera and telescope, and the Earth - one million miles away. Credits: NASA/NOAA A NASA camera aboard the Deep Space Climate Observatory (DSCOVR) satellite captured a unique view of the moon as it moved in front of the sunlit side of Earth last month. The series of test images shows the fully illuminated “dark side” of the moon that is never visible from Earth. The images were captured by NASA’s Earth Polychromatic Imaging Camera (EPIC), a four megapixel CCD camera and telescope on the DSCOVR satellite orbiting 1 million miles from Earth. From its position between the sun and Earth, DSCOVR conducts its primary mission of real-time solar wind monitoring for the National Oceanic and Atmospheric Administration (NOAA). Read more: www.nasa.gov/feature/goddard/from-a-million-miles-away-na... NASA image use policy. 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 Like us on Facebook Find us on Instagram

From a Million Miles Away, NASA Camera Shows Moon Crossing Face of Earth

NASA Image and Video Library

2017-12-08

This animation still image shows the far side of the moon, illuminated by the sun, as it crosses between the DISCOVR spacecraft's Earth Polychromatic Imaging Camera (EPIC) camera and telescope, and the Earth - one million miles away. Credits: NASA/NOAA A NASA camera aboard the Deep Space Climate Observatory (DSCOVR) satellite captured a unique view of the moon as it moved in front of the sunlit side of Earth last month. The series of test images shows the fully illuminated “dark side” of the moon that is never visible from Earth. The images were captured by NASA’s Earth Polychromatic Imaging Camera (EPIC), a four megapixel CCD camera and telescope on the DSCOVR satellite orbiting 1 million miles from Earth. From its position between the sun and Earth, DSCOVR conducts its primary mission of real-time solar wind monitoring for the National Oceanic and Atmospheric Administration (NOAA). Read more: www.nasa.gov/feature/goddard/from-a-million-miles-away-na... NASA image use policy. 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 Like us on Facebook Find us on Instagram

Highly siderophile elements in Earth's mantle as a clock for the Moon-forming impact.

PubMed

Jacobson, Seth A; Morbidelli, Alessandro; Raymond, Sean N; O'Brien, David P; Walsh, Kevin J; Rubie, David C

2014-04-03

According to the generally accepted scenario, the last giant impact on Earth formed the Moon and initiated the final phase of core formation by melting Earth's mantle. A key goal of geochemistry is to date this event, but different ages have been proposed. Some argue for an early Moon-forming event, approximately 30 million years (Myr) after the condensation of the first solids in the Solar System, whereas others claim a date later than 50 Myr (and possibly as late as around 100 Myr) after condensation. Here we show that a Moon-forming event at 40 Myr after condensation, or earlier, is ruled out at a 99.9 per cent confidence level. We use a large number of N-body simulations to demonstrate a relationship between the time of the last giant impact on an Earth-like planet and the amount of mass subsequently added during the era known as Late Accretion. As the last giant impact is delayed, the late-accreted mass decreases in a predictable fashion. This relationship exists within both the classical scenario and the Grand Tack scenario of terrestrial planet formation, and holds across a wide range of disk conditions. The concentration of highly siderophile elements (HSEs) in Earth's mantle constrains the mass of chondritic material added to Earth during Late Accretion. Using HSE abundance measurements, we determine a Moon-formation age of 95 ± 32 Myr after condensation. The possibility exists that some late projectiles were differentiated and left an incomplete HSE record in Earth's mantle. Even in this case, various isotopic constraints strongly suggest that the late-accreted mass did not exceed 1 per cent of Earth's mass, and so the HSE clock still robustly limits the timing of the Moon-forming event to significantly later than 40 Myr after condensation.

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.

Core-Mantle Partitioning of Volatile Elements and the Origin of Volatile Elements in Earth and Moon

NASA Technical Reports Server (NTRS)

Righter, K.; Pando, K.; Danielson, L.; Nickodem, K.

2014-01-01

Depletions of siderophile elements in mantles have placed constraints on the conditions on core segregation and differentiation in bodies such as Earth, Earth's Moon, Mars, and asteroid 4 Vesta. Among the siderophile elements there are a sub-set that are also volatile (volatile siderophile elements or VSE; Ga, Ge, In, As, Sb, Sn, Bi, Zn, Cu, Cd), and thus can help to constrain the origin of volatile elements in these bodies, and in particular the Earth and Moon. One of the fundamental observations of the geochemistry of the Moon is the overall depletion of volatile elements relative to the Earth, but a satisfactory explanation has remained elusive. Hypotheses for Earth include addition during accretion and core formation and mobilized into the metallic core, multiple stage origin, or addition after the core formed. Any explanation for volatile elements in the Earth's mantle must also be linked to an explanation of these elements in the lunar mantle. New metal-silicate partitioning data will be applied to the origin of volatile elements in both the Earth and Moon, and will evaluate theories for exogenous versus endogenous origin of volatile elements.

The spectral irradiance of the moon

USGS Publications Warehouse

Kieffer, H.H.; Stone, T.C.

2005-01-01

Images of the Moon at 32 wavelengths from 350 to 2450 nm have been obtained from a dedicated observatory during the bright half of each month over a period of several years. The ultimate goal is to develop a spectral radiance model of the Moon with an angular resolution and radiometric accuracy appropriate for calibration of Earth-orbiting spacecraft. An empirical model of irradiance has been developed that treats phase and libration explicitly, with absolute scale founded on the spectra of the star Vega and returned Apollo samples. A selected set of 190 standard stars are observed regularly to provide nightly extinction correction and long-term calibration of the observations. The extinction model is wavelength-coupled and based on the absorption coefficients of a number of gases and aerosols. The empirical irradiance model has the same form at each wavelength, with 18 coefficients, eight of which are constant across wavelength, for a total of 328 coefficients. Over 1000 lunar observations are fitted at each wavelength; the average residual is less than 1%. The irradiance model is actively being used in lunar calibration of several spacecraft instruments and can track sensor response changes at the 0.1% level. ?? 2005. The American Astronomical Society. All rights reserved.

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.

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.

Volatiles in the Earth and Moon: Constraints on planetary formation and evolution

NASA Astrophysics Data System (ADS)

Parai, Rita

The volatile inventories of the Earth and Moon reflect unique histories of volatile acquisition and loss in the early Solar System. The terrestrial volatile inventory was established after the giant impact phase of accretion, and the planet subsequently settled into a regime of long-term volatile exchange between the mantle and surface reservoirs in association with plate tectonics. Therefore, volatiles in the Earth and Moon shed light on a diverse array of processes that shaped planetary bodies in the Solar System as they evolved to their present-day states. Here we investigate new constraints on volatile depletion in the early Solar System, early outgassing of the terrestrial mantle, and the long-term evolution of the deep Earth volatile budget. We develop a Monte Carlo model of long-term water exchange between the mantle and surface reservoirs. Previous estimates of the deep Earth return flux of water are up to an order of magnitude too large, and incorporation of recycled slabs on average rehydrates the upper mantle but dehydrates the plume source. We find evidence for heterogeneous recycling of atmospheric argon and xenon into the upper mantle from noble gases in Southwest Indian Ridge basalts. Xenon isotope systematics indicate that xenon budgets of mid-ocean ridge and plume-related mantle sources are dominated by recycled atmospheric xenon, though the two sources have experienced different degrees of degassing. Differences between the mid-ocean ridge and plume sources were initiated within the first 100 million years of Earth history, and the two sources have never subsequently been homogenized. New high-precision xenon isotopic data contribute to an emerging portrait of two mantle reservoirs with distinct histories of outgassing and incorporation of recycled material in association with plate tectonics. Xenon isotopes indicate that the Moon likely formed within ˜70 million years of the start of the Solar System. To further investigate early Solar System

Fast accretion of the Earth with a late Moon-forming giant impact

PubMed Central

Yu, Gang; Jacobsen, Stein B.

2011-01-01

Constraints on the formation history of the Earth are critical for understanding of planet formation processes. 182Hf-182W chronometry of terrestrial rocks points to accretion of Earth in approximately 30 Myr after the formation of the solar system, immediately followed by the Moon-forming giant impact (MGI). Nevertheless, some N-body simulations and 182Hf-182W and 87Rb-87Sr chronology of some lunar rocks have been used to argue for a later formation of the Moon at 52 to > 100 Myr. This discrepancy is often explained by metal-silicate disequilibrium during giant impacts. Here we describe a model of the 182W isotopic evolution of the accreting Earth, including constraints from partitioning of refractory siderophile elements (Ni, Co, W, V, and Nb) during core formation, which can explain the discrepancy. Our modeling shows that the concentrations of the siderophile elements of the mantle are consistent with high-pressure metal-silicate equilibration in a terrestrial magma ocean. Our analysis shows that the timing of the MGI is inversely correlated with the time scale of the main accretion stage of the Earth. Specifically, the earliest time the MGI could have taken place right at approximately 30 Myr, corresponds to the end of main-stage accretion at approximately 30 Myr. A late MGI (> 52 Myr) requires the main stage of the Earth’s accretion to be completed rapidly in < 10.7 ± 2.5 Myr. These are the two end member solutions and a continuum of solutions exists in between these extremes. PMID:22006299

Geochemical evidence for the formation of the Moon by impact induced fission of the proto-Earth

NASA Technical Reports Server (NTRS)

Waenke, H.; Dreibus, G.

1984-01-01

Geochemical evidence is discussed which advocates the theory that the Moon was formed by impact induced fission of the Earth. The Earth's mantle exhibits a number of geochemical peculiarities which make our planet a unique object in the solar system. Terrestrial basalts are compared with those from the Eucrite parent body and the Shergotty parent body. Also the Moon's composition is very close to the Earth's in all details except the lower FeO content which is explained. Evidence is discussed for the plausible physical process of formation of the Moon by impact induced fission. Also the theory that impact induced fission occurred at the moment at which accretion of the Earth was not totally complete is briefly discussed.

Variation of Lunar Sodium During Passage of the Moon through the Earth's Magnetotail

NASA Technical Reports Server (NTRS)

Potter, Andrew E.; Killen, Rosemary M.; Morgan, Thomas H.

2000-01-01

We measured sodium emission above the lunar equator over a range of lunar altitudes from 100 to 4000 km. The measurements were repeated approximately every 24 hours from June 7 to 16, 1998, covering the period during which the Moon passed through the Earth's magnetotail. Sodium temperatures derived from the altitude dependence of emission intensity ranged from 1200 to 2900 K. This result supports the view that photodesorption is a primary source of sodium in the exosphere since the most probable temperature of sodium form this source is in this range. Passage of the Moon through the Earth's magnetotail (where solar wind is essentially absent) affected the sodium density, such that it was higher before the Moon entered the Earth's magnetotail than after the Moon left it. This suggests that the solar wind plays a role in production of lunar sodium. We propose that its function is to mobilize sodium and bring it to the surface, where photodesorption can eject it into the exosphere. A two-step process such as this could help to explain the latitude dependence of sodium density, which varies as the second or higher power of cosine latitude.

Creating an isotopically similar Earth-Moon system with correct angular momentum from a giant impact

NASA Astrophysics Data System (ADS)

Wyatt, Bryant M.; Petz, Jonathan M.; Sumpter, William J.; Turner, Ty R.; Smith, Edward L.; Fain, Baylor G.; Hutyra, Taylor J.; Cook, Scott A.; Gresham, John H.; Hibbs, Michael F.; Goderya, Shaukat N.

2018-04-01

The giant impact hypothesis is the dominant theory explaining the formation of our Moon. However, the inability to produce an isotopically similar Earth-Moon system with correct angular momentum has cast a shadow on its validity. Computer-generated impacts have been successful in producing virtual systems that possess many of the observed physical properties. However, addressing the isotopic similarities between the Earth and Moon coupled with correct angular momentum has proven to be challenging. Equilibration and evection resonance have been proposed as means of reconciling the models. In the summer of 2013, the Royal Society called a meeting solely to discuss the formation of the Moon. In this meeting, evection resonance and equilibration were both questioned as viable means of removing the deficiencies from giant impact models. The main concerns were that models were multi-staged and too complex. We present here initial impact conditions that produce an isotopically similar Earth-Moon system with correct angular momentum. This is done in a single-staged simulation. The initial parameters are straightforward and the results evolve solely from the impact. This was accomplished by colliding two roughly half-Earth-sized impactors, rotating in approximately the same plane in a high-energy, off-centered impact, where both impactors spin into the collision.

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.

MoonBEAM: A Beyond Earth-Orbit Gamma-Ray Burst Detector for Gravitational-Wave Astronomy

NASA Technical Reports Server (NTRS)

Hui, C. M.; Briggs, M. S.; Goldstein, A. M.; Jenke, P. A.; Kocevski, D.; Wilson-Hodge, C. A.

2018-01-01

Moon Burst Energetics All-sky Monitor (MoonBEAM) is a CubeSat concept of deploying gamma-ray detectors in cislunar space to improve localization precision for gamma-ray bursts by utilizing the light travel time difference between different orbits. We present here a gamma-ray SmallSat concept in Earth-Moon L3 halo orbit that is capable of rapid response and provide a timing baseline for localization improvement when partnered with an Earth-orbit instrument. Such an instrument would probe the extreme processes in cosmic collision of compact objects and facilitate multi-messenger time-domain astronomy to explore the end of stellar life cycles and black hole formations.

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

An Alternative view of Earth's Tectonics : The Moon's explosive origin out of SE Asia.

NASA Astrophysics Data System (ADS)

Coleman, P. F.

2017-12-01

A lunar birth scar is typically considered untenable, under the standard paradigm (GTS-4.6-0 Ga, Giant Impact/Plate Tectonics), since it would have been erased by a combination of Wilson recycling, and erosion. This paradigm, while supported by robust, absolute dating, is still provisional, and, like all scientifc paradigms, is nonetheless open to refutation. It cannot, a priori, rule out such a scar. If empirical evidence were to be discovered, in favor of a lunar birthmark, it would have profound implications for the standard view. Coleman (2015) proposed an alternative paradigm based on an internal explosion of Proto-Earth (PE) that ejected the Moon into orbit and left coeval global signatures, such as; ocean-continent antipodality, the global geoid, origin of water, continents, trenches, fault lines, LIPs, hotspots, seamount chains, from the high TP shock/seismic waves. The abrupt deceleration also led to inertial effects of PE's crustal layers, possibly explaining subduction/obduction and fold and thrust fold belts. One major, first order, line of evidence is the actual fission signature ( 4000+ km long) where the Moon was explosively thrust tangentially (to the core) through ductile mantle (see Fig B) to escape into orbit. The proposed path, (locus Moon's center) is from (0°, 78.5°E) (Fig A), near present day India, to (+14.4°, 119°E) out of SE Asia (See Fig C). Possible evidence in favor of this path (but not limited to) include: the Indian Geoid Anomaly Low ( Moon's exhumation?), the Himalayas and Tibetan Plateau (generated by the Moon's NE collisional movement and temporary hole and mantle rebound), SE Asia with many minor plates and back arc basins ( the Moon's exit zone), the East African Rifts (EARs) form a NE-directed pull apart region (explained as a set explosive crustal fragments or "plates") moving towards this relic unconsolidated Asian sink hole (See Fig D). The existence of a fossilised lunar birth points to a recent Earth-Moon, since

Space tourism: from earth orbit to the moon

NASA Astrophysics Data System (ADS)

Collins, P.

Travel to and from the lunar surface has been known to be feasible since it was first achieved 34 years ago. Since that time there has been enormous progress in related engineering fields such as rocket propulsion, materials and avionics, and about 1 billion has been spent on lunar science and engineering research. Consequently there are no fundamental technical problems facing the development of lunar tourism - only business and investment problems. The outstanding problem is to reduce the cost of launch to low Earth orbit. Recently there has been major progress towards overturning the myth that launch costs are high because of physical limits. Several "X Prize" competitor vehicles currently in test-flight are expected to be able to perform sub-orbital flights at approximately 1/1,000 of the cost of Alan Shepard's similar flight in 1961. This activity could have started 30 years ago if space agencies had had economic rather than political objectives. A further encouraging factor is that the demand for space tourism seems potentially limitless. Starting with sub-orbital flights and growing through orbital activities, travel to the Moon will offer further unique attractions. In every human culture there is immense interest in the Moon arising from millennia of myths. In addition, bird-like flying sports, first described by Robert Heinlein, will become another powerful demand factor. Roundtrips of 1 to 2 weeks are very convenient for travel companies; and the radiation environment will permit visitors several days of surface activity without significant health risks. The paper also discusses economic aspects of lunar tourism, including the benefits it will have for those on Earth. Lunar economic development based on tourism will have much in common with economic development on Earth based on tourism: starting from the fact that many people spontaneously wish to visit popular places, companies in the tourism industry invest to sell a growing range of services to ever

Low Energy Transfer to the Moon

NASA Astrophysics Data System (ADS)

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

In 1991, the Japanese Hiten mission used a low energy transfer with a ballistic capture at the Moon which required less Δ V than a standard Hohmann transfer. In this paper, we apply the dynamical systems techniques developed in our earlier work to reproduce systematically a Hiten-like mission. We approximate the Sun-Earth-Moon-spacecraft 4-body system as two 3-body systems. Using the invariant manifold structures of the Lagrange points of the 3-body systems, we are able to construct low energy transfer trajectories from the Earth which execute ballistic capture at the Moon. The techniques used in the design and construction of this trajectory may be applied in many situations.

Visualizing the Earth and Moon Relationship via Scaled Drawings

ERIC Educational Resources Information Center

Fidler, Chuck; Dotger, Sharon

2009-01-01

Students' difficulties with accurately conceptualizing the relationships among the Earth, Moon, and Sun are well documented. Any teacher who has seen the film "A Private Universe" (Schneps and Sadler 1988) will remember the challenge the interviewees experienced when trying to explain their understanding of this phenomenon. This paper describes a…

Core-Mantle Partitioning of Volatile Elements and the Origin of Volatile Elements in Earth and Moon

NASA Technical Reports Server (NTRS)

Righter, Kevin; Pando, K.; Danielson, L.; Nickodem, K.

2014-01-01

Depletions of volatile siderophile elements (VSE; Ga, Ge, In, As, Sb, Sn, Bi, Zn, Cu, Cd) in mantles of Earth and Moon, constrain the origin of volatile elements in these bodies, and the overall depletion of volatile elements in Moon relative to Earth. A satisfactory explanation has remained elusive [1,2]. We examine the depletions of VSE in Earth and Moon and quantify the amount of depletion due to core formation and volatility of potential building blocks. We calculate the composition of the Earth's PUM during continuous accretion scenarios with constant and variable fO2. Results suggest that the VSE can be explained by a rather simple scenario of continuous accretion leading to a high PT metal-silicate equilibrium scenario that establishes the siderophile element content of Earth's PUM near the end of accretion [3]. Core formation models for the Moon explain most VSE, but calculated contents of In, Sn, and Zn (all with Tc < 750 K) are all still too high after core formation, and must therefore require an additional process to explain the depletions in the lunar mantle. We discuss possible processes including magmatic degassing, evaporation, condensation, and vapor-liquid fractionation in the lunar disk.

MERI: an ultra-long-baseline Moon-Earth radio interferometer.

NASA Astrophysics Data System (ADS)

Burns, J. O.

Radiofrequency aperture synthesis, pioneered by Ryle and his colleagues at Cambridge in the 1960's, has evolved to ever longer baselines and larger arrays in recent years. The limiting resolution at a given frequency for modern ground-based very-long-baseline interferometry is simply determined by the physical diameter of the Earth. A second-generation, totally space-based VLB network was proposed recently by a group at the Naval Research Laboratory. The next logical extension of space-based VLBI would be a station or stations on the Moon. The Moon could serve as an outpost or even the primary correlator station for an extended array of space-based antennas.

The equilibrium of atmospheric sodium. [in atmospheres of Earth, Io, Mercury and Moon

NASA Technical Reports Server (NTRS)

Hunten, Donald M.

1992-01-01

We now have four examples of planetary objects with detectable sodium (and potassium) in their atmospheres: Earth, Io, Mercury and the moon. After a summary of the observational data, this survey discusses proposed sources and sinks. It appears that Io's surface material is rich in frozen SO2, but with around 1 percent of some sodium compound. The Io plasma torus contains ions of S, O and Na, also with at least one molecular ion containing Na. In turn, impact by these ions probably sustains the torus, as well as an extended neutral corona. A primary source for the Earth, Mercury and the moon is meteoroidal bombardment; at Mercury and perhaps the moon it may be supplemented by degassing of atoms from the regolith. Photoionization is important everywhere, although hot electrons are dominant at Io.

The focusing effect of P-wave in the Moon's and Earth's low-velocity core. Analytical solution

NASA Astrophysics Data System (ADS)

Fatyanov, A. G.; Burmin, V. Yu

2018-04-01

The important aspect in the study of the structure of the interiors of planets is the question of the presence and state of core inside them. While for the Earth this task was solved long ago, the question of whether the core of the Moon is in a liquid or solid state up to the present is debatable up to present. If the core of the Moon is liquid, then the velocity of longitudinal waves in it should be lower than in the surrounding mantle. If the core is solid, then most likely, the velocity of longitudinal waves in it is higher than in the mantle. Numerical calculations of the wave field allow us to identify the criteria for drawing conclusions about the state of the lunar core. In this paper we consider the problem of constructing an analytical solution for wave fields in a layered sphere of arbitrary radius. A stable analytic solution is obtained for the wave fields of longitudinal waves in a three-layer sphere. Calculations of the total wave fields and rays for simplified models of the Earth and the Moon with real parameters are presented. The analytical solution and the ray pattern showed that the low-velocity cores of the Earth and the Moon possess the properties of a collecting lens. This leads to the emergence of a wave field focusing area. As a result, focused waves of considerable amplitude appear on the surface of the Earth and the Moon. In the Earth case, they appear before the first PKP-wave arrival. These are so-called "precursors", which continue in the subsequent arrivals of waves. At the same time, for the simplified model of the Earth, the maximum amplitude growth is observed in the 147-degree region. For the Moon model, the maximum amplitude growth is around 180°.

HABITABILITY OF EARTH-MASS PLANETS AND MOONS IN THE KEPLER-16 SYSTEM

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

Quarles, B.; Musielak, Z. E.; Cuntz, M., E-mail: billyq@uta.edu, E-mail: zmusielak@uta.edu, E-mail: cuntz@uta.edu

2012-05-01

We demonstrate that habitable Earth-mass planets and moons can exist in the Kepler-16 system, known to host a Saturn-mass planet around a stellar binary, by investigating their orbital stability in the standard and extended habitable zone (HZ). We find that Earth-mass planets in satellite-like (S-type) orbits are possible within the standard HZ in direct vicinity of Kepler-16b, thus constituting habitable exomoons. However, Earth-mass planets cannot exist in planetary-like (P-type) orbits around the two stellar components within the standard HZ. Yet, P-type Earth-mass planets can exist superior to the Saturnian planet in the extended HZ pertaining to considerably enhanced back-warming inmore » the planetary atmosphere if facilitated. We briefly discuss the potential detectability of such habitable Earth-mass moons and planets positioned in satellite and planetary orbits, respectively. The range of inferior and superior P-type orbits in the HZ is between 0.657-0.71 AU and 0.95-1.02 AU, respectively.« less

Far Side of the Moon

NASA Image and Video Library

1996-02-08

This image of the moon was obtained by the Galileo Solid State imaging system on Dec. 8 at 7 p.m. PST as NASA Galileo spacecraft passed the Earth and was able to view the lunar surface from a vantage point not possible from the Earth. http://photojournal.jpl.nasa.gov/catalog/PIA00225

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.

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.

Formation of the Lunar Fossil Bulges and Its Implication for the Early Earth and Moon

NASA Astrophysics Data System (ADS)

Qin, Chuan; Zhong, Shijie; Phillips, Roger

2018-02-01

First recognized by Laplace over two centuries ago, the Moon's present tidal-rotational bulges are significantly larger than hydrostatic predictions. They are likely relics of a former hydrostatic state when the Moon was closer to the Earth and had larger bulges, and they were established when stresses in a thickening lunar lithosphere could maintain the bulges against hydrostatic adjustment. We formulate the first dynamically self-consistent model of this process and show that bulge formation is controlled by the relative timing of lithosphere thickening and lunar orbit recession. Viable solutions indicate that lunar bulge formation was a geologically slow process lasting several hundred million years, that the process was complete about 4 Ga when the Moon-Earth distance was less than 32 Earth radii, and that the Earth in Hadean was significantly less dissipative to lunar tides than during the last 4 Gyr, possibly implying a frozen hydrosphere due to the fainter young Sun.

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.

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.

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.

The iodine-plutonium-xenon age of the Moon-Earth system revisited.

PubMed

Avice, G; Marty, B

2014-09-13

Iodine-plutonium-xenon isotope systematics have been used to re-evaluate time constraints on the early evolution of the Earth-atmosphere system and, by inference, on the Moon-forming event. Two extinct radionuclides ((129)I, T1/2=15.6 Ma and (244)Pu, T1/2=80 Ma) have produced radiogenic (129)Xe and fissiogenic (131-136)Xe, respectively, within the Earth, the related isotope fingerprints of which are seen in the compositions of mantle and atmospheric Xe. Recent studies of Archaean rocks suggest that xenon atoms have been lost from the Earth's atmosphere and isotopically fractionated during long periods of geological time, until at least the end of the Archaean eon. Here, we build a model that takes into account these results. Correction for Xe loss permits the computation of new closure ages for the Earth's atmosphere that are in agreement with those computed for mantle Xe. The corrected Xe formation interval for the Earth-atmosphere system is [Formula: see text] Ma after the beginning of Solar System formation. This time interval may represent a lower limit for the age of the Moon-forming impact. © 2014 The Author(s) Published by the Royal Society. All rights reserved.

Road map points US to beyond the Moon

NASA Astrophysics Data System (ADS)

Banks, Michael

2008-12-01

The new US administration under President Barack Obama should focus on sending humans to Mars and plan a manned voyage to a near-Earth asteroid. That is the conclusion of a road map published last month by the Planetary Society - a US non-governmental, non-profit organization. The report also says that any future manned missions to the Moon, including a potential lunar base, should instead be funded and performed internationally.

Biogenic oxygen from Earth transported to the Moon by a wind of magnetospheric ions

NASA Astrophysics Data System (ADS)

Terada, Kentaro; Yokota, Shoichiro; Saito, Yoshifumi; Kitamura, Naritoshi; Asamura, Kazushi; Nishino, Masaki N.

2017-01-01

For five days of each lunar orbit, the Moon is shielded from solar wind bombardment by the Earth's magnetosphere, which is filled with terrestrial ions. Although the possibility of the presence of terrestrial nitrogen and noble gases in lunar soil has been discussed based on their isotopic composition 1 , complicated oxygen isotope fractionation in lunar metal 2,3 (particularly the provenance of a 16O-poor component) re­mains an enigma 4,5 . Here, we report observations from the Japanese spacecraft Kaguya of significant numbers of 1-10 keV O+ ions, seen only when the Moon was in the Earth's plasma sheet. Considering the penetration depth into metal of O+ ions with such energy, and the 16O-poor mass-independent fractionation of the Earth's upper atmosphere 6 , we conclude that biogenic terrestrial oxygen has been transported to the Moon by the Earth wind (at least 2.6 × 104 ions cm-2 s-1) and implanted into the surface of the lunar regolith, at around tens of nanometres in depth 3,4 . We suggest the possibility that the Earth's atmosphere of billions of years ago may be preserved on the present-day lunar surface.

Corrections of the finite relativistic contributions to the synodic month period Earth-Moon range oscillations: Agreement between the geocentric and the solar-system barycentric inertial-frame calculations

NASA Astrophysics Data System (ADS)

Nordtvedt, Ken

1993-04-01

We have corrected our calculation of the finite general relativistic contribution to the synodic month period Earth-Moon range oscillation by including previously overlooked terms in the Moon's post-Newtonian equation of motion: the corrected result x(t)~=(3gSr2/c2) cos(ω-Ω)t agrees with the Shahid-Saless calculation which was performed in the geocentric frame. It is also pointed out that at the level of a few millimeters synodic month period amplitude, the Moon's orbit is polarized by the solar radiation pressure force on the Moon.

Surprise! The oft-ignored Moon might actually be important for changing the spins of asteroids during Earth flybys

NASA Astrophysics Data System (ADS)

Tuttle Keane, James; Siu, Hosea C.; Moskovitz, Nicholas A.; Binzel, Richard P.

2015-11-01

Analysis near-Earth asteroid archival data has revealed that asteroids with Earth MOIDs (minimum orbit intersection distance; a proxy for flyby distance) smaller than 1.0-1.5 lunar distances have a systematically larger dispersion in spin rate than more distant flybys (Siu, et al. 2015, DPS). While tidal torques during close encounters are expected to alter the spin states of asteroids (e.g. Scheeres et al. 2000, Icarus), there is no intrinsic reason to expect the observed sharp transition in spin rate distribution at 1.0-1.5 lunar distances, as tidal forces drop off smoothly with distance.While the Moon itself is too diminutive to directly alter the spin-states of asteroids, we show that its presence is enough to significantly affect asteroid encounter trajectories. Asteroids entering the Earth-Moon system are subject to three-body dynamics (due to the combined gravitational effects of the Earth and Moon). Depending on the flyby geometry, the Moon can act as a temporary sink for the asteroid's geocentric orbital energy. This allows some fraction of asteroids to have closer approaches with the Earth than expected when considering the Earth-Moon barycenter alone. In rare cases (~0.1%) this process enables the capture of temporary moons around the Earth (Granvik et al. 2012, Icarus). Asteroids that undergo these "enhanced" flybys can have both closer-than-expected encounter distances (resulting in more significant tidal perturbations), and repeated encounters with the Earth and Moon before leaving the system (resulting in the accumulation of multiple tidal interactions). By numerically solving the circular restricted three-body problem, we show that this process naturally produces a sharp transition in the asteroid population: asteroids with MOIDs less than 1.5 lunar distances can undergo these enhanced close approaches, possibly explaining the sharp transition in the dispersion of asteroid spin rates at this distance. Future work will investigate the efficiency of

The Earth and Moon As Seen by 2001 Mars Odyssey's Thermal Emission Imaging System

NASA Technical Reports Server (NTRS)

2001-01-01

2001 Mars Odyssey's Thermal Emission Imaging System (THEMIS) took this portrait of the Earth and its companion Moon, using the infrared camera, one of two cameras in the instrument. It was taken at a distance of 3,563,735 kilometers (more than 2 million miles) on April 19, 2001 as the 2001 Mars Odyssey spacecraft left the Earth. From this distance and perspective the camera was able to acquire an image that directly shows the true distance from the Earth to the Moon. The Earth's diameter is about 12,750 km, and the distance from the Earth to the Moon is about 385,000 km, corresponding to 30 Earth diameters. The dark region seen on Earth in the infrared temperature image is the cold south pole, with a temperature of minus 50 degrees Celsius (minus 58 degrees Fahrenheit). The small bright region above it is warm Australia. This image was acquired using the 9.1 um infrared filter, one of nine filters that the instrument will use to map the mineral composition and temperature of the martian surface. From this great distance, each picture element (pixel) in the image corresponds to a region 900 by 900 kilometers or greater in size or about size of the state of Texas. Once Odyssey reaches Mars orbit each infrared pixel will cover a region only 100 by 100 meters on the surface, about the size of a major league baseball field.

The Formation of the Earth-Moon System and the Planets

NASA Technical Reports Server (NTRS)

Lissauer, Jack J.; Young, Richard E. (Technical Monitor)

1998-01-01

An overview of current theories of star and planet formation, with emphasis on terrestrial planet accretion and the formation of the Earth-Moon system is presented. These models are based upon observations of the Solar System and of young stars and their environments. They predict that rocky planets should form around most single stars, although it is possible that in some cases such planets are lost to orbital decay within the protoplanetary disk. The frequency of formation of gas giant planets is more difficult to predict theoretically. Terrestrial planets are believed to grow via pairwise accretion until the spacing of planetary orbits becomes large enough that the configuration is stable for the age of the system. Giant impacts during the final stages of growth can produce large planetary satellites, such as Earth's Moon. Giant planets begin their growth like terrestrial planets, but they become massive enough that they are able to accumulate substantial amounts of gas before the protoplanetary disk dissipates.

Formation of the Lunar Fossil Bulges and its Implication for the Early Earth and Moon

NASA Astrophysics Data System (ADS)

Qin, C.; Zhong, S.; Phillips, R. J.

2017-12-01

First recognized by Laplace more than two centuries ago, the lunar gravitational and shape anomalies associated with rotational and tidal bulges are significantly larger than predicted from the hydrostatic theory. The harmonic degree-2 gravitational coefficients of the Moon, C20 and C22 (measuring the size of the rotational and tidal bulges), are 17 and 14 times of their hydrostatic counterparts, respectively, after removal of the effect from large impact basins. The bulges are commonly considered as remnant hydrostatic features, "frozen-in" when the Moon was closer to the Earth, experiencing larger tidal-rotational forces. The extant hypothesis is that as the Moon cooled and migrated outwards, a strong outer layer (lithosphere) thickened and reached a stress state that supported the bulges, which no longer tracked the hydrostatic ellipticity. However, this process is poorly understood and an appropriate dynamical model has not been engaged. Here we present the first dynamically self-consistent model of lunar bulge formation that couples a lunar interior thermal evolution model to the tidal-rotational forcing of the Moon. The forcing magnitude decreases with time as the Moon despins on the receding orbit, while the recession rate is controlled by the Earth's tidal dissipation factor Q. Assuming a viscoelastic rheology, the cooling of the Moon is described by a model with high viscosity lithosphere thickening with time. While conventional methods are not suitable for models with time-dependent viscoelastic structure, a semi-analytical method has been developed to address this problem. We show that the bulge formation is controlled by the relative timing of lithosphere thickening and lunar orbit recession. Based on our calculations, we conclude that the development of the fossil bulges may have taken as long as 400 million years after the formation of lunar lithosphere and was complete when the lunar orbit semi-major axis, a, was 32 Earth's radius, RE. We find a

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.

Moon (Form-Origin)

NASA Astrophysics Data System (ADS)

Tsiapas, Elias

2016-04-01

When the Earth was formed, it was in a state of burning heat. As time went by, temperature on the planet's surface was falling due to radiation and heat transfer, and various components (crusts) began taking solid form at the Earth's poles. The formation of crusts took place at the Earth's poles, because the stirring of burning and fluid masses on the surface of the Earth was significantly slighter there than it was on the equator. Due to centrifugal force and Coriolis Effect, these solid masses headed towards the equator; those originating from the North Pole followed a south-western course, while those originating from the South Pole followed a north-western course and there they rotated from west to east at a lower speed than the underlying burning and liquid earth, because of their lower initial linear velocity, their solid state and inertia. Because inertia is proportional to mass, the initially larger solid body swept all new solid ones, incorporating them to its western side. The density of the new solid masses was higher, because the components on the surface would freeze and solidify first, before the underlying thicker components. As a result, the western side of the initial islet of solid rocks submerged, while the east side elevated. . As a result of the above, this initial islet began to spin in reverse, and after taking on the shape of a sphere, it formed the "heart" of the Moon. The Moon-sphere, rolling on the equator, would sink the solid rocks that continued to descend from the Earth's poles. The sinking rocks partially melted because of higher temperatures in the greater depths that the Moon descended to, while part of the rocks' mass bonded with the Moon and also served as a heat-insulating material, preventing the descended side of the sphere from melting. Combined with the Earth's liquid mass that covered its emerging eastern surface, new sphere-shaped shells were created, with increased density and very powerful structural cohesion. During the

Moon (Form-Origin)

NASA Astrophysics Data System (ADS)

Tsiapas, Elias; Soumelidou, Despina; Tsiapas, Christos

2017-04-01

When the Earth was formed, it was in a state of burning heat. As time went by, temperature on the planet's surface was falling due to radiation and heat transfer, and various components (crusts) began taking solid form at the Earth's poles. The formation of crusts took place at the Earth's poles, because the stirring of burning and fluid masses on the surface of the Earth was significantly slighter there than it was on the equator. Due to centrifugal force and Coriolis Effect, these solid masses headed towards the equator; those originating from the North Pole followed a south-western course, while those originating from the South Pole followed a north-western course and there they rotated from west to east at a lower speed than the underlying burning and liquid earth, because of their lower initial linear velocity, their solid state and inertia. Because inertia is proportional to mass, the initially larger solid body swept all new solid ones, incorporating them to its western side. The density of the new solid masses was higher, because the components on the surface would freeze and solidify first, before the underlying thicker components. As a result, the western side of the initial islet of solid rocks submerged, while the east side elevated. . As a result of the above, this initial islet began to spin in reverse, and after taking on the shape of a sphere, it formed the "heart" of the Moon. The Moon-sphere, rolling on the equator, would sink the solid rocks that continued to descend from the Earth's poles. The sinking rocks partially melted because of higher temperatures in the greater depths that the Moon descended to, while part of the rocks' mass bonded with the Moon and also served as a heat-insulating material, preventing the descended side of the sphere from melting. Combined with the Earth's liquid mass that covered its emerging eastern surface, new sphere-shaped shells were created, with increased density and very powerful structural cohesion. During the

Moon (Form-Origin)

NASA Astrophysics Data System (ADS)

Tsiapas, Elias

2015-04-01

When the Earth was formed, it was in a state of burning heat. As time went by, temperature on the planet's surface was falling due to radiation and heat transfer, and various components (crusts) began taking solid form at the Earth's poles. The formation of crusts took place at the Earth's poles, because the stirring of burning and fluid masses on the surface of the Earth was significantly slighter there than it was on the equator. Due to centrifugal force and Coriolis Effect, these solid masses headed towards the equator; those originating from the North Pole followed a south-western course, while those originating from the South Pole followed a north-western course and there they rotated from west to east at a lower speed than the underlying burning and liquid earth, because of their lower initial linear velocity, their solid state and inertia. Because inertia is proportional to mass, the initially larger solid body swept all new solid ones, incorporating them to its western side. The density of the new solid masses was higher, because the components on the surface would freeze and solidify first, before the underlying thicker components. As a result, the western side of the initial islet of solid rocks submerged, while the east side elevated. . As a result of the above, this initial islet began to spin in reverse, and after taking on the shape of a sphere, it formed the "heart" of the Moon. The Moon-sphere, rolling on the equator, would sink the solid rocks that continued to descend from the Earth's poles. The sinking rocks partially melted because of higher temperatures in the greater depths that the Moon descended to, while part of the rocks' mass bonded with the Moon and also served as a heat-insulating material, preventing the descended side of the sphere from melting. Combined with the Earth's liquid mass that covered its emerging eastern surface, new sphere-shaped shells were created, with increased density and very powerful structural cohesion. During the

Moon (Form-Origin)

NASA Astrophysics Data System (ADS)

Tsiapas, Elias

2014-05-01

When the Earth was formed, it was in a state of burning heat. As time went by, temperature on the planet's surface was falling due to radiation and heat transfer, and various components (crusts) began taking solid form at the Earth's poles. The formation of crusts took place at the Earth's poles, because the stirring of burning and fluid masses on the surface of the Earth was significantly slighter there than it was on the equator. Due to centrifugal force and Coriolis Effect, these solid masses headed towards the equator; those originating from the North Pole followed a south-western course, while those originating from the South Pole followed a north-western course and there they rotated from west to east at a lower speed than the underlying burning and liquid earth, because of their lower initial linear velocity, their solid state and inertia. Because inertia is proportional to mass, the initially larger solid body swept all new solid ones, incorporating them to its western side. The density of the new solid masses was higher, because the components on the surface would freeze and solidify first, before the underlying thicker components. As a result, the western side of the initial islet of solid rocks submerged, while the east side elevated. . As a result of the above, this initial islet began to spin in reverse, and after taking on the shape of a sphere, it formed the "heart" of the Moon. The Moon-sphere, rolling on the equator, would sink the solid rocks that continued to descend from the Earth's poles. The sinking rocks partially melted because of higher temperatures in the greater depths that the Moon descended to, while part of the rocks' mass bonded with the Moon and also served as a heat-insulating material, preventing the descended side of the sphere from melting. Combined with the Earth's liquid mass that covered its emerging eastern surface, new sphere-shaped shells were created, with increased density and very powerful structural cohesion. During the

Google Moon Press Conference

NASA Image and Video Library

2009-07-19

Michael Weiss-Malik, Product Manager for Moon in Google Earth, Google, Inc., speaks during a press conference, Monday, July 20, 2009, announcing the launch of Moon in Google Earth, an immersive 3D atlas of the Moon, accessible within Google Earth 5.0, Monday, July 20, 2009, at the Newseum in Washington. Photo Credit: (NASA/Bill Ingalls)

Results of the Compensated Earth-Moon-Earth Retroreflector Laser Link (CEMERLL) Experiment

NASA Technical Reports Server (NTRS)

Wilson, K. E.; Leatherman, P. R.; Cleis, R.; Spinhirne, J.; Fugate, R. Q.

1997-01-01

Adaptive optics techniques can be used to realize a robust low bit-error-rate link by mitigating the atmosphere-induced signal fades in optical communications links between ground-based transmitters and deep-space probes. Phase I of the Compensated Earth-Moon-Earth Retroreflector Laser Link (CEMERLL) experiment demonstrated the first propagation of an atmosphere-compensated laser beam to the lunar retroreflectors. A 1.06-micron Nd:YAG laser beam was propagated through the full aperture of the 1.5-m telescope at the Starfire Optical Range (SOR), Kirtland Air Force Base, New Mexico, to the Apollo 15 retroreflector array at Hadley Rille. Laser guide-star adaptive optics were used to compensate turbulence-induced aberrations across the transmitter's 1.5-m aperture. A 3.5-m telescope, also located at the SOR, was used as a receiver for detecting the return signals. JPL-supplied Chebyshev polynomials of the retroreflector locations were used to develop tracking algorithms for the telescopes. At times we observed in excess of 100 photons returned from a single pulse when the outgoing beam from the 1.5-m telescope was corrected by the adaptive optics system. No returns were detected when the outgoing beam was uncompensated. The experiment was conducted from March through September 1994, during the first or last quarter of the Moon.

Converting the ISS to an Earth-Moon Transport System Using Nuclear Thermal Propulsion

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

Paniagua, John; Maise, George; Powell, James

2008-01-21

Using Nuclear Thermal Propulsion (NTP), the International Space Station (ISS) can be placed into a cyclic orbit between the Earth and the Moon for 2-way transport of personnel and supplies to a permanent Moon Base. The ISS cycler orbit apogees 470,000 km from Earth, with a period of 13.66 days. Once a month, the ISS would pass close to the Moon, enabling 2-way transport between it and the surface using a lunar shuttle craft. The lunar shuttle craft would land at a desired location on the surface during a flyby and return to the ISS during a later flyby. Atmore » Earth perigee 7 days later at 500 km altitude, there would be 2-way transport between it and Earth's surface using an Earth shuttle craft. The docking Earth shuttle would remain attached to the ISS as it traveled towards the Moon, while personnel and supplies transferred to a lunar shuttle spacecraft that would detach and land at the lunar base when the ISS swung around the Moon. The reverse process would be carried out to return personnel and materials from the Moon to the Earth. The orbital mechanics for the ISS cycle are described in detail. Based on the full-up mass of 400 metric tons for the ISS, an ISP of 900 seconds, and a delta V burn of 3.3 km/sec to establish the orbit, 200 metric tons of liquid H-2 propellant would be required. The 200 metric tons could be stored in 3 tanks, each 8 meters in diameter and 20 meters in length. An assembly of 3 MITEE NTP engines would be used, providing redundancy if an engine were to fail. Two different MITEE design options are described. Option 1 is an 18,000 Newton, 100 MW engine with a thrust to weight ratio of 6.6/1; Option 2 is a 180,000 Newton, 1000 MW engine with a thrust to weight ratio of 23/1. Burn times to establish the orbit are {approx}1 hour for the large 3 engine assembly, and 10 hours for the small 3 engine assembly. Both engines would use W-UO2 cermet fuel at {approx}2750 K which has demonstrated the capability to operate for at least 50 hours in

Children's Concepts of the Shape and Size of the Earth, Sun and Moon

NASA Astrophysics Data System (ADS)

Bryce, T. G. K.; Blown, E. J.

2013-02-01

Children's understandings of the shape and relative sizes of the Earth, Sun and Moon have been extensively researched and in a variety of ways. Much is known about the confusions which arise as young people try to grasp ideas about the world and our neighbouring celestial bodies. Despite this, there remain uncertainties about the conceptual models which young people use and how they theorise in the process of acquiring more scientific conceptions. In this article, the relevant published research is reviewed critically and in-depth in order to frame a series of investigations using semi-structured interviews carried out with 248 participants aged 3-18 years from China and New Zealand. Analysis of qualitative and quantitative data concerning the reasoning of these subjects (involving cognitive categorisations and their rank ordering) confirmed that (a) concepts of Earth shape and size are embedded in a 'super-concept' or 'Earth notion' embracing ideas of physical shape, 'ground' and 'sky', habitation of and identity with Earth; (b) conceptual development is similar in cultures where teachers hold a scientific world view and (c) children's concepts of shape and size of the Earth, Sun and Moon can be usefully explored within an ethnological approach using multi-media interviews combined with observational astronomy. For these young people, concepts of the shape and size of the Moon and Sun were closely correlated with their Earth notion concepts and there were few differences between the cultures despite their contrasts. Analysis of the statistical data used Kolmogorov-Smirnov Two-Sample Tests with hypotheses confirmed at K-S alpha level 0.05; rs : p < 0.01.

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.

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

Dynamics of Orbits near 3:1 Resonance in the Earth-Moon System

NASA Technical Reports Server (NTRS)

Dichmann, Donald J.; Lebois, Ryan; Carrico, John P., Jr.

2013-01-01

The Interstellar Boundary Explorer (IBEX) spacecraft is currently in a highly elliptical orbit around Earth with a period near 3:1 resonance with the Moon. Its orbit is oriented so that apogee does not approach the Moon. Simulations show this orbit to be remarkably stable over the next twenty years. This article examines the dynamics of such orbits in the Circular Restricted 3-Body Problem (CR3BP). We look at three types of periodic orbits, each exhibiting a type of symmetry of the CR3BP. For each of the orbit types, we assess the local stability using Floquet analysis. Although not all of the periodic solutions are stable in the mathematical sense, any divergence is so slow as to produce practical stability over several decades. We use Poincare maps with twenty-year propagations to assess the nonlinear stability of the orbits, where the perturbation magnitudes are related to the orbit uncertainty for the IBEX mission. Finally we show that these orbits belong to a family of orbits connected in a bifurcation diagram that exhibits exchange of stability. The analysis of these families of period orbits provides a valuable starting point for a mission orbit trade study.

Trajectory Optimization for Crewed Missions to an Earth-Moon L2 Halo Orbit

NASA Astrophysics Data System (ADS)

Dowling, Jennifer

Baseline trajectories to an Earth-Moon L2 halo orbit and round trip trajectories for crewed missions have been created in support of an advanced Orion mission concept. Various transfer durations and orbit insertion locations have been evaluated. The trajectories often include a deterministic mid-course maneuver that decreases the overall change in velocity in the trajectory. This paper presents the application of primer vector theory to study the existence, location, and magnitude of the mid-course maneuver in order to understand how to build an optimal round trip trajectory to an Earth-Moon L2 halo orbit. The lessons learned about when to add mid-course maneuvers can be applied to other mission designs.

The Earth and Moon As Seen by 2001 Mars Odyssey Thermal Emission Imaging System

NASA Image and Video Library

2001-05-01

NASA Mars Odyssey spacecraft took this portrait of the Earth and its companion Moon. It was taken at a distance of 3,563,735 kilometers more than 2 million miles on April 19, 2001 as the 2001 Mars Odyssey spacecraft left the Earth.

Searching for and characterising extrasolar Earth-like planets and moons

NASA Astrophysics Data System (ADS)

Schneider, Jean

2002-10-01

The physical bases of the detection and characterisation of extrasolar Earth-like planets and moons in the reflected light and thermal emission regimes are reviewed. They both have their advantages and disadvantages, including artefacts, in the determination of planet physical parameters (mass, size, albedo, surface and atmospheric conditions etc.). After a short panorama of detection methods and the first findings, new perspectives for these different aspects are also presented. Finally brief account of the ground based programmes and space-based projects and their potentialities for Earth-like planets is made and discussed.

The economics of mining the Martian moons

NASA Technical Reports Server (NTRS)

Leonard, Raymond S.; Blacic, James D.; Vaniman, David T.

1987-01-01

The costs for extracting and shipping volatiles such as water, carbon, and nitrogen that might be found on Phobos and Deimos are estimated. The costs are compared to the cost of shipping the same volatiles from earth, assuming the use of nuclear powered mining facilities and freighters. Mineral resources and possible products from the Martian moons, possible markets for these products, and the costs of transporting these resources to LEO or GEO or to transportation nodal points are examined. Most of the technology needed to mine the moons has already been developed. The need for extraterrestrial sources of propellants for ion propulsion systems and ways in which the mining of the moons would reduce the cost of space operations near earth are discussed. It is concluded that it would be commercially viable to mine the Martian moons, making a profit of at least a 10 percent return on capital.

EARTH, MOON, SUN, AND CV ACCRETION DISKS

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

Montgomery, M. M.

2009-11-01

Net tidal torque by the secondary on a misaligned accretion disk, like the net tidal torque by the Moon and the Sun on the equatorial bulge of the spinning and tilted Earth, is suggested by others to be a source to retrograde precession in non-magnetic, accreting cataclysmic variable (CV) dwarf novae (DN) systems that show negative superhumps in their light curves. We investigate this idea in this work. We generate a generic theoretical expression for retrograde precession in spinning disks that are misaligned with the orbital plane. Our generic theoretical expression matches that which describes the retrograde precession of Earths'more » equinoxes. By making appropriate assumptions, we reduce our generic theoretical expression to those generated by others, or to those used by others, to describe retrograde precession in protostellar, protoplanetary, X-ray binary, non-magnetic CV DN, quasar, and black hole systems. We find that spinning, tilted CV DN systems cannot be described by a precessing ring or by a precessing rigid disk. We find that differential rotation and effects on the disk by the accretion stream must be addressed. Our analysis indicates that the best description of a retrogradely precessing spinning, tilted, CV DN accretion disk is a differentially rotating, tilted disk with an attached rotating, tilted ring located near the innermost disk annuli. In agreement with the observations and numerical simulations by others, we find that our numerically simulated CV DN accretion disks retrogradely precess as a unit. Our final, reduced expression for retrograde precession agrees well with our numerical simulation results and with selective observational systems that seem to have main-sequence secondaries. Our results suggest that a major source to retrograde precession is tidal torques like that by the Moon and the Sun on the Earth. In addition, these tidal torques should be common to a variety of systems where one member is spinning and tilted, regardless

Human Exploration on the Moon, Mars and NEOs: PEX.2/ICEUM12B

NASA Astrophysics Data System (ADS)

Foing, Bernard H.

2016-07-01

The session COSPAR-16-PEX.2: "Human Exploration on the Moon, Mars and NEOs", co-sponsored by Commissions B, F will include solicited and contributed talks and poster/interactive presentations. It will also be part of the 12th International Conference on Exploration and Utilisation of the Moon ICEUM12B from the ILEWG ICEUM series started in 1994. It will address various themes and COSPAR communities: - Sciences (of, on, from) the Moon enabled by humans - Research from cislunar and libration points - From robotic villages to international lunar bases - Research from Mars & NEOs outposts - Humans to Phobos/Deimos, Mars and NEOS - Challenges and preparatory technologies, field research operations - Human and robotic partnerships and precursor missions - Resource utilisation, life support and sustainable exploration - Stakeholders for human exploration One half-day session will be dedicated to a workshop format and meetings/reports of task groups: Science, Technology, Agencies, Robotic village, Human bases, Society & Commerce, Outreach, Young Explorers. COSPAR has provided through Commissions, Panels and Working Groups (such as ILEWG, IMEWG) an international forum for supporting and promoting the robotic and human exploration of the Moon, Mars and NEOS. Proposed sponsors : ILEWG, ISECG, IKI, ESA, NASA, DLR, CNES, ASI, UKSA, JAXA, ISRO, SRON, CNSA, SSERVI, IAF, IAA, Lockheed Martin, Google Lunar X prize, UNOOSA

Student Moon Observations and Spatial-Scientific Reasoning

NASA Astrophysics Data System (ADS)

Cole, Merryn; Wilhelm, Jennifer; Yang, Hongwei

2015-07-01

Relationships between sixth grade students' moon journaling and students' spatial-scientific reasoning after implementation of an Earth/Space unit were examined. Teachers used the project-based Realistic Explorations in Astronomical Learning curriculum. We used a regression model to analyze the relationship between the students' Lunar Phases Concept Inventory (LPCI) post-test score variables and several predictors, including moon journal score, number of moon journal entries, student gender, teacher experience, and pre-test score. The model shows that students who performed better on moon journals, both in terms of overall score and number of entries, tended to score higher on the LPCI. For every 1 point increase in the overall moon journal score, participants scored 0.18 points (out of 20) or nearly 1% point higher on the LPCI post-test when holding constant the effects of the other two predictors. Similarly, students who increased their scores by 1 point in the overall moon journal score scored approximately 1% higher in the Periodic Patterns (PP) and Geometric Spatial Visualization (GSV) domains of the LPCI. Also, student gender and teacher experience were shown to be significant predictors of post-GSV scores on the LPCI in addition to the pre-test scores, overall moon journal score, and number of entries that were also significant predictors on the LPCI overall score and the PP domain. This study is unique in the purposeful link created between student moon observations and spatial skills. The use of moon journals distinguishes this study further by fostering scientific observation along with skills from across science, technology, engineering, and mathematics disciplines.

Measuring the Orbital Period of the Moon Using a Digital Camera

ERIC Educational Resources Information Center

Hughes, Stephen W.

2006-01-01

A method of measuring the orbital velocity of the Moon around the Earth using a digital camera is described. Separate images of the Moon and stars taken 24 hours apart were loaded into Microsoft PowerPoint and the centre of the Moon marked on each image. Four stars common to both images were connected together to form a "home-made" constellation.…

Smart-1 Moon Impact Operations

NASA Technical Reports Server (NTRS)

Ayala, Andres; Rigger, Ralf

2007-01-01

This paper describes the operations to control the Moon impact of the 3-axis stabilized spacecraft SMART-1 in September 2006. SMART-1 was launched on 27/09/2003. It was the first ESA mission to use an Electric Propulsion (EP) engine as the main motor to spiral out of the Earth gravity field and reach a scientific moon orbit [1]. During September 2005 the last EP maneuvers were performed using the remaining Xenon, in order to compensate for the 3rd body perturbations of the Sun and Earth. These operations extended the mission for an additional year. Afterwards the EP performance became unpredictable and low, so that no meaningful operation for the moon impact could be done. To move the predicted impact point on the 16/8/2006 into visibility from Earth an alternative Delta-V strategy was designed. Due to their alignment, the attitude thrusters could not be used directly to generate the Delta-V, so this strategy was based on controlled angular momentum biasing. Firing along the velocity vector around apolune, the remaining Hydrazine left from the attitude control budget was used, to shift the impact to the required coordinates.

Gallium isotopic evidence for extensive volatile loss from the Moon during its formation

PubMed Central

Kato, Chizu; Moynier, Frédéric

2017-01-01

The distribution and isotopic composition of volatile elements in planetary materials holds a key to the characterization of the early solar system and the Moon’s formation. The Moon and Earth are chemically and isotopically very similar. However, the Moon is highly depleted in volatile elements and the origin of this depletion is still debated. We present gallium isotopic and elemental measurements in a large set of lunar samples to constrain the origin of this volatile depletion. We show that while Ga has a geochemical behavior different from zinc, both elements show a systematic enrichment in the heavier isotopes in lunar mare basalts and Mg-suite rocks compared to the silicate Earth, pointing to a global-scale depletion event. On the other hand, the ferroan anorthosites are isotopically heterogeneous, suggesting a secondary distribution of Ga at the surface of the Moon by volatilization and condensation. The isotopic difference of Ga between Earth and the Moon and the isotopic heterogeneity of the crustal ferroan anorthosites suggest that the volatile depletion occurred following the giant impact and during the lunar magma ocean phase. These results point toward a Moon that has lost its volatile elements during a whole-scale evaporation event and that is now relatively dry compared to Earth. PMID:28782027

Sources of Extraterrestrial Rare Earth Elements:To the Moon and Beyond

NASA Astrophysics Data System (ADS)

McLeod, C. L.; Krekeler, M. P. S.

2017-08-01

The resource budget of Earth is limited. Rare-earth elements (REEs) are used across the world by society on a daily basis yet several of these elements have <2500 years of reserves left, based on current demand, mining operations, and technologies. With an increasing population, exploration of potential extraterrestrial REE resources is inevitable, with the Earth's Moon being a logical first target. Following lunar differentiation at 4.50-4.45 Ga, a late-stage (after 99% solidification) residual liquid enriched in Potassium (K), Rare-earth elements (REE), and Phosphorus (P), (or "KREEP") formed. Today, the KREEP-rich region underlies the Oceanus Procellarum and Imbrium Basin region on the lunar near-side (the Procellarum KREEP Terrain, PKT) and has been tentatively estimated at preserving 2.2 × 10^8 km^3 of KREEP-rich lithologies. The majority of lunar samples (Apollo, Luna, or meteoritic samples) contain REE-bearing minerals as trace phases, e.g., apatite and/or merrillite, with merrillite potentially contributing up to 3% of the PKT. Other lunar REE-bearing lunar phases include monazite, yittrobetafite (up to 94,500 ppm yttrium), and tranquillityite (up to 4.6 wt % yttrium, up to 0.25 wt % neodymium), however, lunar sample REE abundances are low compared to terrestrial ores. At present, there is no geological, mineralogical, or chemical evidence to support REEs being present on the Moon in concentrations that would permit their classification as ores. However, the PKT region has not yet been mapped at high resolution, and certainly has the potential to yield higher REE concentrations at local scales (<10s of kms). Future lunar exploration and mapping efforts may therefore reveal new REE deposits. Beyond the Moon, Mars and other extraterrestrial materials are host to REEs in apatite, chevkinite-perrierite, merrillite, whitlockite, and xenotime. These phases are relatively minor components of the meteorites studied to date, constituting <0.6% of the total sample

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

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

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

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

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

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

Google Moon Press Conference

NASA Image and Video Library

2009-07-19

Andrew Chaikin, author of "A Man on the Moon" speaks during a press conference, Monday, July 20, 2009, announcing the launch of Moon in Google Earth, an immersive 3D atlas of the Moon, accessible within Google Earth 5.0, Monday, July 20, 2009, at the Newseum in Washington. Photo Credit: (NASA/Bill Ingalls)

Google Moon Press Conference

NASA Image and Video Library

2009-07-19

Buzz Aldrin, the second man to walk on the moon, speaks during a press conference, Monday, July 20, 2009, announcing the launch of Moon in Google Earth, an immersive 3D atlas of the Moon, accessible within Google Earth 5.0, Monday, July 20, 2009, at the Newseum in Washington. Photo Credit: (NASA/Bill Ingalls)

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.

First decadal lunar results from the Moon and Earth Radiation Budget Experiment.

PubMed

Matthews, Grant

2018-03-01

A need to gain more confidence in computer model predictions of coming climate change has resulted in greater analysis of the quality of orbital Earth radiation budget (ERB) measurements being used today to constrain, validate, and hence improve such simulations. These studies conclude from time series analysis that for around a quarter of a century, no existing satellite ERB climate data record is of a sufficient standard to partition changes to the Earth from those of un-tracked and changing artificial instrumentation effects. This led to the creation of the Moon and Earth Radiation Budget Experiment (MERBE), which instead takes existing decades old climate data to a higher calibration standard using thousands of scans of Earth's Moon. The Terra and Aqua satellite ERB climate records have been completely regenerated using signal-processing improvements, combined with a substantial increase in precision from more comprehensive in-flight spectral characterization techniques. This study now builds on previous Optical Society of America work by describing new Moon measurements derived using accurate analytical mapping of telescope spatial response. That then allows a factor of three reduction in measurement noise along with an order of magnitude increase in the number of retrieved independent lunar results. Given decadal length device longevity and the use of solar and thermal lunar radiance models to normalize the improved ERB results to the International System of Units traceable radiance scale of the "MERBE Watt," the same established environmental time series analysis techniques are applied to MERBE data. They evaluate it to perhaps be of sufficient quality to immediately begin narrowing the largest of climate prediction uncertainties. It also shows that if such Terra/Aqua ERB devices can operate into the 2020s, it could become possible to halve these same uncertainties decades sooner than would be possible with existing or even planned new observing systems.

Moon-Based INSAR Geolocation and Baseline Analysis

NASA Astrophysics Data System (ADS)

Liu, Guang; Ren, Yuanzhen; Ye, Hanlin; Guo, Huadong; Ding, Yixing; Ruan, Zhixing; Lv, Mingyang; Dou, Changyong; Chen, Zhaoning

2016-07-01

Earth observation platform is a host, the characteristics of the platform in some extent determines the ability for earth observation. Currently most developing platforms are satellite, in contrast carry out systematic observations with moon based Earth observation platform is still a new concept. The Moon is Earth's only natural satellite and is the only one which human has reached, it will give people different perspectives when observe the earth with sensors from the moon. Moon-based InSAR (SAR Interferometry), one of the important earth observation technology, has all-day, all-weather observation ability, but its uniqueness is still a need for analysis. This article will discuss key issues of geometric positioning and baseline parameters of moon-based InSAR. Based on the ephemeris data, the position, liberation and attitude of earth and moon will be obtained, and the position of the moon-base SAR sensor can be obtained by coordinate transformation from fixed seleno-centric coordinate systems to terrestrial coordinate systems, together with the Distance-Doppler equation, the positioning model will be analyzed; after establish of moon-based InSAR baseline equation, the different baseline error will be analyzed, the influence of the moon-based InSAR baseline to earth observation application will be obtained.

Google Moon Press Conference

NASA Image and Video Library

2009-07-19

Apollo 11 astronaut Buzz Aldrin, the second man to walk on the Moon, speaks during a press conference, Monday, July 20, 2009, announcing the launch of Moon in Google Earth, an immersive 3D atlas of the Moon, accessible within Google Earth 5.0, Monday, July 20, 2009, at the Newseum in Washington. Photo Credit: (NASA/Bill Ingalls)

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.

Observed tidal braking in the earth/moon/sun system

NASA Technical Reports Server (NTRS)

Christodoulidis, D. C.; Smith, D. E.; Williamson, R. G.; Klosko, S. M.

1987-01-01

The low degree and order terms in the spherical harmonic model of the tidal potential were observed through the perturbations which are induced on near-earth satellite orbital motions. Evaluations of tracking observations from 17 satellites and a GEM-T1 geopotential model were used in the tidal recovery which was made in the presence of over 600 long-wavelength coefficients from 32 major and minor tides. Wahr's earth tidal model was used as a basis for the recovery of the ocean tidal terms. Using this tidal model, the secular change in the moon's mean motion due to tidal dissipation was found to be -25.27 + or - 0.61 arcsec/century squared. The estimation of lunar acceleration agreed with that observed from lunar laser ranging techniques (-24.9 + or - 1.0 arcsec/century squared), with the corresponding tidal braking of earth's rotation being -5.98 + or - 0.22 x 10 to the minus 22 rad/second squared. If the nontidal braking of the earth due to the observed secular change in the earth's second zonal harmonic is considered, satellite techniques yield a total value of the secular change of the earth's rotation rate of -4.69 + or - 0.36 x 10 to the minus 22 rad/second squared.

Observed tidal braking in the earth/moon/sun system

NASA Technical Reports Server (NTRS)

Christodoulidis, D. C.; Smith, D. E.; Williamson, R. G.; Klosko, S. M.

1988-01-01

The low degree and order terms in the spherical harmonic model of the tidal potential were observed through the perturbations which are induced on near-earth satellite orbital motions. Evaluations of tracking observations from 17 satellites and a GEM-T1 geopotential model were used in the tidal recovery which was made in the presence of over 600 long-wavelength coefficients from 32 major and minor tides. Wahr's earth tidal model was used as a basis for the recovery of the ocean tidal terms. Using this tidal model, the secular change in the moon's mean motion due to tidal dissipation was found to be -25.27 + or - 0.61 arcsec/century-squared. The estimation of lunar acceleration agreed with that observed from lunar laser ranging techniques (-24.9 + or - 1.0 arcsec/century-squared), with the corresponding tidal braking of earth's rotation being -5.98 + or - 0.22 X 10 to the -22 rad/second-squared. If the nontidal braking of the earth due to the observed secular change in the earth's second zonal harmonic is considered, satellite techniques yield a total value of the secular change in the earth's rotation rate of -4.69 + or - 0.36 X 10 to the -22 rad/second-squared.

First simultaneous detection of terrestrial ionospheric molecular ions in the Earth's inner magnetosphere and at the Moon

NASA Astrophysics Data System (ADS)

Dandouras, I.; Poppe, A. R.; Fillingim, M. O.; Kistler, L. M.; Mouikis, C. G.; Rème, H.

2017-09-01

First coordinated observation of escaping heavy molecular ions in the Earth's inner magnetosphere and at the Moon. Quantifying the underlying escape mechanisms is important in order to understand the long-term (billion years scale) evolution of the atmospheric composition, and in particular the evolution of the N/O ratio, which is essential for habitability. Terrestrial heavy ions, transported to the Moon, suggest also that the Earth's atmosphere of billions of years ago may be preserved on the present-day lunar regolith.

Navigating the Return Trip from the Moon Using Earth-Based Ground Tracking and GPS

NASA Technical Reports Server (NTRS)

Berry, Kevin; Carpenter, Russell; Moreau, Michael C.; Lee, Taesul; Holt, Gregg N.

2009-01-01

NASA s Constellation Program is planning a human return to the Moon late in the next decade. From a navigation perspective, one of the most critical phases of a lunar mission is the series of burns performed to leave lunar orbit, insert onto a trans-Earth trajectory, and target a precise re-entry corridor in the Earth s atmosphere. A study was conducted to examine sensitivity of the navigation performance during this phase of the mission to the type and availability of tracking data from Earth-based ground stations, and the sensitivity to key error sources. This study also investigated whether GPS measurements could be used to augment Earth-based tracking data, and how far from the Earth GPS measurements would be useful. The ability to track and utilize weak GPS signals transmitted across the limb of the Earth is highly dependent on the configuration and sensitivity of the GPS receiver being used. For this study three GPS configurations were considered: a "standard" GPS receiver with zero dB antenna gain, a "weak signal" GPS receiver with zero dB antenna gain, and a "weak signal" GPS receiver with an Earth-pointing direction antenna (providing 10 dB additional gain). The analysis indicates that with proper selection and configuration of the GPS receiver on the Orion spacecraft, GPS can potentially improve navigation performance during the critical final phases of flight prior to Earth atmospheric entry interface, and may reduce reliance on two-way range tracking from Earth-based ground stations.

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.

Navigation Design and Analysis for the Orion Earth-Moon Mission

NASA Technical Reports Server (NTRS)

DSouza, Christopher; Zanetti, Renato

2014-01-01

This paper details the design of the cislunar optical navigation system being proposed for the Orion Earth-Moon (EM) missions. In particular, it presents the mathematics of the navigation filter. The unmodeled accelerations and their characterization are detailed. It also presents the analysis that has been performed to understand the performance of the proposed system, with particular attention paid to entry flight path angle constraints and the delta-V performance.

Super Moon Rises

NASA Image and Video Library

2011-03-19

The full moon is seen as it rises near the National Mall, Saturday, March 19, 2011, in Washington. The full moon tonight is called a "Super Moon" since it is at its closest to Earth. Photo Credit: (NASA/Paul E. Alers)

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

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)

Isotopic evolution of the protoplanetary disk and the building blocks of Earth and the Moon.

PubMed

Schiller, Martin; Bizzarro, Martin; Fernandes, Vera Assis

2018-03-21

Nucleosynthetic isotope variability among Solar System objects is often used to probe the genetic relationship between meteorite groups and the rocky planets (Mercury, Venus, Earth and Mars), which, in turn, may provide insights into the building blocks of the Earth-Moon system. Using this approach, it has been inferred that no primitive meteorite matches the terrestrial composition and the protoplanetary disk material from which Earth and the Moon accreted is therefore largely unconstrained. This conclusion, however, is based on the assumption that the observed nucleosynthetic variability of inner-Solar-System objects predominantly reflects spatial heterogeneity. Here we use the isotopic composition of the refractory element calcium to show that the nucleosynthetic variability in the inner Solar System primarily reflects a rapid change in the mass-independent calcium isotope composition of protoplanetary disk solids associated with early mass accretion to the proto-Sun. We measure the mass-independent 48 Ca/ 44 Ca ratios of samples originating from the parent bodies of ureilite and angrite meteorites, as well as from Vesta, Mars and Earth, and find that they are positively correlated with the masses of their parent asteroids and planets, which are a proxy of their accretion timescales. This correlation implies a secular evolution of the bulk calcium isotope composition of the protoplanetary disk in the terrestrial planet-forming region. Individual chondrules from ordinary chondrites formed within one million years of the collapse of the proto-Sun reveal the full range of inner-Solar-System mass-independent 48 Ca/ 44 Ca ratios, indicating a rapid change in the composition of the material of the protoplanetary disk. We infer that this secular evolution reflects admixing of pristine outer-Solar-System material into the thermally processed inner protoplanetary disk associated with the accretion of mass to the proto-Sun. The identical calcium isotope composition of

View of earth during return from moon taken from Apollo 8 spacecraft

NASA Image and Video Library

1968-12-24

AS8-15-2561 (21-27 Dec. 1968) --- View of Earth as photographed by the Apollo 8 astronauts on their return trip from the moon. Note that the terminator is straighter than on the outbound pictures. The terminator crosses Australia. India is visible. The sun reflection is within the Indian Ocean.

Diagrammatic Representational Constraints of Spatial Scale in Earth-Moon System Astronomy Instruction

ERIC Educational Resources Information Center

Taylor, Roger S.; Grundstrom, Erika D.

2011-01-01

Given that astronomy heavily relies on visual representations it is especially likely for individuals to assume that instructional materials, such as visual representations of the Earth-Moon system (EMS), would be relatively accurate. However, in our research, we found that images in middle-school textbooks and educational webpages were commonly…

The Tethered Moon

NASA Technical Reports Server (NTRS)

Zahnle, K.; Lupu, R.; Dobrovolskis, A.

2014-01-01

Cosmic collisions between terrestrial planets resemble somewhat the life cycle of the phoenix: worlds collide, are consumed in flame, and after the debris has cleared, shiny new worlds emerge aglow with possibilities. And glow they do, for they are molten. How brightly they glow, and for how long, is determined by their atmospheres and their moons. A reasonable initial condition on Earth after the Moon-forming impact is that it begins as a hot global magma ocean. We therefore begin our study with the mantle as a liquid ocean with a surface temperature on the order of 3000-4000 K at a time some 100-1000 years after the impact, by which point we can hope that early transients have settled down.

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.

Improved pointing information for SCIAMACHY from in-flight measurements of the viewing directions towards sun and moon

NASA Astrophysics Data System (ADS)

Bramstedt, Klaus; Stone, Thomas C.; Gottwald, Manfred; Noël, Stefan; Bovensmann, Heinrich; Burrows, John P.

2017-07-01

The SCanning Imaging Absorption spectroMeter for Atmospheric CHartographY (SCIAMACHY) on Envisat (2002-2012) performed nadir, limb, solar/lunar occultation and various monitoring measurements. The pointing information of the instrument is determined by the attitude information of the Envisat platform with its star trackers together with the encoder readouts of both the azimuth and the elevation scanner of SCIAMACHY. In this work, we present additional sources of attitude information from the SCIAMACHY measurements itself. The basic principle is the same as used by the star tracker: we measure the viewing direction towards celestial objects, i.e. sun and moon, to detect possible mispointings. In sun over limb port observations, we utilise the vertical scans over the solar disk. In horizontal direction, SCIAMACHY's sun follower device (SFD) is used to adjust the viewing direction. Moon over limb port measurements use for both the vertical and the horizontal direction the adjustment by the SFD. The viewing direction is steered towards the intensity centroid of the illuminated part of the lunar disk. We use reference images from the USGS Robotic Lunar Observatory (ROLO) to take into account the inhomogeneous surface and the variations by lunar libration and phase to parameterise the location of the intensity centroid from the observation geometry. Solar observations through SCIAMACHY's so-called sub-solar port (with a viewing direction closely to zenith) also use the SFD in the vertical direction. In the horizontal direction the geometry of the port defines the viewing direction. Using these three type of measurements, we fit improved mispointing parameters by minimising the pointing offsets in elevation and azimuth. The geolocation of all retrieved products will benefit from this; the tangent heights are especially improved. The altitudes assigned to SCIAMACHY's solar occultation measurements are changed in the range of -130 to -330 m, the lunar occultation

Celestial reference frames and the gauge freedom in the post-Newtonian mechanics of the Earth-Moon system

NASA Astrophysics Data System (ADS)

Kopeikin, Sergei; Xie, Yi

2010-11-01

We introduce the Jacobi coordinates adopted to the advanced theoretical analysis of the relativistic Celestial Mechanics of the Earth-Moon system. Theoretical derivation utilizes the relativistic resolutions on reference frames adopted by the International Astronomical Union (IAU) in 2000. The resolutions assume that the Solar System is isolated and space-time is asymptotically flat at infinity and the primary reference frame covers the entire space-time, has its origin at the Solar System barycenter (SSB) with spatial axes stretching up to infinity. The SSB frame is not rotating with respect to a set of distant quasars that are assumed to be at rest on the sky forming the International Celestial Reference Frame (ICRF). The second reference frame has its origin at the Earth-Moon barycenter (EMB). The EMB frame is locally inertial and is not rotating dynamically in the sense that equation of motion of a test particle moving with respect to the EMB frame, does not contain the Coriolis and centripetal forces. Two other local frames—geocentric and selenocentric—have their origins at the center of mass of Earth and Moon respectively and do not rotate dynamically. Each local frame is subject to the geodetic precession both with respect to other local frames and with respect to the ICRF because of their relative motion with respect to each other. Theoretical advantage of the dynamically non-rotating local frames is in a more simple mathematical description of the metric tensor and relative equations of motion of the Moon with respect to Earth. Each local frame can be converted to kinematically non-rotating one after alignment with the axes of ICRF by applying the matrix of the relativistic precession as recommended by the IAU resolutions. The set of one global and three local frames is introduced in order to decouple physical effects of gravity from the gauge-dependent effects in the equations of relative motion of the Moon with respect to Earth.

Moon As Seen By NIMS

NASA Image and Video Library

1996-02-08

These four images of the Moon are from data acquired by NASA Galileo spacecraft Near-Earth Mapping Spectrometer during Galileo December 1992 Earth/Moon flyby. http://photojournal.jpl.nasa.gov/catalog/PIA00231

View of Moon over Earth limb taken by the Expedition 37 crew.

NASA Image and Video Library

2013-10-19

ISS037-E-017169 (19 Oct. 2013) --- The European Space Agency's fourth Automated Transfer Vehicle (ATV-4), also known as the Albert Einstein, is seen in the foreground of an image featuring the home planet and its moon as photographed by one of Expedition 37 crew members aboard the Earth-orbiting International Space Station.

7th Class Students' Opinions on Sun, Earth and Moon System

ERIC Educational Resources Information Center

Aydin, Suleyman

2017-01-01

This study is conducted to detect the students' perceptions on Sun, Moon and Earth (SME) system and define the 7th grade students' attitudes on the subject. In the study, since it was aimed to detect and evaluate the students' perceptions on some basic astronomical concepts without changing the natural conditions, a descriptive approach was…

Interior of the Moon

NASA Technical Reports Server (NTRS)

Weber, Renee C.

2013-01-01

A variety of geophysical measurements made from Earth, from spacecraft in orbit around the Moon, and by astronauts on the lunar surface allow us to probe beyond the lunar surface to learn about its interior. Similarly to the Earth, the Moon is thought to consist of a distinct crust, mantle, and core. The crust is globally asymmetric in thickness, the mantle is largely homogeneous, and the core is probably layered, with evidence for molten material. This chapter will review a range of methods used to infer the Moon's internal structure, and briefly discuss the implications for the Moon's formation and evolution.

Dynamical reference frames in the planetary and earth-moon systems

NASA Technical Reports Server (NTRS)

Standish, E. M.; Williams, G.

1990-01-01

Estimates of the accuracies of the ephemerides are reviewed using data for planetary and lunar systems to determine the efficacy of the inherent dynamical reference frame. The varied observational data are listed and given with special attention given to ephemeris improvements. The importance of ranging data is discussed with respect to the inner four planets and the moon, and the discrepancy of 1 arcsec/century between mean motions determined by optical observations versus ranging data is addressed. The Viking mission data provide inertial mean motions for the earth and Mars of 0.003 arcsec/century which will deteriorate to 0.01 arcsec after about 10 years. Uncertainties for other planets and the moon are found to correspond to approximately the same level of degradation. In general the data measurements and error estimates are improving the ephemerides, although refitting the data cannot account for changes in mean motion.

NASA Armstrong Flight Research Center's communications facility with radar dish and the eclipsed moon overhead during Jan. 31 Super Blue Blood Moon.

NASA Image and Video Library

2018-01-31

California's NASA Armstrong Flight Research Center photographer Carla Thomas takes photos on January 31 of the rare opportunity to capture a supermoon, a blue moon and a lunar eclipse at the same time. A supermoon occurs when the Moon is closer to Earth in its orbit and appearing 14 percent brighter than usual. As the second full moon of the month, this moon is also commonly known as a blue moon, though it will not be blue in appearance. The super blue moon passed through Earth's shadow and took on a reddish tint, known as a blood moon. This total lunar eclipse occurs when the Sun, Earth, and a full moon form a near-perfect lineup in space. The Moon passes directly behind the Earth into its umbra (shadow).

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.

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.

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.

Radioactivity of the moon and planets

NASA Astrophysics Data System (ADS)

Surkov, Iu. A.

The major results of studies of the radioactivity of the moon and terrestrial planets are reviewed. Measurements of the cosmogenic and natural radioactivity of the moon and Mars were obtained from planetary orbiter measurements, and those of Venus by in situ measurements, in addition to measurements of lunar samples brought back to earth. For the case of the moon, the Western maria on the near side are found to be the most radioactive areas, with highlands on both sides of the moon exhibiting lower radioactivity than the maria and lunar radioactivity levels in general less than those of the earth, which is correlated with different chemical compositions of the two bodies. The potassium, uranium and thorium contents of the landing sites of Veneras 8, 9 and 10 are shown to differ from each other, but be similar to those of terrestrial basalts, which they also resemble in density. Gamma-radiation and X-ray fluorescence measurements of Mars indicate the content of natural radioelements to be similar to that of the eruptive rocks of the earth crust, with Martian rocks of volcanic formations similar to terrestrial and lunar basalts, and those of the ancient terra formations more closely resembling the anorthosite-norite-troctolite association of the lunar highlands. It is pointed out that natural radioelements contents of all the bodies examined indicate a single chemical differentiation process, while cosmogenic radiation contents can aid in determining cosmic ray intensities as well as the sequences of geological events.

Rubidium Isotope Composition of the Earth and the Moon: Evidence for the Origin of Volatile Loss During Planetary Accretion

NASA Astrophysics Data System (ADS)

Pringle, E. A.; Moynier, F.

2016-12-01

The Earth-Moon system has a variety of chemical and isotopic characteristics that provide clues to understanding the mechanism of lunar formation. One important observation is the depletion in moderately volatile elements in the Moon compared to the Earth. This volatile element depletion may be a signature of volatile loss during the Moon-forming Giant Impact. Stable isotopes are powerful tracers of such a process, since volatile loss via evaporation enriches the residue in heavy isotopes. However, early studies searching for the fingerprint of volatile loss failed to find any resolvable variations [1]. Recent work has now revealed heavy isotope enrichments in the Moon relative to the Earth for the moderately volatile elements Zn [2,3] and K [4]. The purely lithophile nature of Rb (in contrast to the chalcophile/lithophile nature of Zn) and the higher volatility of Rb compared to K make Rb an ideal element with which to study the origin of lunar volatile element depletion. We have developed a new method for the high-precision measurement of Rb isotope ratios by MC-ICP-MS. The Rb isotope compositions of terrestrial rocks define a narrow range, indicating that Rb isotope fractionation during igneous differentiation is limited (<30 ppm/amu). There is a clear signature of Rb loss during evaporation in volatile-depleted achondrites and lunar rocks. In particular, eucrites are significantly enriched in 87Rb (up to several per mil) relative to chondrites. Similarly, lunar basalts are enriched in 87Rb compared to terrestrial basalts, by 200 ppm for 87Rb/85Rb. These data are the first measurements of a resolvable difference in Rb isotope composition between the Earth and the Moon. The variations in Rb isotope composition between the Earth and the Moon are consistent with Rb isotope fractionation due to evaporation. References: [1] Humayun & Clayton GCA 1995. [2] Paniello et al. Nature 2012. [3] Kato et al. Nat. Comm. 2015. [4] Wang and Jacobsen Nature in press.

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.

The Moon as a 100% Isolation Barrier for Earth During Exobiological Examination of Solar System Sample Return Missions

NASA Astrophysics Data System (ADS)

DiGregorio, B. E.

2018-04-01

The only 100% guarantee of protecting Earth's biosphere from a hazardous back contamination event is to use the Moon as a sample return examination facility to qualify samples for eventual return to Earth.

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

Teaching Chemistry Using From the Earth to the Moon

NASA Astrophysics Data System (ADS)

Goll, James G.; Mundinger, Stacie L.

2003-03-01

The space program and media based on it have provided fascinating examples that can be used to expore chemical principles. The HBO series From the Earth to the Moon and a documentary Moonshot provide examples for teaching chemical principles from the Apollo missions. A docking problem between two spacecrafts occurred during the Apollo 14 mission. This situation can be used to discuss the conditions necessary for a chemical reaction. A catastrophic fire on Apollo 1 can be used to illustrate the influence of different conditions on the rate of a reaction. Lightning striking Apollo 12 during liftoff showed the consequence of adding ions to solution. The landing of Apollo 12, which touched down only 535 feet from Surveyor 3, can be used to teach accuracy and absolute and relative error. The astronauts of Apollo 15 discovered a sample of the primordial lunar crust, and during Apollo 17, astronauts discovered orange dust on the moon. These discoveries can be used to demonstrate the importance of trained observation skills and analytical thinking.

The Moon's Origin.

ERIC Educational Resources Information Center

Cadogan, Peter

1983-01-01

Presents findings and conclusions about the origin of the moon, favoring the capture hypothesis of lunar origin. Advantage of the hypothesis is that it allows the moon to have been formed elsewhere, specifically in a hotter part of the solar nebula, accounting for chemical differences between earth and moon. (JN)

Mars is the Earth's Only Nearby Early Life Analog, but the Moon is on the Path to Get There

NASA Astrophysics Data System (ADS)

Schmitt, H. H.

2017-02-01

Mars provides a geological integration of the early solar system impacts recorded by the Moon and the contemporaneous water-rich pre-biotic period on Earth. Consideration of human missions to Mars needs to include a return to the Moon to stay.

Worlds Without Moons

NASA Astrophysics Data System (ADS)

Kohler, Susanna

2017-04-01

Many of the exoplanets that weve discovered lie in compact systems with orbits very close to their host star. These systems are especially interesting in the case of cool stars where planets lie in the stars habitable zone as is the case, for instance, for the headline-making TRAPPIST-1 system.But other factors go into determining potential habitability of a planet beyond the rough location where water can remain liquid. One possible consideration: whether the planets have moons.Supporting HabitabilityLocations of equality between the Hill and Roche radius for five different potential moon densities. The phase space allows for planets of different semi-major axes and stellar host masses. Two example systems are shown, Kepler-80 and TRAPPIST-1, with dots representing the planets within them. [Kane 2017]Earths Moon is thought to have been a critical contributor to our planets habitability. The presence of a moon stabilizes its planets axial tilt, preventing wild swings in climate as the stars radiation shifts between the planets poles and equator. But what determines if a planet can have a moon?A planet can retain a moon in a stable orbit anywhere between an outer boundary of the Hill radius (beyond which the planets gravity is too weak to retain the moon) and an inner boundary of the Roche radius (inside which the moon would be torn apart by tidal forces). The locations of these boundaries depend on both the planets and moons properties, and they can be modified by additional perturbative forces from the host star and other planets in the system.In a new study, San Francisco State University scientist Stephen R. Kane modeled these boundaries for planets specifically in compact systems, to determine whether such planets can host moons to boost their likelihood of habitability.Allowed moon density as a function of semimajor axis for the TRAPPIST-1 system, for two different scenarios with different levels of perturbations. The vertical dotted lines show the locations

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

Google Moon Press Conference

NASA Image and Video Library

2009-07-19

NASA Deputy Administrator Lori Garver, speaks during a press conference, Monday, July 20, 2009, announcing the launch of Moon in Google Earth, an immersive 3D atlas of the Moon, accessible within Google Earth 5.0, Monday, July 20, 2009, at the Newseum in Washington. Photo Credit: (NASA/Bill Ingalls)

SMART-1 leaves Earth on a long journey to the Moon

NASA Astrophysics Data System (ADS)

2003-09-01

highly efficient and lightweight propulsion system that is ideal for long-duration deep space missions in and beyond our solar system. SMART-1’s propulsion system consists in a single ion engine fuelled by 82 kg of xenon gas and pure solar energy. This plasma thruster relies on the “Hall effect” to accelerate xenon ions to speed up to 16,000 m/s (or 57 600 km/hr). It is able to deliver 70 mN of thrust with a specific impulse (the ratio between thrust and propellant consumption) 5 to 10 times better than traditional chemical thrusters and for much longer durations (months or even years, compared to the few minutes’ operating times typical of traditional chemical engines). The ion engine is scheduled to go into action on 30 September. At first, it will fire almost continuously -stopping only when the spacecraft is in the Earth’s shadow - to accelerate the probe (at about 0.2 mm/s2) and raise the altitude of its perigee (the lowest point of its orbit) from 654 to 14 000 km. This manoeuvre will take about 80 days to complete and will place the spacecraft safely above the radiation belts that surround the Earth. Commissioning will be completed within 2 weeks, after which ESA’s control centre at ESOC will be in contact with the spacecraft for two 8-hour periods every week. Once at a safe distance from Earth, SMART-1 will fire its thruster for periods of several days to progressively raise its apogee (the maximum altitude of its orbit) to the orbit of the Moon. At 200 000 km from Earth, it will begin receiving significant tugs from the Moon as it passes by. It will then perform three gravity-assist manoeuvres while flying by the Moon in late December 2004, late January and February 2005. Eventually, SMART-1 will be “captured” and enter a near-polar elliptical lunar orbit in March 2005. SMART-1 will then use its thruster to reduce the altitude and eccentricity of this orbit. During this 18-month transfer phase, the solar-electric primary propulsion�

The formation of the moon

NASA Technical Reports Server (NTRS)

O'Keefe, J. A., III

1974-01-01

Supporting evidence for the fission hypothesis for the origin of the moon is offered. The maximum allowable amount of free iron now present in the moon would not suffice to extract the siderophiles from the lunar silicates with the observed efficiency. Hence extraction must have been done with a larger amount of iron, as in the mantle of the earth, of which the moon was once a part, according to the fission hypothesis. The fission hypothesis gives a good resolution of the tektite paradox. Tektites are chemically much like products of the mantle of the earth; but no physically possible way has been found to explain their production from the earth itself. Perhaps they are a product of late, deep-seated lunar volcanism. If so, the moon must have inside it some material with a strong resemblance to the earth's mantle.

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

Google Moon Press Conference

NASA Image and Video Library

2009-07-19

Brian McLendon, VP of Engineering, Google, Inc., speaks during a press conference, Monday, July 20, 2009, announcing the launch of Moon in Google Earth, an immersive 3D atlas of the Moon, accessible within Google Earth 5.0, Monday, July 20, 2009, at the Newseum in Washington. Photo Credit: (NASA/Bill Ingalls)

Isotopic evolution of the protoplanetary disk and the building blocks of Earth and the Moon

NASA Astrophysics Data System (ADS)

Schiller, Martin; Bizzarro, Martin; Fernandes, Vera Assis

2018-03-01

Nucleosynthetic isotope variability among Solar System objects is often used to probe the genetic relationship between meteorite groups and the rocky planets (Mercury, Venus, Earth and Mars), which, in turn, may provide insights into the building blocks of the Earth–Moon system. Using this approach, it has been inferred that no primitive meteorite matches the terrestrial composition and the protoplanetary disk material from which Earth and the Moon accreted is therefore largely unconstrained. This conclusion, however, is based on the assumption that the observed nucleosynthetic variability of inner-Solar-System objects predominantly reflects spatial heterogeneity. Here we use the isotopic composition of the refractory element calcium to show that the nucleosynthetic variability in the inner Solar System primarily reflects a rapid change in the mass-independent calcium isotope composition of protoplanetary disk solids associated with early mass accretion to the proto-Sun. We measure the mass-independent 48Ca/44Ca ratios of samples originating from the parent bodies of ureilite and angrite meteorites, as well as from Vesta, Mars and Earth, and find that they are positively correlated with the masses of their parent asteroids and planets, which are a proxy of their accretion timescales. This correlation implies a secular evolution of the bulk calcium isotope composition of the protoplanetary disk in the terrestrial planet-forming region. Individual chondrules from ordinary chondrites formed within one million years of the collapse of the proto-Sun reveal the full range of inner-Solar-System mass-independent 48Ca/44Ca ratios, indicating a rapid change in the composition of the material of the protoplanetary disk. We infer that this secular evolution reflects admixing of pristine outer-Solar-System material into the thermally processed inner protoplanetary disk associated with the accretion of mass to the proto-Sun. The identical calcium isotope composition of Earth

Dynamical Sequestration of the Moon-Forming Impactor in Co-Orbital Resonance with Earth

NASA Astrophysics Data System (ADS)

Kortenkamp, Stephen J.; Hartmann, William J.

2015-11-01

Recent concerns about the giant impact hypothesis for the origin of the moon, and an associated “isotope crisis” are assuaged if the impactor was a local object that formed near Earth and the impact occurred relatively late. We investigated a scenario that may meet these criteria, with the moon-forming impactor originating in 1:1 co-orbital resonance with Earth. Using N-body numerical simulations we explored the dynamical consequences of placing Mars-mass companions in various co-orbital configurations with a proto-Earth having 90% of its current mass. We modeled configurations that include the four terrestrial planets as well as configurations that also include the four giant planets. In both the 4- and 8-planet models we found that a single additional Mars-mass companion typically remains a stable co-orbital of Earth for the entire 250 million year (Myr) duration of our simulations (33 of 34 simulations). In an effort to destabilize such a system we carried out an additional 45 simulations that included a second Mars-mass co-orbital companion. Even with two Mars-mass companions sharing Earth’s orbit most of these models (28) also remained stable for the entire 250 Myr duration of the simulations. Of the 17 two-companion models that eventually became unstable 12 impacts were observed between Earth and an escaping co-orbital companion. The average delay we observed for an impact of a Mars-mass companion with Earth was 101 Myr, and the longest delay was 221 Myr. Several of the stable simulations involved unusual 3-planet co-orbital configurations that could exhibit interesting observational signatures in plantetary transit surveys.

Dust: A major environmental hazard on the earth's moon

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

Heiken, G.; Vaniman, D.; Lehnert, B.

1990-01-01

On the Earth's Moon, obvious hazards to humans and machines are created by extreme temperature fluctuations, low gravity, and the virtual absence of any atmosphere. The most important other environmental factor is ionizing radiation. Less obvious environmental hazards that must be considered before establishing a manned presence on the lunar surface are the hazards from micrometeoroid bombardment, the nuisance of electro-statically-charged lunar dust, and an alien visual environment without familiar clues. Before man can establish lunar bases and lunar mining operations, and continue the exploration of that planet, we must develop a means of mitigating these hazards. 4 refs.

Tungsten isotopes and the origin of the Moon

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

Kruijer, Thomas S.; Kleine, Thorsten

Here, the giant impact model of lunar origin predicts that the Moon mainly consists of impactor material. As a result, the Moon is expected to be isotopically distinct from the Earth, but it is not. To account for this unexpected isotopic similarity of the Earth and Moon, several solutions have been proposed, including (i) post-giant impact Earth–Moon equilibration, (ii) alternative models that make the Moon predominantly out of proto-Earth mantle, and (iii) formation of the Earth and Moon from an isotopically homogeneous disk reservoir. Here we use W isotope systematics of lunar samples to distinguish between these scenarios. We reportmore » high-precision 182W data for several low-Ti and high-Ti mare basalts, as well as for Mg-suite sample 77215, and lunar meteorite Kalahari 009, which complement data previously obtained for KREEP-rich samples. In addition, we utilize high-precision Hf isotope and Ta/W ratio measurements to empirically quantify the superimposed effects of secondary neutron capture on measured 182W compositions. Our results demonstrate that there are no resolvable radiogenic 182W variations within the Moon, implying that the Moon differentiated later than 70 Ma after Solar System formation. In addition, we find that samples derived from different lunar sources have indistinguishable 182W excesses, confirming that the Moon is characterized by a small, uniform ~+26 parts-per-million excess in 182W over the present-day bulk silicate Earth. This 182W excess is most likely caused by disproportional late accretion to the Earth and Moon, and after considering this effect, the pre-late veneer bulk silicate Earth and the Moon have indistinguishable 182W compositions. Mixing calculations demonstrate that this Earth–Moon 182W similarity is an unlikely outcome of the giant impact, which regardless of the amount of impactor material incorporated into the Moon should have generated a significant 182W excess in the Moon. Consequently, our results imply

Tungsten isotopes and the origin of the Moon

DOE PAGES

Kruijer, Thomas S.; Kleine, Thorsten

2017-08-04

Here, the giant impact model of lunar origin predicts that the Moon mainly consists of impactor material. As a result, the Moon is expected to be isotopically distinct from the Earth, but it is not. To account for this unexpected isotopic similarity of the Earth and Moon, several solutions have been proposed, including (i) post-giant impact Earth–Moon equilibration, (ii) alternative models that make the Moon predominantly out of proto-Earth mantle, and (iii) formation of the Earth and Moon from an isotopically homogeneous disk reservoir. Here we use W isotope systematics of lunar samples to distinguish between these scenarios. We reportmore » high-precision 182W data for several low-Ti and high-Ti mare basalts, as well as for Mg-suite sample 77215, and lunar meteorite Kalahari 009, which complement data previously obtained for KREEP-rich samples. In addition, we utilize high-precision Hf isotope and Ta/W ratio measurements to empirically quantify the superimposed effects of secondary neutron capture on measured 182W compositions. Our results demonstrate that there are no resolvable radiogenic 182W variations within the Moon, implying that the Moon differentiated later than 70 Ma after Solar System formation. In addition, we find that samples derived from different lunar sources have indistinguishable 182W excesses, confirming that the Moon is characterized by a small, uniform ~+26 parts-per-million excess in 182W over the present-day bulk silicate Earth. This 182W excess is most likely caused by disproportional late accretion to the Earth and Moon, and after considering this effect, the pre-late veneer bulk silicate Earth and the Moon have indistinguishable 182W compositions. Mixing calculations demonstrate that this Earth–Moon 182W similarity is an unlikely outcome of the giant impact, which regardless of the amount of impactor material incorporated into the Moon should have generated a significant 182W excess in the Moon. Consequently, our results imply

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

Google Moon Press Conference

NASA Image and Video Library

2009-07-19

Alan Eustace, Senior VP of Engineering and Research, Google, Inc., speaks during a press conference, Monday, July 20, 2009, announcing the launch of Moon in Google Earth, an immersive 3D atlas of the Moon, accessible within Google Earth 5.0, Monday, July 20, 2009, at the Newseum in Washington. Photo Credit: (NASA/Bill Ingalls)

Oxygen isotopic evidence for accretion of Earth's water before a high-energy Moon-forming giant impact.

PubMed

Greenwood, Richard C; Barrat, Jean-Alix; Miller, Martin F; Anand, Mahesh; Dauphas, Nicolas; Franchi, Ian A; Sillard, Patrick; Starkey, Natalie A

2018-03-01

The Earth-Moon system likely formed as a result of a collision between two large planetary objects. Debate about their relative masses, the impact energy involved, and the extent of isotopic homogenization continues. We present the results of a high-precision oxygen isotope study of an extensive suite of lunar and terrestrial samples. We demonstrate that lunar rocks and terrestrial basalts show a 3 to 4 ppm (parts per million), statistically resolvable, difference in Δ 17 O. Taking aubrite meteorites as a candidate impactor material, we show that the giant impact scenario involved nearly complete mixing between the target and impactor. Alternatively, the degree of similarity between the Δ 17 O values of the impactor and the proto-Earth must have been significantly closer than that between Earth and aubrites. If the Earth-Moon system evolved from an initially highly vaporized and isotopically homogenized state, as indicated by recent dynamical models, then the terrestrial basalt-lunar oxygen isotope difference detected by our study may be a reflection of post-giant impact additions to Earth. On the basis of this assumption, our data indicate that post-giant impact additions to Earth could have contributed between 5 and 30% of Earth's water, depending on global water estimates. Consequently, our data indicate that the bulk of Earth's water was accreted before the giant impact and not later, as often proposed.

Origin of the moon by capture

NASA Astrophysics Data System (ADS)

Singer, S. Fred

A coherent account is presented here based on the hypothesis that the moon formed separately in a heliocentric orbit similar to the earth's and was later captured by the earth. The adoption of this hypothesis, together with the observed depletion of iron in the moon, sets some important constraints on the condensation and agglomeration phenomena in the primeval solar nebula that led to the formation of planetesimals, and ultimately to planets. Capture of the moon also defines a severe heating event whereby the earth's kinetic energy of rotation is largely dissipated internally by the mechanism of tidal friction. From this melting event dates the geologic, atmospheric, and oceanic history of the earth. An attempt is made to account for the unique development of the earth, especially in relation to Mars and Venus, its neighboring planets. A capture origin of the moon that employs a 'push-pull' tidal theory does not strain the laws of physics, involves a minimum of ad hoc assumptions, and has a probability that is commensurate with the evidence of the existence of a unique moon.

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.

New approaches to the Moon's isotopic crisis.

PubMed

Melosh, H J

2014-09-13

Recent comparisons of the isotopic compositions of the Earth and the Moon show that, unlike nearly every other body known in the Solar System, our satellite's isotopic ratios are nearly identical to the Earth's for nearly every isotopic system. The Moon's chemical make-up, however, differs from the Earth's in its low volatile content and perhaps in the elevated abundance of oxidized iron. This surprising situation is not readily explained by current impact models of the Moon's origin and offers a major clue to the Moon's formation, if we only could understand it properly. Current ideas to explain this similarity range from assuming an impactor with the same isotopic composition as the Earth to postulating a pure ice impactor that completely vaporized upon impact. Several recent proposals follow from the suggestion that the Earth-Moon system may have lost a great deal of angular momentum during early resonant interactions. The isotopic constraint may be the most stringent test yet for theories of the Moon's origin. © 2014 The Author(s) Published by the Royal Society. All rights reserved.

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

Google Moon Press Conference

NASA Image and Video Library

2009-07-19

Miles O'Brien, former chief science and tech correspondent for CNN, speaks during a press conference, Monday, July 20, 2009, announcing the launch of Moon in Google Earth, an immersive 3D atlas of the Moon, accessible within Google Earth 5.0, Monday, July 20, 2009, at the Newseum in Washington. Photo Credit: (NASA/Bill Ingalls)

Google Moon Press Conference

NASA Image and Video Library

2009-07-19

Tiffany Montague, Technical Program Manager for NASA and Google Lunar X PRIZE, Google, Inc., speaks during a press conference, Monday, July 20, 2009, announcing the launch of Moon in Google Earth, an immersive 3D atlas of the Moon, accessible within Google Earth 5.0, Monday, July 20, 2009, at the Newseum in Washington. Photo Credit: (NASA/Bill Ingalls)

Google Moon Press Conference

NASA Image and Video Library

2009-07-19

Yoshinori Yoshimura, a respresentative from the Japan Aerospace Exploration Agency (JAXA), speaks during a press conference, Monday, July 20, 2009, announcing the launch of Moon in Google Earth, an immersive 3D atlas of the Moon, accessible within Google Earth 5.0, Monday, July 20, 2009, at the Newseum in Washington. Photo Credit: (NASA/Bill Ingalls)

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

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

An analysis of the moon's surface using reflected illumination from the earth during a waning crescent lunar phase

NASA Technical Reports Server (NTRS)

Hammond, Ernest C., Jr.; Linton-Petza, Maggie

1989-01-01

There have been many articles written concerning the lunar after-glow, the spectacular reflection from the moon's surface, and the possible observation of luminescence on the dark side of the moon. The researcher, using a 600 mm cassegrain telescope lense and Kodak 400 ASA T-Max film, photographed the crescent moon whose dark side was clearly visible by the reflected light from earth. The film was digitized to a Perkin-Elmer 1010M microdensitometer for enhancement and enlargement. The resulting pictures indicate a completely different land pattern formation than observed during a full moon. An attempt is made to analyze the observed structures and to compare them to the pictures observed during the normal full moon. There are boundaries on the digitized dark section of the moon that can be identified with structures seen during the normal full moon. But, these variations do change considerably under enhancement.

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.

Impact origin of the Moon

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

Slattery, W.L.

1998-12-31

A few years after the Apollo flights to the Moon, it became clear that all of the existing theories on the origin of the Moon would not satisfy the growing body of constraints which appeared with the data gathered by the Apollo flights. About the same time, researchers began to realize that the inner (terrestrial) planets were not born quietly -- all had evidences of impacts on their surfaces. This fact reinforced the idea that the planets had formed by the accumulation of planetesimals. Since the Earth`s moon is unique among the terrestrial planets, a few researchers realized that perhapsmore » the Moon originated in a singular event; an event that was quite probable, but not so probable that one would expect all the terrestrial planets to have a large moon. And thus was born the idea that a giant impact formed the Moon. Impacts would be common in the early solar system; perhaps a really large impact of two almost fully formed planets of disparate sizes would lead to material orbiting the proto-earth, a proto-moon. This idea remained to be tested. Using a relatively new, but robust, method of doing the hydrodynamics of the collision (Smoothed-Particle Hydrodynamics), the author and his colleagues (W. Benz, Univ. of Arizona, and A.G.W. Cameron, Harvard College Obs.) did a large number of collision simulations on a supercomputer. The author found two major scenarios which would result in the formation of the Moon. The first was direct formation; a moon-sized object is boosted into orbit by gravitational torques. The second is when the orbiting material forms a disk, which, with subsequent evolution can form the Moon. In either case the physical and chemical properties of the newly formed Moon would very neatly satisfy the physical and chemical constraints of the current Moon. Also, in both scenarios the surface of the Earth would be quite hot after the collision. This aspect remains to be explored.« less

New approaches to the Moon's isotopic crisis

PubMed Central

Melosh, H. J.

2014-01-01

Recent comparisons of the isotopic compositions of the Earth and the Moon show that, unlike nearly every other body known in the Solar System, our satellite's isotopic ratios are nearly identical to the Earth's for nearly every isotopic system. The Moon's chemical make-up, however, differs from the Earth's in its low volatile content and perhaps in the elevated abundance of oxidized iron. This surprising situation is not readily explained by current impact models of the Moon's origin and offers a major clue to the Moon's formation, if we only could understand it properly. Current ideas to explain this similarity range from assuming an impactor with the same isotopic composition as the Earth to postulating a pure ice impactor that completely vaporized upon impact. Several recent proposals follow from the suggestion that the Earth–Moon system may have lost a great deal of angular momentum during early resonant interactions. The isotopic constraint may be the most stringent test yet for theories of the Moon's origin. PMID:25114301

Modeling Hf-W Evolution for Earth, Moon and Mars in Grand Tack Accretion Simulations: The Isotopic Consequences of Rapid Accretion

NASA Astrophysics Data System (ADS)

Zube, N.; Nimmo, F.; Jacobson, S. A.; Fischer, R. A.

2017-12-01

Short-lived isotopes, such as the decay of lithophile 182Hf into siderophile 182W with a half-life of 9 My, can provide constraints on the timescales of planetary core formation and accretion. Classical accretion scenarios have produced Hf-W isotopic outcomes like those measured presently on the Earth [2,3]. We examine Grand Tack accretion simulations [4,5] and determine the mantle equilibration conditions necessary to produce the observed tungsten isotopic anomaly. Additionally, we follow Hf-W evolution for pairs of bodies that experience a last giant impact fitting the conditions of Earth's Moon-forming collision. In this way, we determine the likelihood of producing the observed almost indistinguishable W isotope anomalies of the Earth and Moon mantles [6]. We model Hf-W evolution for growing planets in 141 N-body simulations during late accretion in the Grand Tack scenario. For each case, we vary the equilibration factor during collisions—the fraction of impactor core that experiences re-equilibration with the entire target mantle—in steps ranging from none (cores merging) to complete equilibration. For Earth-like and Mars-like surviving planets, we find that cases with a high equilibration factor (k > 0.8) and an intermediate (2:1 - 4:1) ratio of initial embryo mass to planetesimal mass were most frequently able to approximate the observed W measurements for Earth and Mars. The equilibration factor required is more restrictive than the one found for classical accretion scenarios [2,3] and may not be consistent with fluid-dynamical predictions [7]. Moons made of impactor material from Earth's last giant impact are only able to result in an Earth-Moon pair having sufficiently similar W anomalies with a likelihood of 8% or less across all simulations. This indicates that a scenario where the Moon isotopically equilibrated with the Earth's mantle after the impact [8] may be required to explain the measured values. [1] Kleine et al. 2009 [2] Nimmo et al. 2010

Our Battered Moon

ERIC Educational Resources Information Center

Damonte, Kathleen

2004-01-01

Most people have probably heard the tale about the Moon being made out of Swiss cheese because, on Earth, the Moon looks like it is full of holes. Those holes are actually impact craters, circular depressions that formed when objects, such as rocks that orbit the Sun, smashed into the surface of the Moon. The activity described in this article,…

Moon - North Pole

NASA Image and Video Library

1996-01-29

This view of the north polar region of the Moon was obtained by NASA's Galileo camera during the spacecraft flyby of the Earth-Moon system on December 7 and 8, 1992. http://photojournal.jpl.nasa.gov/catalog/PIA00126

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.

Advanced propulsion for LEO-Moon transport. 3: Transportation model. M.S. Thesis - California Univ.

NASA Technical Reports Server (NTRS)

Henley, Mark W.

1992-01-01

A simplified computational model of low Earth orbit-Moon transportation system has been developed to provide insight into the benefits of new transportation technologies. A reference transportation infrastructure, based upon near-term technology developments, is used as a departure point for assessing other, more advanced alternatives. Comparison of the benefits of technology application, measured in terms of a mass payback ratio, suggests that several of the advanced technology alternatives could substantially improve the efficiency of low Earth orbit-Moon transportation.

Children's Concepts of the Shape and Size of the Earth, Sun and Moon

ERIC Educational Resources Information Center

Bryce, T. G. K.; Blown, E. J.

2013-01-01

Children's understandings of the shape and relative sizes of the Earth, Sun and Moon have been extensively researched and in a variety of ways. Much is known about the confusions which arise as young people try to grasp ideas about the world and our neighbouring celestial bodies. Despite this, there remain uncertainties about the conceptual models…

Lunar-based Earth observation geometrical characteristics research

NASA Astrophysics Data System (ADS)

Ren, Yuanzhen; Liu, Guang; Ye, Hanlin; Guo, Huadong; Ding, Yixing; Chen, Zhaoning

2016-07-01

As is known to all, there are various platforms for carrying sensors to observe Earth, such as automobiles, aircrafts and satellites. Nowadays, we focus on a new platform, Moon, because of its longevity, stability and vast space. These advantages make it to be the next potential platform for observing Earth, enabling us to get the consistent and global measurements. In order to get a better understanding of lunar-based Earth observation, we discuss its geometrical characteristics. At present, there are no sensors on the Moon for observing Earth and we are not able to obtain a series of real experiment data. As a result, theoretical modeling and numerical calculation are used in this paper. At first, we construct an approximate geometrical model of lunar-based Earth observation, which assumes that Earth and Moon are spheres. Next, we calculate the position of Sun, Earth and Moon based on the JPL ephemeris. With the help of positions data and geometrical model, it is possible for us to decide the location of terminator and substellar points. However, in order to determine their precise position in the conventional terrestrial coordinate system, reference frames transformations are introduced as well. Besides, taking advantages of the relative positions of Sun, Earth and Moon, we get the total coverage of lunar-based Earth optical observation. Furthermore, we calculate a more precise coverage, considering placing sensors on different positions of Moon, which is influenced by its attitude parameters. In addition, different ephemeris data are compared in our research and little difference is found.

Teaching Future Teachers Basic Astronomy Concepts--Sun-Earth-Moon Relative Movements--at a Time of Reform in Science Education

ERIC Educational Resources Information Center

Trumper, Ricardo

2006-01-01

In view of students' alternative conceptions about basic concepts in astronomy, we conducted a series of constructivist activities with future elementary and junior high school teachers aimed at changing their conceptions about the cause of seasonal changes, and of several characteristics of the Sun-Earth-Moon relative movements like Moon phases,…

The problem of iron partition between Earth and Moon during simultaneous formation as a double planet system

NASA Technical Reports Server (NTRS)

Cassidy, W. A.

1984-01-01

A planetary model is described which requires fractional vapor/liquid condensation, planet accumulation during condensation, a late start for accumulation of the Moon, and volatile accretion to the surfaces of each planet only near the end of the accumulation process. In the model, initial accumulation of small objects is helped if the agglomerating particles are somewhat sticky. Assuming that growth proceeds through this range, agglomeration continues. If the reservoir of vapor is being preferentially depleted in iron by fractional condensation, an iron-rich planetary core forms. As the temperature decreases, condensing material becomes progressively richer in silicates and poorer in iron, forming the silicate-rich mantle of an already differentiated Earth. A second center of agglomeration successfully forms near the growing Earth after most of the iron in the reservoir has been used up. The bulk composition of the Moon then is similar to the outer mantle of the accumulating Earth.

"Earth, Sun and Moon": Computer Assisted Instruction in Secondary School Science--Achievement and Attitudes

ERIC Educational Resources Information Center

Ercan, Orhan; Bilen, Kadir; Ural, Evrim

2016-01-01

This study investigated the impact of a web-based teaching method on students' academic achievement and attitudes in the elementary education fifth grade Science and Technology unit, "System of Earth, Sun and Moon". The study was a quasi-experimental study with experimental and control groups comprising 54 fifth grade students attending…

Anthropic selection for the Moon's mass.

PubMed

Waltham, Dave

2004-01-01

This paper investigates whether anthropic selection explains the unusually large size of our Moon. It is shown that obliquity stability of the Earth is possible across a wide range of different starting conditions for the Earth-Moon system. However, the lunar mass and angular momentum from the actual Earth-Moon system are remarkable in that they very nearly produce an unstable obliquity. This may be because the particular properties of our Earth-Moon system simultaneously allow a stable obliquity and a slow rotation rate. A slow rotation rate may have been anthropically selected because it minimizes the equator-pole temperature difference, thus minimizing climatic fluctuations. The great merit of this idea is that it can be tested using extrasolar planet search programs planned for the near future. If correct, such anthropic selection predicts that most extrasolar planetary systems will have significantly larger perturbation frequencies than our own Solar System.

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.

Planetary Defense From Space: Part 1-Keplerian Theory

NASA Astrophysics Data System (ADS)

Maccone, Claudio

A system of two space bases housing missiles is proposed to achieve the Planetary Defense of the Earth against dangerous asteroids and comets. We show that the layout of the Earth-Moon system with the five relevant Lagrangian (or libration) points in space leads naturally to only one, unmistakable location of these two space bases within the sphere of influence of the Earth. These locations are at the two Lagrangian points L1 (in between the Earth and the Moon) and L3 (in the direction opposite to the Moon from the Earth). We show that placing bases of missiles at L1 and L3 would cause those missiles to deflect the trajectory of asteroids by hitting them orthogonally to their impact trajectory toward the Earth, so as to maximize their deflection. We show that the confocal conics are the best class of trajectories fulfilling this orthogonal deflection requirement. An additional remark is that the theory developed in this paper is just a beginning of a larger set of future research work. In fact, while in this paper we only develop the Keplerian analytical theory of the Optimal Planetary Defense achievable from the Earth-Moon Lagrangian points L1 and L3, much more sophisticated analytical refinements would be needed to: Take into account many perturbation forces of all kinds acting on both the asteroids and missiles shot from L1 and L3; add more (non-optimal) trajectories of missiles shot from either the Lagrangian points L4 and L5 of the Earth-Moon system or from the surface of the Moon itself; encompass the full range of missiles currently available to the US (and possibly other countries) so as to really see "which asteroids could be diverted by which missiles", even in the very simplified scheme outlined here. Outlined for the first time in February 2002, our Confocal Planetary Defense concept is a Keplerian Theory that proved simple enough to catch the attention of scholars, representatives of the US Military and popular writers. These developments could

Illustration Comparing Apparent Sizes of Moons

NASA Image and Video Library

2013-08-15

This image from NASA Mars rover Curiosity provides a comparison for how big the moons of Mars appear to be, as seen from the surface of Mars, in relation to the size that Earth moon appears to be when seen from the surface of Earth.

ScienceCast 29: Did Earth Have Two Moons?

NASA Image and Video Library

2011-09-22

Did our planet once have two moons? Some researchers say so. Moreover, the missing satellite might still be up there--splattered across the far side of the Moon. NASA's GRAIL mission could help confirm or refute the "two moon" hypothesis.

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.

Comparing the Atmospheres of Mercury and the Earth's Moon

NASA Technical Reports Server (NTRS)

Morgan, Thomas H.; Killen, Rosemary M.; Hurley, Dana M.

2012-01-01

The exospheres of Mercury and the Earth's Moon are fundamentally similar, but the differences that do exist between them can help us to develop a better understanding of the processes at work on the two bodies that produce and remove volatiles. The major differences are derived from (1) the different compositions of the two surfaces, (2) the different particle and field em'ironments above the surface of each body (particularly the presence of intrinsic magnetic field of Mercury), and (3) the larger flux of interplanetary dust incident at the orbit of Mercury. The first difference, surface composition, is the most intractable problem, but the most challenging part of that problem, the composition of the Hermean regolith, may be at least partially addressed as the MESSENGER mission completes work over the next year. Much progress has been made with respect to exploring the second difference above--spacecraft such as Helios, Ulysses, WIND, and ACE have measured the solar wind and its composition both in Earth orbit and at distances encompassing the orbit of Mercury. While our knowledge of the solar wind is incomplete, again it is far more detailed than a simple 1/R(sup 2) law would predict. Another problem is that of the flux of charged particles to the surfaces. While Mercury's magnetosphere is the subject of current study with MESSENGER, the influx of charged particles on the Moon has gone beyond a cos (psi) picture, where psi is the solar zenith angle. We know that the influx of ions at the Moon is affected by magnetic anomalies, by craters, and by surface charging. The third external difference is the differing flux of interplanetary dust incident on the two surfaces. In this talk we will consider: (1) the species that one can compare now for these two exospheres (Na, K, and He); (2) the species that you might be able to compare with future measurements (Ca and Mg); arid (3) how intensive ground-based observations of the easiest lunar species to observe from the

A novel interplanetary optical navigation algorithm based on Earth-Moon group photos by Chang'e-5T1 probe

NASA Astrophysics Data System (ADS)

Bu, Yanlong; Zhang, Qiang; Ding, Chibiao; Tang, Geshi; Wang, Hang; Qiu, Rujin; Liang, Libo; Yin, Hejun

2017-02-01

This paper presents an interplanetary optical navigation algorithm based on two spherical celestial bodies. The remarkable characteristic of the method is that key navigation parameters can be estimated depending entirely on known sizes and ephemerides of two celestial bodies, especially positioning is realized through a single image and does not rely on traditional terrestrial radio tracking any more. Actual Earth-Moon group photos captured by China's Chang'e-5T1 probe were used to verify the effectiveness of the algorithm. From 430,000 km away from the Earth, the camera pointing accuracy reaches 0.01° (one sigma) and the inertial positioning error is less than 200 km, respectively; meanwhile, the cost of the ground control and human resources are greatly reduced. The algorithm is flexible, easy to implement, and can provide reference to interplanetary autonomous navigation in the solar system.

Tidal Locking Of The Earth

NASA Astrophysics Data System (ADS)

Koohafkan, Michael

2006-05-01

The Moon's orbit and spin period are nearly synchronized, or tidally locked. Could the Moon's orbit and the Earth's spin eventually synchronize as well? The Moon's gravitational pull on the Earth produces tides in our oceans, and tidal friction gradually lengthens our days. Less obvious gravitational interactions between the Earth and Moon may also have effects on Earth's spin. The Earth is slightly distorted into an egg-like shape, and the torque exerted by the Moon on our equatorial bulge slowly changes the tilt of our spin axis. How do effects such as these change as the Moon drifts away from Earth? I will examine gravitational interactions between Earth and Moon to learn how they contribute to the deceleration of the Earth's rotation. My goal is to determine the amount of time it would take for the Earth's rotational speed to decelerate until the period of a single rotation matches the period of the Moon's orbit around Earth -- when the Earth is ``tidally locked'' with the Moon. I aim to derive a general mathematical expression for the rotational deceleration of the Earth due to Moon's gravitational influences.