GOATS - Orbitology Component

NASA Technical Reports Server (NTRS)

Haber, Benjamin M.; Green, Joseph J.

2010-01-01

The GOATS Orbitology Component software was developed to specifically address the concerns presented by orbit analysis tools that are often written as stand-alone applications. These applications do not easily interface with standard JPL first-principles analysis tools, and have a steep learning curve due to their complicated nature. This toolset is written as a series of MATLAB functions, allowing seamless integration into existing JPL optical systems engineering modeling and analysis modules. The functions are completely open, and allow for advanced users to delve into and modify the underlying physics being modeled. Additionally, this software module fills an analysis gap, allowing for quick, high-level mission analysis trades without the need for detailed and complicated orbit analysis using commercial stand-alone tools. This software consists of a series of MATLAB functions to provide for geometric orbit-related analysis. This includes propagation of orbits to varying levels of generalization. In the simplest case, geosynchronous orbits can be modeled by specifying a subset of three orbit elements. The next case is a circular orbit, which can be specified by a subset of four orbit elements. The most general case is an arbitrary elliptical orbit specified by all six orbit elements. These orbits are all solved geometrically, under the basic problem of an object in circular (or elliptical) orbit around a rotating spheroid. The orbit functions output time series ground tracks, which serve as the basis for more detailed orbit analysis. This software module also includes functions to track the positions of the Sun, Moon, and arbitrary celestial bodies specified by right ascension and declination. Also included are functions to calculate line-of-sight geometries to ground-based targets, angular rotations and decompositions, and other line-of-site calculations. The toolset allows for the rapid execution of orbit trade studies at the level of detail required for the early stage of mission concept development.

The Generalized Sundman Transformation for Propagation of High-Eccentricity Elliptical Orbits

DTIC Science & Technology

2002-01-01

or the Kustaanheimo - Stiefel transformation (Ref. 8). • n = 3/2 or dt = cr3/2ds. We shall focus on this transformation . • n = 2 or dt = cr2ds. The...Paper AAS 02-109 The generalized Sundman transformation for propagation of high-eccentricity elliptical orbits Matthew Berry and...generalized Sundman transformation for propagation of high-eccentricity elliptical orbits 5a. CONTRACT NUMBER 5b. GRANT NUMBER 5c. PROGRAM ELEMENT NUMBER 6

Human Mars Mission: Launch Window from Earth Orbit. Pt. 1

NASA Technical Reports Server (NTRS)

Young, Archie

1999-01-01

The determination of orbital window characteristics is of major importance in the analysis of human interplanetary missions and systems. The orbital launch window characteristics are directly involved in the selection of mission trajectories, the development of orbit operational concepts, and the design of orbital launch systems. The orbital launch window problem arises because of the dynamic nature of the relative geometry between outgoing (departure) asymptote of the hyperbolic escape trajectory and the earth parking orbit. The orientation of the escape hyperbola asymptotic relative to earth is a function of time. The required hyperbola energy level also varies with time. In addition, the inertial orientation of the parking orbit is a function of time because of the perturbations caused by the Earth's oblateness. Thus, a coplanar injection onto the escape hyperbola can be made only at a point in time when the outgoing escape asymptote is contained by the plane of parking orbit. Even though this condition may be planned as a nominal situation, it will not generally represent the more probable injection geometry. The general case of an escape injection maneuver performed at a time other than the coplanar time will involve both a path angle and plane change and, therefore, a DELTA V penalty. Usually, because of the DELTA V penalty the actual departure injection window is smaller in duration than that determined by energy requirement alone. This report contains the formulation, characteristics, and test cases for five different launch window modes for Earth orbit. These modes are: (1) One impulsive maneuver from a Highly Elliptical Orbit (HEO) (2) Two impulsive maneuvers from a Highly Elliptical Orbit (HEO) (3) One impulsive maneuver from a Low Earth Orbit (LEO) (4) Two impulsive maneuvers from LEO (5) Three impulsive maneuvers from LEO.

LAREDO: LAunching, REndezvous and DOcking Simulation Tool

DTIC Science & Technology

2006-08-01

the Clohessy - Wiltshire equation for small eccentricities and relative distances, as shown in Eq. (12). z 2 y x 2 azz ax2y ay2x3x +−= +−= ++= ω ω...ωω && &&& &&& (12) In case of circular orbits, the LAREDO tool orbital maneuvers are all based on the Clohessy - Wiltshire equations4, where the set...Elliptical maneuvers guidance and control The Clohessy - Wiltshire equations described in the above section cannot be applied when the orbits have a

Unstable Box Orbits in Cuspy Elliptical Galaxies

NASA Technical Reports Server (NTRS)

Hasan, H.; Pfenniger, D.

1996-01-01

The aim of this work is to gain physical insight into the role played by a concentrated central mass in affecting the shape of elliptical galaxies, by examining its effect on the stability of box orbits which are the backbone of triaxial elliptical galaxies. Ample observational evidence is now available for the existence of a central mass concentration or central cusps in galaxies. The central mass is expected to cause orbital stochasticity and chaotic mixing of orbits, which could have ramifications on galactic evolution. We investigate here the interplay between potential cuspiness and eccentricity on the stability of axial orbits in a scale-free potential in a simple, preliminary attempt to characterize this effect.

Optimal trajectories based on linear equations

NASA Technical Reports Server (NTRS)

Carter, Thomas E.

1990-01-01

The Principal results of a recent theory of fuel optimal space trajectories for linear differential equations are presented. Both impulsive and bounded-thrust problems are treated. A new form of the Lawden Primer vector is found that is identical for both problems. For this reason, starting iteratives from the solution of the impulsive problem are highly effective in the solution of the two-point boundary-value problem associated with bounded thrust. These results were applied to the problem of fuel optimal maneuvers of a spacecraft near a satellite in circular orbit using the Clohessy-Wiltshire equations. For this case two-point boundary-value problems were solved using a microcomputer, and optimal trajectory shapes displayed. The results of this theory can also be applied if the satellite is in an arbitrary Keplerian orbit through the use of the Tschauner-Hempel equations. A new form of the solution of these equations has been found that is identical for elliptical, parabolic, and hyperbolic orbits except in the way that a certain integral is evaluated. For elliptical orbits this integral is evaluated through the use of the eccentric anomaly. An analogous evaluation is performed for hyperbolic orbits.

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.

Electric sail elliptic displaced orbits with advanced thrust model

NASA Astrophysics Data System (ADS)

Niccolai, Lorenzo; Quarta, Alessandro A.; Mengali, Giovanni

2017-09-01

This paper analyzes the performance of an Electric Solar Wind Sail for generating and maintaining an elliptic, heliocentric, displaced non-Keplerian orbit. In this sense, this paper extends and completes recent studies regarding the performances of an Electric Solar Wind Sail that covers a circular, heliocentric, displaced orbit of given characteristics. The paper presents the general equations that describe the elliptic orbit maintenance in terms of both spacecraft attitude and performance requirements, when a refined thrust model (recently proposed for the preliminary mission design) is taken into account. In particular, the paper also discusses some practical applications on particular mission scenarios in which an analytic solution of the governing equations has been found.

Navigating highly elliptical earth orbiters with simultaneous VLBI from orthogonal baseline pairs

NASA Technical Reports Server (NTRS)

Frauenholz, Raymond B.

1986-01-01

Navigation strategies for determining highly elliptical orbits with VLBI are described. The predicted performance of wideband VLBI and Delta VLBI measurements obtained by orthogonal baseline pairs are compared for a 16-hr equatorial orbit. It is observed that the one-sigma apogee position accuracy improves two orders of magnitude to the meter level when Delta VLBI measurements are added to coherent Doppler and range, and the simpler VLBI strategy provides nearly the same orbit accuracy. The effects of differential measurement noise and acquisition geometry on orbit accuracy are investigated. The data reveal that quasar position uncertainty limits the accuracy of wideband Delta VLBI measurements, and that polar motion and baseline uncertainties and offsets between station clocks affect the wideband VLBI data. It is noted that differential one-way range (DOR) has performance nearly equal to that of the more complex Delta DOR and is recommended for use on spacecraft in high elliptical orbits.

Constellation Design of Geosynchronous Navigation Satellites Which Maximizes Availability and Accuracy Over a Specified Region of the Earth

DTIC Science & Technology

2008-03-01

Society, Washington DC, 1999. 11. Ferringer, Matthew P. and David B. Spencer . “Satellite Constellation Design Optimization Via Multiple-Objective...5 GA Genetic Algorithms . . . . . . . . . . . . . . . . . . . . . . 5 HEO Highly Elliptical Orbit...and their phasing relationship. He analyzed different combinations of GEO, Highly Elliptical Orbit (HEO)1 and Tundra2 orbits to create a global

Origin and continuation of 3/2, 5/2, 3/1, 4/1 and 5/1 resonant periodic orbits in the circular and elliptic restricted three-body problem

NASA Astrophysics Data System (ADS)

Antoniadou, Kyriaki I.; Libert, Anne-Sophie

2018-06-01

We consider a planetary system consisting of two primaries, namely a star and a giant planet, and a massless secondary, say a terrestrial planet or an asteroid, which moves under their gravitational attraction. We study the dynamics of this system in the framework of the circular and elliptic restricted three-body problem, when the motion of the giant planet describes circular and elliptic orbits, respectively. Originating from the circular family, families of symmetric periodic orbits in the 3/2, 5/2, 3/1, 4/1 and 5/1 mean-motion resonances are continued in the circular and the elliptic problems. New bifurcation points from the circular to the elliptic problem are found for each of the above resonances, and thus, new families continued from these points are herein presented. Stable segments of periodic orbits were found at high eccentricity values of the already known families considered as whole unstable previously. Moreover, new isolated (not continued from bifurcation points) families are computed in the elliptic restricted problem. The majority of the new families mainly consists of stable periodic orbits at high eccentricities. The families of the 5/1 resonance are investigated for the first time in the restricted three-body problems. We highlight the effect of stable periodic orbits on the formation of stable regions in their vicinity and unveil the boundaries of such domains in phase space by computing maps of dynamical stability. The long-term stable evolution of the terrestrial planets or asteroids is dependent on the existence of regular domains in their dynamical neighbourhood in phase space, which could host them for long-time spans. This study, besides other celestial architectures that can be efficiently modelled by the circular and elliptic restricted problems, is particularly appropriate for the discovery of terrestrial companions among the single-giant planet systems discovered so far.

Elliptical-like orbits on a warped spandex fabric: A theoretical/experimental undergraduate research project

NASA Astrophysics Data System (ADS)

Middleton, Chad A.; Weller, Dannyl

2016-04-01

We present a theoretical and experimental analysis of the elliptical-like orbits of a marble rolling on a warped spandex fabric. We arrive at an expression describing the angular separation between successive apocenters, or equivalently successive pericenters, in both the small and large slope regimes. We find that a minimal angular separation of ˜197° is predicted for orbits with small radial distances when the surface is void of a central mass. We then show that for small radii and large central masses, when the orbiting marble is deep within the well, the angular separation between successive apocenters transitions to values greater than 360°. We lastly compare these expressions to those describing elliptical-like orbits about a static, spherically symmetric massive object in the presence of a constant vacuum energy, as described by general relativity.

A quasi-intermittency

NASA Astrophysics Data System (ADS)

He, Da-Ren; Wang, Xu-Ming; Wang, Ying-Mei; Wang, Wen-Xiu; Chen, He-Sheng

2002-03-01

A kind of discontinuous and noninvertible area-preserving maps can display behaviors as a dissipative one, so it may be addressed as a "quasi-dissipative system"^1. In a quasi-dissipative system the disappearance of some elliptic periodic orbits and the elliptic islands around them via a collision with the discontinuous border of the system function can be observed. A chaotic quasi-attractor dominates behavior of the system after the disappearance of the elliptic periodic orbit and a sequence of transition elliptic periodic orbits. When the chaotic quasi-attractor just appears, the chaotic time sequence shows a random intersperse between laminar and turbulence phases. All these are very similar to the properties of type V intermittency happened in a dissipative system. So, we may call the phenomenon as a "type V quasi-intermittency". However, there can be only some remnants of the last disappeared transition elliptic island instead of its "ghost", therefore type V quasi-intermittency does not obey the characteristic scaling laws of type V intermittency. ^1 J. Wang et al., Phys.Rev.E, 64(2001)026202.

Experiment definition phase shuttle laboratory (LDRL-10.6 experiment): Shuttle sortie to elliptical orbit satellite

NASA Technical Reports Server (NTRS)

Goodwin, F. E.; Nussmeier, T. A.; Stokes, L. S.; Vourgourakis, E. J.

1976-01-01

The following topics were reviewed: (1) design options for shuttle terminal, (2) elliptical orbit satellite design options, (3) shuttle terminal details, (4) technology status and development requirements, (5) transmitter technology, and (6) carbon dioxide laser life studies.

Mars Reconnaissance Orbiter Aerobraking Daily Operations and Collision Avoidance

NASA Technical Reports Server (NTRS)

Long, Stacia M.; You, Tung-Han; Halsell, C. Allen; Bhat, Ramachand S.; Demcak, Stuart W.; Graat, Eric J.; Higa, Earl S.; Highsmith, Dolan E.; Mottinger, Neil A.; Jah, Moriba K.

2007-01-01

The Mars Reconnaissance Orbiter reached Mars on March 10, 2006 and performed a Mars orbit insertion maneuver of 1 km/s to enter into a large elliptical orbit. Three weeks later, aerobraking operations began and lasted about five months. Aerobraking utilized the atmospheric drag to reduce the large elliptical orbit into a smaller, near circular orbit. At the time of MRO aerobraking, there were three other operational spacecraft orbiting Mars and the navigation team had to minimize the possibility of a collision. This paper describes the daily operations of the MRO navigation team during this time as well as the collision avoidance strategy development and implementation.

The rectilinear three-body problem as a basis for studying highly eccentric systems

NASA Astrophysics Data System (ADS)

Voyatzis, G.; Tsiganis, K.; Gaitanas, M.

2018-01-01

The rectilinear elliptic restricted three-body problem (TBP) is the limiting case of the elliptic restricted TBP when the motion of the primaries is described by a Keplerian ellipse with eccentricity e'=1, but the collision of the primaries is assumed to be a non-singular point. The rectilinear model has been proposed as a starting model for studying the dynamics of motion around highly eccentric binary systems. Broucke (AIAA J 7:1003-1009, 1969) explored the rectilinear problem and obtained isolated periodic orbits for mass parameter μ =0.5 (equal masses of the primaries). We found that all orbits obtained by Broucke are linearly unstable. We extend Broucke's computations by using a finer search for symmetric periodic orbits and computing their linear stability. We found a large number of periodic orbits, but only eight of them were found to be linearly stable and are associated with particular mean motion resonances. These stable orbits are used as generating orbits for continuation with respect to μ and e'<1. Also, continuation of periodic solutions with respect to the mass of the small body can be applied by using the general TBP. FLI maps of dynamical stability show that stable periodic orbits are surrounded in phase space with regions of regular orbits indicating that systems of very highly eccentric orbits can be found in stable resonant configurations. As an application we present a stability study for the planetary system HD7449.

Orbit Maneuver for Responsive Coverage Using Electric Propulsion

DTIC Science & Technology

2010-03-01

24 4. Results and Analysis ...Orbit Analysis ............................................................................28 Figure 3.6 Circular Orbit Analysis ...29 Figure 3.7 Elliptical Orbit Analysis

Time Harmonic Two-Dimensional Cavity Scar Statistics: Convex Mirrors and Bowtie

DOE PAGES

Warne, Larry Kevin; Jorgenson, Roy Eberhardt; Kotulski, Joseph Daniel; ...

2011-02-10

Here, this article examines the localization of time harmonic high-frequency modal fields in two-dimensional cavities along periodic paths between opposing sides of the cavity. The cases where these orbits lead to unstable localized modes are known as scars. This article examines the enhancements for these unstable orbits when the opposing mirrors are convex, constructing the high-frequency field in the scar region using elliptic cylinder coordinates in combination with a random reflection phase from the outer chaotic region. Finally, the enhancements when the cavity is symmetric as well as asymmetric about the orbit are examined.

Modeling the Effects of Spacecraft Venting on Instrument Measurements of the Martian Atmosphere for an Elliptical Orbit

NASA Technical Reports Server (NTRS)

Petro, Elaine; Hughes, David

2011-01-01

Analysis has been performed for MAVEN mission. Due to the elliptical orbit, large pressure variations in orbit will be experienced, there is a need to understand how internal pressures change and the flux of gas from vents could potentially bias instrument measurements. Goal of this analysis is to predict the effect that atmospheric gases trapped and vented from spacecraft volumes could have on instrument measurements.

Optimal Low-Thrust Limited-Power Transfers between Arbitrary Elliptic Coplanar Orbits

NASA Technical Reports Server (NTRS)

daSilvaFernandes, Sandro; dasChagasCarvalho, Francisco

2007-01-01

In this work, a complete first order analytical solution, which includes the short periodic terms, for the problem of optimal low-thrust limited-power transfers between arbitrary elliptic coplanar orbits in a Newtonian central gravity field is obtained through Hamilton-Jacobi theory and a perturbation method based on Lie series.

Quantum-Classical Connection for Hydrogen Atom-Like Systems

ERIC Educational Resources Information Center

Syam, Debapriyo; Roy, Arup

2011-01-01

The Bohr-Sommerfeld quantum theory specifies the rules of quantization for circular and elliptical orbits for a one-electron hydrogen atom-like system. This article illustrates how a formula connecting the principal quantum number "n" and the length of the major axis of an elliptical orbit may be arrived at starting from the quantum…

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

DTIC Science & Technology

1991-01-01

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

The 2-D lattice theory of Flower Constellations

NASA Astrophysics Data System (ADS)

Avendaño, Martín E.; Davis, Jeremy J.; Mortari, Daniele

2013-08-01

The 2-D lattice theory of Flower Constellations, generalizing Harmonic Flower Constellations (the symmetric subset of Flower Constellations) as well as the Walker/ Mozhaev constellations, is presented here. This theory is a new general framework to design symmetric constellations using a 2× 2 lattice matrix of integers or by its minimal representation, the Hermite normal form. From a geometrical point of view, the phasing of satellites is represented by a regular pattern (lattice) on a two-Dimensional torus. The 2-D lattice theory of Flower Constellations does not require any compatibility condition and uses a minimum set of integer parameters whose meaning are explored throughout the paper. This general minimum-parametrization framework allows us to obtain all symmetric distribution of satellites. Due to the J_2 effect this design framework is meant for circular orbits and for elliptical orbits at critical inclination, or to design elliptical constellations for the unperturbed Keplerian case.

The 3D elliptic restricted three-body problem: periodic orbits which bifurcate from limiting restricted problems. Complex instability

NASA Astrophysics Data System (ADS)

Ollé, Mercè; Pacha, Joan R.

1999-11-01

In the present work we use certain isolated symmetric periodic orbits found in some limiting Restricted Three-Body Problems to obtain, by numerical continuation, families of symmetric periodic orbits of the more general Spatial Elliptic Restricted Three Body Problem. In particular, the Planar Isosceles Restricted Three Body Problem, the Sitnikov Problem and the MacMillan problem are considered. A stability study for the periodic orbits of the families obtained - specially focused to detect transitions to complex instability - is also made.

Formation Design Strategy for SCOPE High-Elliptic Formation Flying Mission

NASA Technical Reports Server (NTRS)

Tsuda, Yuichi

2007-01-01

The new formation design strategy using simulated annealing (SA) optimization is presented. The SA algorithm is useful to survey a whole solution space of optimum formation, taking into account realistic constraints composed of continuous and discrete functions. It is revealed that this method is not only applicable for circular orbit, but also for high-elliptic orbit formation flying. The developed algorithm is first tested with a simple cart-wheel motion example, and then applied to the formation design for SCOPE. SCOPE is the next generation geomagnetotail observation mission planned in JAXA, utilizing a formation flying techonology in a high elliptic orbit. A distinctive and useful heuristics is found by investigating SA results, showing the effectiveness of the proposed design process.

Controlling orbital angular momentum of an optical vortex by varying its ellipticity

NASA Astrophysics Data System (ADS)

Kotlyar, Victor V.; Kovalev, Alexey A.

2018-03-01

An exact analytical expression is obtained for the orbital angular momentum (OAM) of a Gaussian optical vortex with a different degree of ellipticity. The OAM turned out to be proportional to the ratio of two Legendre polynomials of adjoining orders. It is shown that if an elliptical optical vortex is embedded into the center of the waist of a circularly symmetrical Gaussian beam, then the normalized OAM of such laser beam is fractional and it does not exceed the topological charge n. If, on the contrary, a circularly symmetrical optical vortex is embedded into the center of the waist of an elliptical Gaussian beam, then the OAM is equal to n. If the optical vortex and the Gaussian beam have the same (or matched) ellipticity degree, then the OAM of the laser beam is greater than n. Continuous varying of the OAM of a laser beam by varying its ellipticity degree can be used in optical trapping for accelerated motion of microscopic particles along an elliptical trajectory as well as in quantum informatics for detecting OAM-entangled photons.

Human Mars Mission: Launch Window from Earth Orbit. Pt. 1

NASA Technical Reports Server (NTRS)

Young, Archie

1999-01-01

The determination of orbital window characteristics is of major importance in the analysis of human interplanetary missions and systems. The orbital launch window characteristics are directly involved in the selection of mission trajectories, the development of orbit operational concepts, and the design of orbital launch systems. The orbital launch window problem arises because of the dynamic nature of the relative geometry between outgoing (departure) asymptote of the hyperbolic escape trajectory and the earth parking orbit. The orientation of the escape hyperbola asymptotic relative to the earth is a function of time. The required hyperbola energy level also varies with time. In addition, the inertial orientation of the parking orbit is a function of time because of the perturbations caused by the Earth's oblateness. Thus, a coplanar injection onto the escape hyperbola can be made only at a point in time when the outgoing escape asymptote is contained by the plane of parking orbit. Even though this condition may be planned as a nominal situation, it will not generally represent the more probable injection geometry. The general case of an escape injection maneuver performed at a time other than the coplanar time will involve both a path angle and plane change and, therefore, a delta V penalty. Usually, because of the delta V penalty the actual departure injection window is smaller in duration than that determined by energy requirement alone. This report contains the formulation, characteristics, and test cases for five different launch window modes for Earth orbit. These modes are: 1) One impulsive maneuver from a Highly Elliptical Orbit (HEO); 2) Two impulsive maneuvers from a Highly Elliptical Orbit (HEO); 3) One impulsive maneuver from a Low Earth Orbit (LEO); 4) Two impulsive maneuvers form LEO; and 5) Three impulsive maneuvers form LEO. The formulation of these five different launch window modes provides a rapid means of generating realistic parametric data for space exploration studies. Also the formulation provides vector and geometrical data sufficient for use as a good starting point in detail trajectory analysis based on calculus of variations, steepest descent, or parameter optimization program techniques.

Human Exploration Missions Study Launch Window from Earth Orbit

NASA Technical Reports Server (NTRS)

Young, Archie

2001-01-01

The determination of orbital launch window characteristics is of major importance in the analysis of human interplanetary missions and systems. The orbital launch window characteristics are directly involved in the selection of mission trajectories, the development of orbit operational concepts, and the design of orbital launch systems. The orbital launch window problem arises because of the dynamic nature of the relative geometry between outgoing (departure) asymptote of the hyperbolic escape trajectory and the earth parking orbit. The orientation of the escape hyperbola asymptotic relative to earth is a function of time. The required hyperbola energy level also varies with time. In addition, the inertial orientation of the parking orbit is a function of time because of the perturbations caused by the Earth's oblateness. Thus, a coplanar injection onto the escape hyperbola can be made only at a point in time when the outgoing escape asymptote is contained by the plane of parking orbit. Even though this condition may be planned as a nominal situation, it will not generally represent the more probable injection geometry. The general case of an escape injection maneuver performed at a time other than the coplanar time will involve both a path angle and plane change and, therefore, a Delta(V) penalty. Usually, because of the Delta(V) penalty the actual departure injection window is smaller in duration than that determined by energy requirement alone. This report contains the formulation, characteristics, and test cases for five different launch window modes for Earth orbit. These modes are: (1) One impulsive maneuver from a Low Earth Orbit (LEO), (2) Two impulsive maneuvers from LEO, (3) Three impulsive maneuvers from LEO, (4) One impulsive maneuvers from a Highly Elliptical Orbit (HEO), (5) Two impulsive maneuvers from a Highly Elliptical Orbit (HEO) The formulation of these five different launch window modes provides a rapid means of generating realistic parametric data for space exploration studies. Also the formulation provides vector and geometrical data sufficient for use as a good starting point in detail trajectory analysis based on calculus of variations, steepest descent, or parameter optimization program techniques.

Temporary satellite capture of comets by Jupiter

NASA Astrophysics Data System (ADS)

Emel'yanenko, N. Yu.

2012-05-01

This paper studies the dynamical evolution of 97 Jupiter-family comets over an 800-year time period. More than two hundred encounters with Jupiter are investigated, with the observed comets moving during a certain period of time in an elliptic jovicentric orbit. In most cases this is an ordinary temporary satellite capture of a comet in Everhart's sense, not associated with a transition of the small body into Jupiter's family of satellites. The phenomenon occurs outside the Hill sphere with comets with a high Tisserand constant relative to Jupiter; the comets' orbits have a small inclination to the ecliptic plane. An analysis of 236 encounters has allowed the determination within the planar pair two-body problem of a region of orbits in the plane ( a, e) whose semimajor axes and eccentricities contribute to the phenomenon under study. Comets with orbits belonging to this region experience a temporary satellite capture during some of their encounters; the jovicentric distance function has several minima; and the encounters are characterized by reversions of the line of apsides and some others features of their combination that are intrinsic to comets in this region. Therefore, this region is called a region of comets with specific features in their encounters with Jupiter. Twenty encounters (out of 236), whereby the comet enters an elliptic jovicentric orbit in the Hill sphere, are identified and investigated. The size and shape of the elliptic heliocentric orbits enabling this transition are determined. It is found that in 11 encounters the motion of small bodies in the Hill sphere has features the most important of which is multiple minima of the jovicentric distance function. The study of these 20 encounters has allowed the introduction of the concept of temporary gravitational capture of a small body into the Hill sphere. An analysis of variations in the Tisserand constant in these (20) encounters of the observable comets shows that their motion is unstable in Hill's sense.

Venus and Mars Obstacles in the Solar Wind

NASA Astrophysics Data System (ADS)

Luhmann, J. G.; Mitchell, D. L.; Acuna, M. H.; Russell, C. T.; Brecht, S. H.; Lyon, J. G.

2000-10-01

Comparisons of the magnetosheaths of Venus and Mars contrast the relative simplicity of the Venus solar wind interaction and the ``Jekyll and Hyde" nature of the Mars interaction. Magnetometer observations from Mars Global Surveyor during the elliptical science phasing orbits and Pioneer Venus Orbiter in its normally elliptical orbit are compared, with various models used to compensate for the different near-polar periapsis of MGS and near-equator periapsis of PVO. Gasdynamic or MHD fluid models of flow around a conducting sphere provide a remarkably good desciption of the Venus case, and the Mars case when the strong Martian crustal magnetic anomalies are in the flow wake. In the case of Venus, large magnetosheath field fluctuations can be reliably tied to occurrence of a subsolar quasiparallel bow shock resulting from a small interplanetary field cone angle (angle between flow and field) upstream. At Mars one must also contend with such large fluctuations from the bow shock, but also from unstable solar wind proton distributions due to finite ion gyroradius effects, and from the complicated obstacle presented to the solar wind when the crustal magnetic anomalies are on the ram face or terminator. We attempt to distinguish between these factors at Mars, which are important for interpretation of the upcoming NOZOMI and Mars Express mission measurements. The results also provide more insights into a uniquely complex type of solar system solar wind interaction involving crustal fields akin to the Moon's, combined with a Venus-like ionospheric obstacle.

Origin of orbital debris impacts on LDEF's trailing surfaces

NASA Technical Reports Server (NTRS)

Kessler, Donald J.

1993-01-01

A model was developed to determine the origin of orbital impacts measured on the training surfaces of LDEF. The model calculates the expected debris impact crater distribution around LDEF as a function of debris orbital parameters. The results show that only highly elliptical, low inclination orbits could be responsible for these impacts. The most common objects left in this type of orbit are orbital transfer stages used by the U.S. and ESA to place payloads into geosynchronous orbit. Objects in this type of orbit are difficult to catalog by the U.S. Space Command; consequently there are independent reasons to believe that the catalog does not adequately represent this population. This analysis concludes that the relative number of cataloged objects with highly elliptical, low inclination orbits must be increased by a factor of 20 to be consistent with the LDEF data.

Formation flying for electric sails in displaced orbits. Part I: Geometrical analysis

NASA Astrophysics Data System (ADS)

Wang, Wei; Mengali, Giovanni; Quarta, Alessandro A.; Yuan, Jianping

2017-09-01

We present a geometrical methodology for analyzing the formation flying of electric solar wind sail based spacecraft that operate in heliocentric, elliptic, displaced orbits. The spacecraft orbit is maintained by adjusting its propulsive acceleration modulus, whose value is estimated using a thrust model that takes into account a variation of the propulsive performance with the sail attitude. The properties of the relative motion of the spacecraft are studied in detail and a geometrical solution is obtained in terms of relative displaced orbital elements, assumed to be small quantities. In particular, for the small eccentricity case (i.e. for a near-circular displaced orbit), the bounds characterized by the extreme values of relative distances are analytically calculated, thus providing an useful mathematical tool for preliminary design of the spacecraft formation structure.

Aerobraking orbital transfer vehicle

NASA Technical Reports Server (NTRS)

Scott, Carl D. (Inventor); Nagy, Kornel (Inventor); Roberts, Barney B. (Inventor); Ried, Robert C. (Inventor); Kroll, Kenneth R. (Inventor); Gamble, Joe (Inventor)

1989-01-01

An aerobraking orbital transfer vehicle which includes an aerobraking device which also serves as a heat shield in the shape of a raked-off elliptic or circular cone with a circular or elliptical base, and with an ellipsoid or other blunt shape nose. The aerobraking device is fitted with a toroid-like skirt and is integral with the support structure of the propulsion system and other systems of the space vehicle. The vehicle is intended to be transported in components to a space station in lower earth orbit where it is assembled for use as a transportation system from low earth orbit to geosynchronous earth orbit and return. Conventional guidance means are included for autonomous flight.

Spin flip in single quantum ring with Rashba spin–orbit interation

NASA Astrophysics Data System (ADS)

Liu, Duan-Yang; Xia, Jian-Bai

2018-03-01

We theoretically investigate spin transport in the elliptical ring and the circular ring with Rashba spin–orbit interaction. It is shown that when Rashba spin–orbit interaction is relatively weak, a single circular ring can not realize spin flip, however an elliptical ring may work as a spin-inverter at this time, and the influence of the defect of the geometry is not obvious. Howerver if a giant Rashba spin–orbit interaction strength has been obtained, a circular ring can work as a spin-inverter with a high stability. Project supported by the National Natural Science Foundation of China (Grant No. 11504016).

Design and optimal control of on-orbit servicing trajectory for target vehicle in non-coplanar elliptical orbit

NASA Astrophysics Data System (ADS)

Zhou, Wenyong; Yuan, Jianping; Luo, Jianjun

2005-11-01

Autonomous on-orbit servicing provides flexibility to space systems and has great value both in civil and in military. When a satellite performs on-orbit servicing tasks, flying around is the basic type of motion. This paper is concerned with the design and control problems of a chaser satellite flying around a target spacecraft in non-coplanar elliptical orbit for a long time. At first, a mathematical model used to design a long-term flying around trajectory is presented, which is applicable to the situation that the target spacecraft flies in an elliptical orbit. The conditions of the target at the centre of the flying around path are deduced. Considering the safety and task requirements, a long-term flying around trajectory is designed. Taking into account perturbations and navigation errors which can cause the trajectory unstable and mission impossible, a two-impulse control method is put forward. Genetic algorithm is used to minimize the cost function which considers fuel consumption and bias simultaneously. Some simulation works are carried out and the results indicate the flying around mathematical model and the trajectory control method can be used in the design and control of a long-term flying around trajectory.

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

NASA Astrophysics Data System (ADS)

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

2018-03-01

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

The stability of perfect elliptic disks. 1: The maximum streaming case

NASA Technical Reports Server (NTRS)

Levine, Stephen E.; Sparke, Linda S.

1994-01-01

Self-consistent distribution functions are constructed for two-dimensional perfect elliptic disks (for which the potential is exactly integrable) in the limit of maximum streaming; these are tested for stability by N-body integration. To obtain a discrete representation for each model, simulated annealing is used to choose a set of orbits which sample the distribution function and reproduce the required density profile while carrying the greatest possible amount of angular momentum. A quiet start technique is developed to place particles on these orbits uniformly in action-angle space, making the initial conditions as smooth as possible. The roundest models exhibit spiral instabilities similar to those of cold axisymmetric disks; the most elongated models show bending instabilities like those seen in prolate systems. Between these extremes, there is a range of axial ratios 0.25 approximately less than b/a approximately less than 0.6 within which these models appear to be stable. All the methods developed in this investigation can easily be extended to integrable potentials in three dimensions.

Reprocessing the Elliptical Orbiting Galileo Satellites E14 and E18: Preliminary Results

NASA Astrophysics Data System (ADS)

Männel, Benjamin

2017-04-01

In August 2014, the two Galileo satellites FOC-1 (E18) and FOC-2 (E14) were - due to a technical problem - launched into a wrong, elliptic orbit. In a recovery mission a series of orbit maneuvers were performed to raise the perigee to an altitude where both spacecrafts could be introduced to the Galileo navigation service. After this period of orbit maintenance both satellites started to transmit navigation signals at November 29, 2014 (E18) and March 17, 2015 (E14). However, as it was not possible to recover the nominal orbits due to propellant limitations, both spacecrafts orbit the Earth with a numerical eccentricity of 0.16 and an inclination of 50.2°. Very soon, it was assumed that both satellites could be highly useful for studies on general relativity, especially as the Galileo spacecrafts are equipped with very stable passive hydrogen masers. A prerequisite for dedicated studies in this field are highly accurate satellite orbits and clock corrections. Preliminary results for orbit and satellite clock determination will be presented based on an initial reprocessing over the past 2.5 years. The presentation focuses firstly on orbit modeling aspects with respect to the elliptically orbits. Secondly the derived clock corrections for the on-board passive clocks are assessed with respect to the reference clock at ground stations. The results will be discussed also with respect to the proposed Galileo-based studies on the gravitational redshift.

Design, Integration and Flight Test of a Pair of Autonomous Spacecraft Flying in Formation

DTIC Science & Technology

2013-05-01

representatives from the Air Force Research Laboratory, NASA’s Goddard Space Flight Center, the Jet Propulsion Laboratory, Boeing, Lockheed Martin, as...categories: elliptical , hyperbolic and parabolic (known as “Keplerian orbits”), each with their own characteristics and applications. These equations...of M-SAT’s operation is that of an elliptical nature, or more precisely a near-circular orbit. The primary method of determining the orbital elements

Attractive manifold-based adaptive solar attitude control of satellites in elliptic orbits

NASA Astrophysics Data System (ADS)

Lee, Keum W.; Singh, Sahjendra N.

2011-01-01

The paper presents a novel noncertainty-equivalent adaptive (NCEA) control system for the pitch attitude control of satellites in elliptic orbits using solar radiation pressure (SRP). The satellite is equipped with two identical solar flaps to produce control moments. The adaptive law is based on the attractive manifold design using filtered signals for synthesis, which is a modification of the immersion and invariance (I&I) method. The control system has a modular controller-estimator structure and has separate tunable gains. A special feature of this NCEA law is that the trajectories of the satellite converge to a manifold in an extended state space, and the adaptive law recovers the performance of a deterministic controller. This recovery of performance cannot be obtained with certainty-equivalent adaptive (CEA) laws. Simulation results are presented which show that the NCEA law accomplishes precise attitude control of the satellite in an elliptic orbit, despite large parameter uncertainties.

Libration of arguments of circumbinary-planet orbits at resonance

NASA Astrophysics Data System (ADS)

Schubart, Joachim

2017-06-01

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

Contingency plans for the ISEE-3 libration-point mission

NASA Technical Reports Server (NTRS)

Dunham, D. W.

1979-01-01

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

Effects of the eccentricity of the primaries in powered Swing-By maneuvers

NASA Astrophysics Data System (ADS)

Ferreira, Alessandra F. S.; Prado, Antônio F. B. A.; Winter, Othon C.; Santos, Denilson P. S.

2017-04-01

The present paper studies the powered Swing-By maneuver when performed in an elliptical system of primaries. It means that there is a spacecraft travelling in a system governed by the gravity fields of two bodies that are in elliptical orbits around their center of mass. The paper particularly analyzes the effects of the parameters relative to the Swing-By (Vinf-,rp, ψ), the orbit of the secondary body around the primary one (e, ν) and the elements that specify the impulse applied (δV, α) to the spacecraft. The impulse is applied when the spacecraft passes by the periapsis of its orbit around the body, where it performs the Swing-By, with different magnitudes and directions. The inclusion of the orbital eccentricity of the primaries in this problem makes it closer to reality, considering that there are many known systems with eccentricities different from zero. In particular, there are several moons in the Solar System which orbits are not circular, as well as some smaller bodies, like the dwarf planet Haumea and its moons, which have eccentricities of 0.25 or even larger. The behavior of the energy variation of the spacecraft is shown in details, as well as the cases where captures and collisions occur. The results show the conditions that optimize this maneuver, according to some given parameters, and how much can be obtained in terms of gains or losses of energy using the best conditions found by the algorithm developed here.

Mars exploration, Venus swingby and conjunction class mission modes, time period 2000 to 2045

NASA Technical Reports Server (NTRS)

Young, A. C.; Mulqueen, J. A.; Skinner, J. E.

1984-01-01

Trajectory and mission requirement data are presented for Earth-Mars opposition class and conjunction class round trip stopover mission opportunities available during the time period year 2000 to year 2045. The opposition class mission employs the gravitational field of Venus to accelerate the space vehicle on either the outbound or inbound leg. The gravitational field of Venus was used to reduce the propulsion requirement associated with the opposition class mission. Representative space vehicle systems are sized to compare the initial mass required in low Earth orbit of one mission opportunity with another mission opportunity. The interplanetary space vehicle is made up of the spacecraft and the space vehicle acceleration system. The space vehicle acceleration system consists of three propulsion stages. The first propulsion stage performs the Earth escape maneuver; the second stage brakes the spacecraft and Earth braking stage into the Mars elliptical orbit and effects the escape maneuver from the Mars elliptical orbit. The third propulsion stage brakes the mission module into an elliptical orbit at Earth return. The interplanetary space vehicle was assumed to be assembled in and depart from the space station circular orbit.

Cluster flight control for fractionated spacecraft on an elliptic orbit

NASA Astrophysics Data System (ADS)

Xu, Ming; Liang, Yuying; Tan, Tian; Wei, Lixin

2016-08-01

This paper deals with the stabilization of cluster flight on an elliptic reference orbit by the Hamiltonian structure-preserving control using the relative position measurement only. The linearized Melton's relative equation is utilized to derive the controller and then the full nonlinear relative dynamics are employed to numerically evaluate the controller's performance. In this paper, the hyperbolic and elliptic eigenvalues and their manifolds are treated without distinction notations. This new treatment not only contributes to solving the difficulty in feedback of the unfixed-dimensional manifolds, but also allows more opportunities to set the controlled frequencies of foundational motions or to optimize control gains. Any initial condition can be stabilized on a Kolmogorov-Arnold-Moser torus near a controlled elliptic equilibrium. The motions are stabilized around the natural relative trajectories rather than track a reference relative configuration. In addition, the bounded quasi-periodic trajectories generated by the controller have advantages in rapid reconfiguration and unpredictable evolution.

The behavior of cold gas in spheroidal galactic potentials

NASA Astrophysics Data System (ADS)

Simonson, G. F.

1982-03-01

The motions of cold gas residing in various spheroidal galactic potential wells are investigated, both analytically and through extensive numerical calculations. It is found that a gaseous layer embedded in the potential has a preferred orientation, in which individual gas clouds have orbits which do not precess. The gas will damp to the preferred orbits, through the combined effects of differential precession and radial excursions from circular trajectories, on time scales of less than one to two billion years for orbits of moderate radius. For elliptical galaxies with embedded gas disks this work provides a clear discriminator between prolate and oblate mass distributions. The preferred gas orbits lie in the equatorial planes of both of these potentials, so if a gas disk is seen projected against the minor axis of an elliptical, that galaxy is truly prolate, while if the lane is aligned with the major axis, the system is oblate. Tabulated observations show that both prolate and oblate ellipticals exist, in perhaps equal numbers. True axial ratios and spatial orientations can also be determined for these objects.

Energy analysis in the elliptic restricted three-body problem

NASA Astrophysics Data System (ADS)

Qi, Yi; de Ruiter, Anton

2018-07-01

The gravity assist or flyby is investigated by analysing the inertial energy of a test particle in the elliptic restricted three-body problem (ERTBP), where two primary bodies are moving in elliptic orbits. First, the expression of the derivation of energy is obtained and discussed. Then, the approximate expressions of energy change in a circular neighbourhood of the smaller primary are derived. Numerical computation indicates that the obtained expressions can be applied to study the flyby problem of the nine planets and the Moon in the Solar system. Parameters related to the flyby are discussed analytically and numerically. The optimal conditions, including the position and time of the periapsis, for a flyby orbit are found to make a maximum energy gain or loss. Finally, the mechanical process of a flyby orbit is uncovered by an approximate expression in the ERTBP. Numerical computations testify that our analytical results well approximate the mechanical process of flyby orbits obtained by the numerical simulation in the ERTBP. Compared with the previous research established in the patched-conic method and numerical calculation, our analytical investigations based on a more elaborate derivation get more original results.

Energy Analysis in the Elliptic Restricted Three-body Problem

NASA Astrophysics Data System (ADS)

Qi, Yi; de Ruiter, Anton

2018-05-01

The gravity assist or flyby is investigated by analyzing the inertial energy of a test particle in the elliptic restricted three-body problem (ERTBP), where two primary bodies are moving in elliptic orbits. Firstly, the expression of the derivation of energy is obtained and discussed. Then, the approximate expressions of energy change in a circular neighborhood of the smaller primary are derived. Numerical computation indicates that the obtained expressions can be applied to study the flyby problem of the nine planets and the Moon in the solar system. Parameters related to the flyby are discussed analytically and numerically. The optimal conditions, including the position and time of the periapsis, for a flyby orbit are found to make a maximum energy gain or loss. Finally, the mechanical process of a flyby orbit is uncovered by an approximate expression in the ERTBP. Numerical computations testify that our analytical results well approximate the mechanical process of flyby orbits obtained by the numerical simulation in the ERTBP. Compared with the previous research established in the patched-conic method and numerical calculation, our analytical investigations based on a more elaborate derivation get more original results.

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.

Logarithmic spiral trajectories generated by Solar sails

NASA Astrophysics Data System (ADS)

Bassetto, Marco; Niccolai, Lorenzo; Quarta, Alessandro A.; Mengali, Giovanni

2018-02-01

Analytic solutions to continuous thrust-propelled trajectories are available in a few cases only. An interesting case is offered by the logarithmic spiral, that is, a trajectory characterized by a constant flight path angle and a fixed thrust vector direction in an orbital reference frame. The logarithmic spiral is important from a practical point of view, because it may be passively maintained by a Solar sail-based spacecraft. The aim of this paper is to provide a systematic study concerning the possibility of inserting a Solar sail-based spacecraft into a heliocentric logarithmic spiral trajectory without using any impulsive maneuver. The required conditions to be met by the sail in terms of attitude angle, propulsive performance, parking orbit characteristics, and initial position are thoroughly investigated. The closed-form variations of the osculating orbital parameters are analyzed, and the obtained analytical results are used for investigating the phasing maneuver of a Solar sail along an elliptic heliocentric orbit. In this mission scenario, the phasing orbit is composed of two symmetric logarithmic spiral trajectories connected with a coasting arc.

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.

Accessibility, stabilizability, and feedback control of continuous orbital transfer.

PubMed

Gurfil, Pini

2004-05-01

This paper investigates the problem of low-thrust orbital transfer using orbital element feedback from a control-theoretic standpoint, concepts of controllability, feedback stabilizability, and their interaction. The Gauss variational equations (GVEs) are used to model the state-space dynamics. First, the notion of accessibility, a weaker form of controllability, is presented. It is then shown that the GVEs are globally accessible. Based on the accessibility result, a nonlinear feedback controller is derived that asymptotically steers a vehicle from an initial elliptic Keplerian orbit to any given elliptic Keplerian orbit. The performance of the new controller is illustrated by simulating an orbital transfer between two geosynchronous Earth orbits. It is shown that the low-thrust controller requires less fuel than an impulsive maneuver for the same transfer time. Closed-form, analytic expressions for the new orbital transfer controller are given. Finally, it is proved, based on a topological nonlinear stabilizability test, that there does not exist a continuous closed-loop controller that can transfer a spacecraft to a parabolic escape trajectory.

Elliptical orbit performance computer program

NASA Technical Reports Server (NTRS)

Myler, T. R.

1981-01-01

A FORTRAN coded computer program which generates and plots elliptical orbit performance capability of space boosters for presentation purposes is described. Orbital performance capability of space boosters is typically presented as payload weight as a function of perigee and apogee altitudes. The parameters are derived from a parametric computer simulation of the booster flight which yields the payload weight as a function of velocity and altitude at insertion. The process of converting from velocity and altitude to apogee and perigee altitude and plotting the results as a function of payload weight is mechanized with the ELOPE program. The program theory, user instruction, input/output definitions, subroutine descriptions and detailed FORTRAN coding information are included.

Geosynchronous Orbit Determination Using Space Surveillance Network Observations and Improved Radiative Force Modeling

DTIC Science & Technology

2004-06-01

equinoctial elements , because both sets of orbital elements reference the equinoctial coordinate system. In fact, to...spacecraft position and velocity vectors, or an element set , which represents the orbit using scalar quantities and angle measurements called orbital ...common element sets used to describe elliptical orbits (including circular orbits ) are Keplerian elements , also called classical orbital

On the Stability of Periodic Mercury-type Rotations

NASA Astrophysics Data System (ADS)

Churkina, Tatyana E.; Stepanov, Sergey Y.

2017-12-01

We consider the stability of planar periodic Mercury-type rotations of a rigid body around its center of mass in an elliptical orbit in a central Newtonian field of forces. Mercurytype rotations mean that the body makes 3 turns around its center of mass during 2 revolutions of the center of mass in its orbit (resonance 3:2). These rotations can be 1) symmetrical 2π- periodic, 2) symmetrical 4π-periodic and 3) asymmetrical 4π-periodic. The stability of rotations of type 1) was investigated by A.P.Markeev. In our paper we present a nonlinear stability analysis for some rotations of types 2) and 3) in 3rd- and 4th-order resonant cases, in the nonresonant case and at the boundaries of regions of linear stability.

A galactic mega-merger

NASA Image and Video Library

2016-01-11

The subject of this NASA/ESA Hubble Space Telescope image is known as NGC 3597. It is the product of a collision between two good-sized galaxies, and is slowly evolving to become a giant elliptical galaxy. This type of galaxy has grown more and more common as the Universe has evolved, with initially small galaxies merging and progressively building up into larger galactic structures over time. NGC 3597 is located approximately 150 million light-years away in the constellation of Crater (The Cup). Astronomers study NGC 3597 to learn more about how elliptical galaxies form — many ellipticals began their lives far earlier in the history of the Universe. Older ellipticals are nicknamed “red and dead” by astronomers because these bloated galaxies are not anymore producing new, bluer, stars in ages, and are thus packed full of old and redder stellar populations. Before infirmity sets in, some freshly formed elliptical galaxies experience a final flush of youth, as is the case with NGC 3597. Galaxies smashing together pool their available gas and dust, triggering new rounds of star birth. Some of this material ends up in dense pockets initially called proto-globular clusters, dozens of which festoon NGC 3597. These pockets will go on to collapse and form fully-fledged globular clusters, large spheres that orbit the centres of galaxies like satellites, packed tightly full of millions of stars.

Rashba and Dresselhaus spin-orbit interactions effects on electronic features of a two dimensional elliptic quantum dot

NASA Astrophysics Data System (ADS)

Mokhtari, P.; Rezaei, G.; Zamani, A.

2017-06-01

In this paper, electronic structure of a two dimensional elliptic quantum dot under the influence of external electric and magnetic fields are studied in the presence of Rashba and Dresselhaus spin-orbit interactions. This investigation is done computationally and to do this, at first, the effective Hamiltonian of the system by considering the spin-orbit coupling is demonstrated in the presence of applied electric and magnetic fields and afterwards the Schrödinger equation is solved using the finite difference approach. Utilizing finite element method, eigenvalues and eigenstates of the system are calculated and the effect of the external fields, the size of the dot as well as the strength of Rashba spin-orbit interaction are studied. Our results indicate that, Spin-orbit interactions, external fields and the dot size have a great influence on the electronic structure of the system.

Charged particles radiation measurements with Liulin-MO dosimeter of FREND instrument aboard ExoMars Trace Gas Orbiter during the transit and in high elliptic Mars orbit

NASA Astrophysics Data System (ADS)

Semkova, Jordanka; Koleva, Rositza; Benghin, Victor; Dachev, Tsvetan; Matviichuk, Yuri; Tomov, Borislav; Krastev, Krasimir; Maltchev, Stephan; Dimitrov, Plamen; Mitrofanov, Igor; Malahov, Alexey; Golovin, Dmitry; Mokrousov, Maxim; Sanin, Anton; Litvak, Maxim; Kozyrev, Andrey; Tretyakov, Vladislav; Nikiforov, Sergey; Vostrukhin, Andrey; Fedosov, Fedor; Grebennikova, Natalia; Zelenyi, Lev; Shurshakov, Vyacheslav; Drobishev, Sergey

2018-03-01

ExoMars is a joint ESA-Rosscosmos program for investigating Mars. Two missions are foreseen within this program: one consisting of the Trace Gas Orbiter (TGO), that carries scientific instruments for the detection of trace gases in the Martian atmosphere and for the location of their source regions, plus an Entry, Descent and landing demonstrator Module (EDM), launched on March 14, 2016; and the other, featuring a rover and a surface platform, with a launch date of 2020. On October 19, 2016 TGO was inserted into high elliptic Mars' orbit. The dosimetric telescope Liulin-MO for measuring the radiation environment onboard the ExoMars 2016 TGO is a module of the Fine Resolution Epithermal Neutron Detector (FREND). Here we present first results from measurements of the charged particle fluxes, dose rates, Linear Energy Transfer (LET) spectra and estimation of dose equivalent rates in the interplanetary space during the cruise of TGO to Mars and first results from dosimetric measurements in high elliptic Mars' orbit. A comparison is made with the dose rates obtained by RAD instrument onboard Mars Science Laboratory during the cruise to Mars in 2011-2012 and with the Galactic Cosmic Rays (GCR) count rates provided by other particle detectors currently in space. The average measured dose rate in Si from GCR during the transit to Mars for the period April 22-September 15, 2016 is 372 ± 37 μGy d-1 and 390 ± 39 μGy d-1 in two perpendicular directions. The dose equivalent rate from GCR for the same time period is about 2 ± 0.3 mSv d-1. This is in good agreement with RAD results for radiation dose rate in Si from GCR in the interplanetary space, taking into account the different solar activity during the measurements of both instruments. About 10% increase of the dose rate, and 15% increase of the dose equivalent rate for 10.5 months flight is observed. It is due to the increase of Liulin-MO particle fluxes for that period and corresponds to the overall GCR intensity increase during the declining phase of the solar activity. Data show that during the cruise to Mars and back (6 months in each direction), taken during the declining of solar activity, the crewmembers of future manned flights to Mars will accumulate at least 60% of the total dose limit for the cosmonaut's/astronaut's career in case their shielding conditions are close to the average shielding of Liulin-MO detectors-about 10 g cm-2. The dosimetric measurements in high elliptic Mars' orbit demonstrate strong dependence of the GCR fluxes near the TGO pericenter on satellite's field of view shadowed by Mars.

The motion of an Earth satellite after imposition of a non-holonomic third-order constraint

NASA Astrophysics Data System (ADS)

Dodonov, V. V.; Soltakhanov, Sh. Kh.; Yushkov, M. P.

2018-05-01

We consider the motion of an Earth satellite in the case when, starting from a certain instant of time, the magnitude of its acceleration remains unchanged. This requirement is equivalent to a second-order nonlinear non-holonomic constraint imposed to the satellite motion. The results of calculations are given for the motion of three Soviet satellites, two of which are located on highly elliptical orbits.

The Kaguya Mission Overview

NASA Astrophysics Data System (ADS)

Kato, Manabu; Sasaki, Susumu; Takizawa, Yoshisada

2010-07-01

The Japanese lunar orbiter Kaguya (SELENE) was successfully launched by an H2A rocket on September 14, 2007. On October 4, 2007, after passing through a phasing orbit 2.5 times around the Earth, Kaguya was inserted into a large elliptical orbit circling the Moon. After the apolune altitude was lowered, Kaguya reached its nominal 100 km circular polar observation orbit on October 19. During the process of realizing the nominal orbit, two subsatellites Okina (Rstar) and Ouna (Vstar) were released into elliptical orbits with 2400 km and 800 km apolune, respectively; both elliptical orbits had 100 km perilunes. After the functionality of bus system was verified, four radar antennas and a magnetometer boom were extended, and a plasma imager was deployed. Acquisition of scientific data was carried out for 10 months of nominal mission that began in mid-December 2007. During the 8-month extended mission, magnetic fields and gamma-rays from lower orbits were measured; in addition to this, low-altitude observations were carried out using a Terrain Camera, a Multiband Imager, and an HDTV camera. New data pertaining to an intense magnetic anomaly and GRS data with higher spatial resolution were acquired to study magnetism and the elemental distribution of the Moon. After some orbital maneuvers were performed by using the saved fuel, the Kaguya spacecraft finally impacted on the southeast part of the Moon. The Kaguya team has archived the initial science data, and since November 2, 2009, the data has been made available to public, and can be accessed at the Kaguya homepage of JAXA. The team continues to also study and publish initial results in international journals. Science purposes of the mission and onboard instruments including initial science results are described in this overview.

Introducing Earth's Orbital Eccentricity

ERIC Educational Resources Information Center

Oostra, Benjamin

2015-01-01

Most students know that planetary orbits, including Earth's, are elliptical; that is Kepler's first law, and it is found in many science textbooks. But quite a few are mistaken about the details, thinking that the orbit is very eccentric, or that this effect is somehow responsible for the seasons. In fact, the Earth's orbital eccentricity is…

Optimal Lorentz-augmented spacecraft formation flying in elliptic orbits

NASA Astrophysics Data System (ADS)

Huang, Xu; Yan, Ye; Zhou, Yang

2015-06-01

An electrostatically charged spacecraft accelerates as it moves through the Earth's magnetic field due to the induced Lorentz force, providing a new means of propellantless electromagnetic propulsion for orbital maneuvers. The feasibility of Lorentz-augmented spacecraft formation flying in elliptic orbits is investigated in this paper. Assuming the Earth's magnetic field as a tilted dipole corotating with Earth, a nonlinear dynamical model that characterizes the orbital motion of Lorentz spacecraft in the vicinity of arbitrary elliptic orbits is developed. To establish a predetermined formation configuration at given terminal time, pseudospectral method is used to solve the optimal open-loop trajectories of hybrid control inputs consisted of Lorentz acceleration and thruster-generated control acceleration. A nontilted dipole model is also introduced to analyze the effect of dipole tilt angle via comparisons with the tilted one. Meanwhile, to guarantee finite-time convergence and system robustness against external perturbations, a continuous fast nonsingular terminal sliding mode controller is designed and the closed-loop system stability is proved by Lyapunov theory. Numerical simulations substantiate the validity of proposed open-loop and closed-loop control schemes, and the results indicate that an almost propellantless formation establishment can be achieved by choosing appropriate objective function in the pseudospectral method. Furthermore, compared to the nonsingular terminal sliding mode controller, the closed-loop controller presents superior convergence rate with only a bit more control effort. And the proposed controller can be applied in other Lorentz-augmented relative orbital control problems.

Optimal aeroassisted orbital transfer with plane change using collocation and nonlinear programming

NASA Technical Reports Server (NTRS)

Shi, Yun. Y.; Nelson, R. L.; Young, D. H.

1990-01-01

The fuel optimal control problem arising in the non-planar orbital transfer employing aeroassisted technology is addressed. The mission involves the transfer from high energy orbit (HEO) to low energy orbit (LEO) with orbital plane change. The basic strategy here is to employ a combination of propulsive maneuvers in space and aerodynamic maneuvers in the atmosphere. The basic sequence of events for the aeroassisted HEO to LEO transfer consists of three phases. In the first phase, the orbital transfer begins with a deorbit impulse at HEO which injects the vehicle into an elliptic transfer orbit with perigee inside the atmosphere. In the second phase, the vehicle is optimally controlled by lift and bank angle modulations to perform the desired orbital plane change and to satisfy heating constraints. Because of the energy loss during the turn, an impulse is required to initiate the third phase to boost the vehicle back to the desired LEO orbital altitude. The third impulse is then used to circularize the orbit at LEO. The problem is solved by a direct optimization technique which uses piecewise polynomial representation for the state and control variables and collocation to satisfy the differential equations. This technique converts the optimal control problem into a nonlinear programming problem which is solved numerically. Solutions were obtained for cases with and without heat constraints and for cases of different orbital inclination changes. The method appears to be more powerful and robust than other optimization methods. In addition, the method can handle complex dynamical constraints.

SIMBOL-X: A Formation Flying Mission on HEO for Exploring the Universe

NASA Technical Reports Server (NTRS)

Gamet, Philippe; Epenoy, R.; Salcedo, C.

2007-01-01

SIMBOL-X is a high energy new generation telescope covering by a single instrument a continuous energy range starting at classical X-rays and extending to hard X-rays, i.e. from 0.5 to 80 keV. It is using in this field a focalizing payload which until now was used for energy below 10 keV only, via the construction of a telescope distributed on two satellites flying in formation. SIMBOL-X permits a gain of two orders of magnitude in sensibility and spatial resolution in comparison to state of the art hard X-rays instruments. The mirror satellite will be in free flight on a high elliptical orbit and will target the object to observe very precisely, thus focusing the hard X-ray emission thanks to this mirror module. At the focal point area which is situated 20 meters behind the mirror satellite, the detector satellite maintains its position on a forced orbit thanks to a radio link with the mirror satellite and a lateral displacement sensor using a beam emitted onboard the mirror satellite. This configuration is said "formation flying". The location of the detector satellite shall be very finely tuned as it carries the focal plane of this distributed telescope. To provide science measurements, the Simbol-X orbit has been chosen High elliptic (HEO), which means elliptical orbit with a high perigee altitude. Preliminary studies where made with an orbit with an altitude of the perigee of 44000km and altitude of the apogee of 253000km. The orbit was seven days ground track repeated in order to maintain a perigee pass over the Malindi ground station to download scientific telemetry. But as studies went on, difficulties in mass budget, link budget, perigee maintenance and formation flying maintenance were raised. This was mainly due to the vicinity of the Moon and its disturbing effect on the satellites orbits. Alternative orbits have been proposed in order to demonstrate the feasibility of the mission. The problematic of bringing the two satellites from their injection orbit to their operational orbit 20 m apart from each other and then maintain this configuration is very challenging. It requires theoretical development of the relative motion between two satellites in high eccentric orbit with large differential disturbance on the two bodies. This paper will present the mission analysis for the Simbol-X satellites with the complex problematic of doing formation flying in high elliptic orbit.

The ELLIPSO (tm) system: Elliptical low orbits for mobile communications and other optimum system elements

NASA Technical Reports Server (NTRS)

Castiel, David

1991-01-01

On 5 Nov. 1990, Ellipsat filed with the FCC the first application to provide voice communication services via low earth orbiting (LEO) satellites. The proposed system, ELLIPSO, aims at achieving end-user costs comparable to those in the cellular industry. On 3 Jun. 1991 Ellipsat filed for the second complement of its system. Ellipsat was also the first company to propose combined position determination and mobile voice services via low-earth orbiting satellites. Ellipsat is still the only proponent of elliptical orbits for any commercial system in the United States. ELLIPSO uses a spectrum efficient combination of FDMA and CDMA techniques. Ellipsat's strategy is to tailor required capacity to user demand, reduce initial system costs and investment risks, and allow the provision of services at affordable end-user prices. ELLIPSO offers optimum features in all the components of its system, elliptical orbits, small satellites, integrated protocol and signalling system, integrated end-user electronics, novel marketing approach based on the cooperation with the tenets of mobile communications, end-user costs that are affordable, and a low risk approach as deployment is tailored to the growth of its customer base. The efficient design of the ELLIPSO constellation and system allows estimated end-user costs in the $.50 per minute range, five to six times less than any other system of comparable capability.

Resolving the Problem of Stellar Orbital Anisotropy

NASA Astrophysics Data System (ADS)

Humphrey, Philip

2006-09-01

Mass profiles of elliptical galaxies provide an insight into dark matter (DM) halo formation, while orbital structure is tied to evolutionary history. Unfortunately the mass-anisotropy degeneracy prevents either from being uniquely determined by stellar kinematics measurements alone. A recent controversy suggesting no DM in elliptical galaxies may be explained by this effect, illustrating the urgent need for better constraints. We propose a 75ks Chandra exposure of NGC4649 to break this degeneracy in a carefully-chosen galaxy. Combined with our deep optical spectra and PN and GC kinematics, this will provide definitive constraints on the mass and orbital anisotropy profiles. By combining all techniques for one galaxy, this will provide a textbook example of how to overcome the degeneracy.

Sustainer electric propulsion system application for spacecraft attitude control

NASA Astrophysics Data System (ADS)

Obukhov, V. A.; Pokryshkin, A. I.; Popov, G. A.; Yashina, N. V.

2010-07-01

Application of electric propulsion system (EPS) requires spacecraft (SC) equipping with large solar panels (SP) for the power supply to electric propulsions. This makes the problem of EPS-equipped SC control at the insertion stage more difficult to solve than in the case of SC equipped with chemical engines, because in addition to the SC attitude control associated with the mission there appears necessity in keeping SP orientation to Sun that is necessary for generation of electric power sufficient for the operation of service systems, purpose-oriented equipment, and EPS. The theoretical study of the control problem is the most interesting for a non-coplanar transfer from high elliptic orbit (HEO) to geostationary orbit (GSO).

IMS/Satellite Situation Center report

NASA Technical Reports Server (NTRS)

1973-01-01

Services planned by the Satellite Situation Center during the International Magnetospheric Study are briefly described. User requirements are emphasized. The following data are presented: orbital parameters for ISIS 2, ESRO 4, and HEOS 2; entry exit times for highly elliptical satellites; plots for highly elliptical earth satellites; and plots and flux tube intersection for low altitude satellites.

Nominal Profile Refinements Report: Target in 120 Nautical Mile Circular Orbit

NASA Technical Reports Server (NTRS)

1974-01-01

The compability of the nominal rendezvous sequence with low target orbits is addressed. It was found that for targets in low earth orbits certain modifications of the nominal sequence are required to achieve a feasible anytime liftoff capability, notably the use of elliptical phasing orbits and the allowance of up to two days for rendezvous under certain phasing conditions.

Optical Communications Study for the Next Generation Space Telescope

NASA Technical Reports Server (NTRS)

Ceniceros, Juan M.

2000-01-01

The Next Generation Space Telescope (NGST), part of NASA's Origins program, is a follow on to the Hubble Space Telescope expected to provide timely new science along with answering fundamental questions. NGST is a large diameter, infrared optimized telescope with imaging and spectrographic detectors which will be used to help study the origin of galaxies. Due to the large data NGST will collect, Goddard Space Flight Center has considered the use of optical communications for data downlink. The Optical Communications Group at the Jet Propulsion Laboratory has performed a study on optical communications systems for NGST. The objective of the study was to evaluate the benefits gained through the use of optical communication technologies. Studies were performed for each of four proposed NGST orbits. The orbits considered were an elliptical orbit about the semi stable second Lagrangian point, a 1 by 3 AU elliptic orbit around the sun, a 1 AU drift orbit, and a 1 AU drift orbit at a 15 degree incline to the ecliptic plane. An appropriate optical communications system was determined for each orbit. Systems were evaluated in terms of mass, power consumption, size, and cost for each of the four proposed orbits.

Searching for orbits around the triple system 45 Eugenia

NASA Astrophysics Data System (ADS)

Mescolotti, B. Y. P. M.; Prado, A. F. B. A.; Chiaradia, A. P. M.; Gomes, V. M.

2017-10-01

Asteroids are small bodies that raises high interest, because they have unknown characteristics. The present research aims to study orbits for a spacecraft around the triple asteroid 45 Eugenia. The quality of the observations made by the spacecraft depends on the distance the spacecraft remains from the bodies of the system. It is used a semi-analytical model that is simple but able to represent the main characteristics of that system. This model is called “Precessing Inclined Bi-Elliptical Problem” (PIBEP). A reference system centered on the main body (Eugenia) and with the reference plane assumed to be in the orbital plane of the second more massive body, here called Petit-Prince, is used. The secondary bodies are assumed to be in elliptical orbits. In addition, it is assumed that the orbits of the smaller bodies are precessing due to the presence of the flattening of the main body (J2). This work analyzes orbits for the spacecraft with passages near Petit-Prince and Princesses, which are the two smaller bodies of the triple system.

Equilibrium Solutions of the Logarithmic Hamiltonian Leapfrog for the N-body Problem

NASA Astrophysics Data System (ADS)

Minesaki, Yukitaka

2018-04-01

We prove that a second-order logarithmic Hamiltonian leapfrog for the classical general N-body problem (CGNBP) designed by Mikkola and Tanikawa and some higher-order logarithmic Hamiltonian methods based on symmetric multicompositions of the logarithmic algorithm exactly reproduce the orbits of elliptic relative equilibrium solutions in the original CGNBP. These methods are explicit symplectic methods. Before this proof, only some implicit discrete-time CGNBPs proposed by Minesaki had been analytically shown to trace the orbits of elliptic relative equilibrium solutions. The proof is therefore the first existence proof for explicit symplectic methods. Such logarithmic Hamiltonian methods with a variable time step can also precisely retain periodic orbits in the classical general three-body problem, which generic numerical methods with a constant time step cannot do.

Study on the effect of ellipticity and misalignment on OAM modes in a ring fiber

NASA Astrophysics Data System (ADS)

Zhang, Li-li; Zhang, Xia; Bai, Cheng-lin

2018-05-01

Based on the optical fiber mode theory and employing the expertized software COMSOL, we study the effect of ellipticity and misalignment on the effective refractive indices, walk-off and intensity distribution of the even and odd eigenmodes that form the basis of the orbital angular momentum (OAM) modes in a ring fiber. Our results show that the effective refractive index difference and the walk-off increase with the ellipticity and misalignment, thus reducing the stability of the OAM modes. We find that the misalignment has a greater impact on the OAM modes than the ellipticity, and both the misalignment and ellipticity affect the lower-order OAM modes more significantly, suggesting that the higher-order OAM modes are more stable during propagation.

Hot SPOT Eclipses in Dwarf Novae

NASA Astrophysics Data System (ADS)

Smak, J.

1996-10-01

Eclipses of the hot spot in four dwarf novae: U Gem, IP Peg, Z Cha, and OY Car are re-analyzed, assuming two models for the shape of the spot. In Model 1 an elliptical spot is assumed, with the semi-axes s_a in the orbital plane and s_b perpendicular to the orbital plane, its center located on the stream trajectory. The results show that such an ellipse is, within errors, tangent to the disk's circumference. In all four cases the resulting dimensions of the spot s_a are larger than the theoretical cross-section of the stream. Accordingly, in Model2 the spot is assumed to consist of a head, centered on the stream trajectory, and a tail, extending downstream, ie., along disk's circumference. In some cases the resulting parameters, eg., mass ratios or disk radii, differ significantly from those obtained with Model 1.

Spiraling elliptic Laguerre-Gaussian soliton in isotropic nonlocal competing cubic-quintic nonlinear media

NASA Astrophysics Data System (ADS)

Wang, Qing; Li, JingZhen; Xie, WeiXin

2018-06-01

This paper introduce a kind of spiraling elliptic Laguerre-Gaussian (SELG) soliton which has complicated structures in its profile and phase, and find that it can be formed in nonlocal cubic, quantic and competing cubic-quintic nonlinear media, respectively. The different-order SELG solitons with the same ellipticity have the same rotation period, cross-term phase coefficient, critical power and different critical orbital angular momentums (OAM). However, with the increase of ellipticity, the rotation period, cross-term phase coefficient, critical power and OAM are all increased. In particular, there are bistable SELG solitons stemmed by the competing effect between self-focusing cubic and self-defocusing quintic nonlinearities.

Direct Measurement of the Topological Charge in Elliptical Beams Using Diffraction by a Triangular Aperture.

PubMed

Melo, Leandro A; Jesus-Silva, Alcenísio J; Chávez-Cerda, Sabino; Ribeiro, Paulo H Souto; Soares, Willamys C

2018-04-23

We introduce a simple method to characterize the topological charge associated with the orbital angular momentum of a m-order elliptic light beam. This method consists in the observation of the far field pattern of the beam carrying orbital angular momentum, diffracted from a triangular aperture. We show numerically and experimentally, for Mathieu, Ince-Gaussian, and vortex Hermite-Gaussian beams, that only isosceles triangular apertures allow us to determine in a precise and direct way, the magnitude m of the order and the number and sign of unitary topological charges of isolated vortices inside the core of these beams.

Analysis of Hansen's Inferior and Superior Partial Anomalies and the Division of the Elliptic Orbit into Two Segments

NASA Astrophysics Data System (ADS)

Sharaf, M. A.; Saad, A. S.

2017-10-01

In this paper, a novel analysis was established to prove how Hansen's inferior and superior partial anomalies k and k_1 can divide the elliptic orbit into two segments. The analysis depends on the departures of r (for k) and 1/r (for k1) from their minima. By these departures, we can find: (i) Transformations relating the eccentric anomaly to k and the true anomaly to k1. (ii) Expressions for k and k_1 in terms of the orbital elements. (iii) The interpretation and the intervals of definition of two moduli (X, S) related to k and k_1. (iv) The extreme values of r and the elliptic equations in terms of k and k1. (v) For r' and r'', the modulus X as a measure of the asymmetry of r' (or r'') from r'' (or r'), and the modulus S12 as a measure of the asymmetry of r' and r'' from the minimum value of r. (vi) A description of the segments represented by k and k1. (vii) The relative position of the radius vector at k0° and k1=180°.

Formation flying for electric sails in displaced orbits. Part II: Distributed coordinated control

NASA Astrophysics Data System (ADS)

Wang, Wei; Mengali, Giovanni; Quarta, Alessandro A.; Yuan, Jianping

2017-09-01

We analyze a cooperative control framework for electric sail formation flying around a heliocentric displaced orbit, aiming at observing the polar region of a celestial body. The chief spacecraft is assumed to move along an elliptic displaced orbit, while each deputy spacecraft adjusts its thrust vector (that is, both its sail attitude and characteristic acceleration) in order to track a prescribed relative trajectory. The relative motion of the electric sail formation system is formulated in the chief rotating frame, where the control inputs of each deputy are the relative sail attitude angles and the relative lightness number with respect to those of the chief. The information exchange among the spacecraft, characterized by the communication topology, is represented by a weighted graph. Two typical cases, according to whether the communication graph is directed or undirected, are discussed. For each case, a distributed coordinated control law is designed in such a way that each deputy not only tracks the chief state, but also makes full use of information from its neighbors, thus increasing the redundancy and robustness of the formation system in case of failure among the communication links. Illustrative examples show the effectiveness of the proposed approach.

The rotational motion of an earth orbiting gyroscope according to the Einstein theory of general relativity

NASA Technical Reports Server (NTRS)

Hoots, F. R.; Fitzpatrick, P. M.

1979-01-01

The classical Poisson equations of rotational motion are used to study the attitude motions of an earth orbiting, rapidly spinning gyroscope perturbed by the effects of general relativity (Einstein theory). The center of mass of the gyroscope is assumed to move about a rotating oblate earth in an evolving elliptic orbit which includes all first-order oblateness effects produced by the earth. A method of averaging is used to obtain a transformation of variables, for the nonresonance case, which significantly simplifies the Poisson differential equations of motion of the gyroscope. Long-term solutions are obtained by an exact analytical integration of the simplified transformed equations. These solutions may be used to predict both the orientation of the gyroscope and the motion of its rotational angular momentum vector as viewed from its center of mass. The results are valid for all eccentricities and all inclinations not near the critical inclination.

Post-Newtonian direct and mixed orbital effects due to the oblateness of the central body

NASA Astrophysics Data System (ADS)

Iorio, L.

2015-06-01

The orbital dynamics of a test particle moving in the nonspherically symmetric field of a rotating oblate primary is impacted also by certain indirect, mixed effects arising from the interplay of the different Newtonian and post-Newtonian accelerations which induce known direct perturbations. We systematically calculate the indirect gravitoelectromagnetic shifts per orbit of the Keplerian orbital elements of the test particle arising from the crossing among the first even zonal harmonic J2 of the central body and the post-Newtonian static and stationary components of its gravitational field. We also work out the Newtonian shifts per orbit of order J22, and the direct post-Newtonian gravitoelectric effects of order J2c-2 arising from the equations of motion. In the case of both the indirect and direct gravitoelectric J2c-2 shifts, our calculation holds for an arbitrary orientation of the symmetry axis of the central body. We yield numerical estimates of their relative magnitudes for systems ranging from Earth's artificial satellites to stars orbiting supermassive black holes. As far as their measurability is concerned, highly elliptical orbital configuration are desirable.

A Compact Trench-Assisted Multi-Orbital-Angular-Momentum Multi-Ring Fiber for Ultrahigh-Density Space-Division Multiplexing (19 Rings × 22 Modes)

PubMed Central

Li, Shuhui; Wang, Jian

2014-01-01

We present a compact (130 μm cladding diameter) trench-assisted multi-orbital-angular-momentum (OAM) multi-ring fiber with 19 rings each supporting 22 modes with 18 OAM ones. Using the high-contrast-index ring and trench designs, the trench-assisted multi-OAM multi-ring fiber (TA-MOMRF) features both low-level inter-mode crosstalk and inter-ring crosstalk within a wide wavelength range (1520 to 1630 nm), which can potentially enable Pbit/s total transmission capacity and hundreds bit/s/Hz spectral efficiency in a single TA-MOMRF. Moreover, the effective refractive index difference of even and odd fiber eigenmodes induced by the ellipticity of ring and fiber bending and their impacts on the purity of OAM mode and mode coupling/crosstalk are analyzed. It is found that high-order OAM modes show preferable tolerance to the ring ellipticity and fiber bending. The designed fiber offers favorable tolerance to both small ellipticity of ring (<−22 dB crosstalk under an ellipticity of 0.5%) and small bend radius (<−20 dB crosstalk under a bend radius of 2 cm). PMID:24458159

The envelope of ballistic trajectories and elliptic orbits

NASA Astrophysics Data System (ADS)

Butikov, Eugene I.

2015-11-01

Simple geometric derivations are given for the shape of the "safety domain" boundary for the family of Keplerian orbits of equal energy in a central gravitational field and for projectile trajectories in a uniform field. Examples of practical uses of the envelope of the family of orbits are discussed and illustrated by computer simulations. This material is appropriate for physics teachers and undergraduate students studying classical mechanics and orbital motions.

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

NASA Technical Reports Server (NTRS)

Fraietta, Michael F.; Bond, Victor R.

1993-01-01

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

Optical Variability Signatures from Massive Black Hole Binaries

NASA Astrophysics Data System (ADS)

Kasliwal, Vishal P.; Frank, Koby Alexander; Lidz, Adam

2017-01-01

The hierarchical merging of dark matter halos and their associated galaxies should lead to a population of supermassive black hole binaries (MBHBs). We consider plausible optical variability signatures from MBHBs at sub-parsec separations and search for these using data from the Catalina Real-Time Transient Survey (CRTS). Specifically, we model the impact of relativistic Doppler beaming on the accretion disk emission from the less massive, secondary black hole. We explore whether this Doppler modulation may be separated from other sources of stochastic variability in the accretion flow around the MBHBs, which we describe as a damped random walk (DRW). In the simple case of a circular orbit, relativistic beaming leads to a series of broad peaks — located at multiples of the orbital frequency — in the fluctuation power spectrum. We extend our analysis to the case of elliptical orbits and discuss the effect of beaming on the flux power spectrum and auto-correlation function using simulations. We present a code to model an observed light curve as a stochastic DRW-type time series modulated by relativistic beaming and apply the code to CRTS data.

Compact normalisations in the elliptic restricted three body problem

NASA Astrophysics Data System (ADS)

Palacián, Jesús F.; Vanegas, Jasson; Yanguas, Patricia

2017-11-01

This paper considers the spatial elliptic restricted three body problem in the case that the particle with negligible mass is revolving around one of the primaries. The system is modelled in an inertial frame through a Hamiltonian function representing a non-autonomous dynamical system with three degrees of freedom that depends periodically on time. Three Lie transformations are applied at first order to eliminate successively the mean anomaly of the infinitesimal particle's motion, the time dependence of the system and the argument of the node of the particle with negligible mass. All the transformations are implemented in a compact way, that is, carrying out the computations by means of infinite series. This approach can be very useful to deal with certain artificial satellite problems or, in general, with systems such that the ratio between the distance of the infinitesimal particle to the body around it orbits and the distance between the two primaries is smaller than one but close to it. In this case the Legendre expansion of the potential converges slowly and many terms of the series must be taken into consideration.

Orbit determination of highly elliptical Earth orbiters using improved Doppler data-processing modes

NASA Technical Reports Server (NTRS)

Estefan, J. A.

1995-01-01

A navigation error covariance analysis of four highly elliptical Earth orbits is described, with apogee heights ranging from 20,000 to 76,800 km and perigee heights ranging from 1,000 to 5,000 km. This analysis differs from earlier studies in that improved navigation data-processing modes were used to reduce the radio metric data. For this study, X-band (8.4-GHz) Doppler data were assumed to be acquired from two Deep Space Network radio antennas and reconstructed orbit errors propagated over a single day. Doppler measurements were formulated as total-count phase measurements and compared to the traditional formulation of differenced-count frequency measurements. In addition, an enhanced data-filtering strategy was used, which treated the principal ground system calibration errors affecting the data as filter parameters. Results suggest that a 40- to 60-percent accuracy improvement may be achievable over traditional data-processing modes in reconstructed orbit errors, with a substantial reduction in reconstructed velocity errors at perigee. Historically, this has been a regime in which stringent navigation requirements have been difficult to meet by conventional methods.

SODA In Train Swarm Example

NASA Image and Video Library

2017-07-13

SODA, Swarm Orbital Dynamics Advisor, a tool that provides the orbital maneuvers required to achieve a desired type of relative swarm motion for satellite missions. For the in-train swarm type, the objective is to phase the satellites ahead and behind one another to achieve a string-of-pearls relative position configuration. SODA maneuvers each satellite by performing a two-impulse elliptical transfer orbit from and back to the same orbit, known as a phasing maneuver.

Optimal Control Strategies for Constrained Relative Orbits

DTIC Science & Technology

2007-09-01

the chief. The work assumes the Clohessy - Wiltshire closeness assump- tion between the deputy and chief is valid, however, elliptical chief orbits are...133 Appendix G. A Closed-Form Solution of the Linear Clohessy - Wiltshire Equa- tions...Counterspace . . . . . . . . . . . . . . . . . . . 1 CW Clohessy - Wiltshire . . . . . . . . . . . . . . . . . . . . . . 4 DARPA Defense Advanced Research

Derivation of capture probabilities for the corotation eccentric mean motion resonances

NASA Astrophysics Data System (ADS)

El Moutamid, Maryame; Sicardy, Bruno; Renner, Stéfan

2017-08-01

We study in this paper the capture of a massless particle into an isolated, first-order corotation eccentric resonance (CER), in the framework of the planar, eccentric and restricted three-body problem near a m + 1: m mean motion commensurability (m integer). While capture into Lindblad eccentric resonances (where the perturber's orbit is circular) has been investigated years ago, capture into CER (where the perturber's orbit is elliptic) has not yet been investigated in detail. Here, we derive the generic equations of motion near a CER in the general case where both the perturber and the test particle migrate. We derive the probability of capture in that context, and we examine more closely two particular cases: (I) if only the perturber is migrating, capture is possible only if the migration is outward from the primary. Notably, the probability of capture is independent of the way the perturber migrates outward; (II) if only the test particle is migrating, then capture is possible only if the algebraic value of its migration rate is a decreasing function of orbital radius. In this case, the probability of capture is proportional to the radial gradient of migration. These results differ from the capture into Lindblad eccentric resonance (LER), where it is necessary that the orbits of the perturber and the test particle converge for capture to be possible.

Model predictive control for spacecraft rendezvous in elliptical orbit

NASA Astrophysics Data System (ADS)

Li, Peng; Zhu, Zheng H.

2018-05-01

This paper studies the control of spacecraft rendezvous with attitude stable or spinning targets in an elliptical orbit. The linearized Tschauner-Hempel equation is used to describe the motion of spacecraft and the problem is formulated by model predictive control. The control objective is to maximize control accuracy and smoothness simultaneously to avoid unexpected change or overshoot of trajectory for safe rendezvous. It is achieved by minimizing the weighted summations of control errors and increments. The effects of two sets of horizons (control and predictive horizons) in the model predictive control are examined in terms of fuel consumption, rendezvous time and computational effort. The numerical results show the proposed control strategy is effective.

YORP: Influence on Rotation Rate

NASA Astrophysics Data System (ADS)

Golubov, A. A.; Krugly, Yu. N.

2010-06-01

We have developed a semi-analytical model for calculating angular acceleration of asteroids due to Yarkovsky-O'Keefe-Radzievskii-Paddack (YORP) effect. The calculation of the YORP effect has been generalized for the case of elliptic orbits. It has been shown that the acceleration does not depend on thermal inertia of the asteroid's surface. The model was applied to the asteroid 1620 Geographos and led to acceleration 2×10^{-18}s^{-2}. This value is close to the acceleration obtained from photometric observations of Geographos by Durech et al. [1].

Non-linear tides in a homogeneous rotating planet or star: global modes and elliptical instability

NASA Astrophysics Data System (ADS)

Barker, Adrian J.; Braviner, Harry J.; Ogilvie, Gordon I.

2016-06-01

We revisit the global modes and instabilities of homogeneous rotating ellipsoidal fluid masses, which are the simplest global models of rotationally and tidally deformed gaseous planets or stars. The tidal flow in a short-period planet may be unstable to the elliptical instability, a hydrodynamic instability that can drive tidal evolution. We perform a global (and local WKB) analysis to study this instability using the elegant formalism of Lebovitz & Lifschitz. We survey the parameter space of global instabilities with harmonic orders ℓ ≤ 5, for planets with spins that are purely aligned (prograde) or anti-aligned (retrograde) with their orbits. In general, the instability has a much larger growth rate if the planetary spin and orbit are anti-aligned rather than aligned. We have identified a violent instability for anti-aligned spins outside of the usual frequency range for the elliptical instability (when n/Ω ≲ -1, where n and Ω are the orbital and spin angular frequencies, respectively) if the tidal amplitude is sufficiently large. We also explore the instability in a rigid ellipsoidal container, which is found to be quantitatively similar to that with a realistic free surface. Finally, we study the effect of rotation and tidal deformation on mode frequencies. We find that larger rotation rates and larger tidal deformations both decrease the frequencies of the prograde sectoral surface gravity modes. This increases the prospect of their tidal excitation, potentially enhancing the tidal response over expectations from linear theory. In a companion paper, we use our results to interpret global simulations of the elliptical instability.

Coupled Attitude and Orbit Dynamics and Control in Formation Flying Systems

NASA Technical Reports Server (NTRS)

Xu, Yun-Jun; Fitz-Coy, Norman; Mason, Paul

2003-01-01

Formation flying systems can range from global constellations offering extended service coverage to clusters of highly coordinated vehicles that perform distributed sensing. Recently, the use of groups of micro-satellites in the areas of near Earth explorations, deep space explorations, and military applications has received considerable attention by researchers and practitioners. To date, most proposed control strategies are based on linear models (e.g., Hill-Clohessy-Wiltshire equations) or nonlinear models that are restricted to circular reference orbits. Also, all models in the literature are uncoupled between relative position and relative attitude. In this paper, a generalized dynamic model is proposed. The reference orbit is not restricted to the circular case. In this formulation, the leader or follower satellite can be in either a circular or an elliptic orbit. In addition to maintaining a specified relative position, the satellites are also required to maintain specified relative attitudes. Thus the model presented couples vehicle attitude and orbit requirements. Orbit perturbations are also included. In particular, the J(sub 2) effects are accounted in the model. Finally, a sliding mode controller is developed and used to control the relative attitude of the formation and the simulation results are presented.

Unique Properties and Prospects: Quantum Theory of the Orbital Angular Momentum of Ince-Gauss Beams

NASA Astrophysics Data System (ADS)

Plick, William; Krenn, Mario; Fickler, Robert; Ramelow, Sven; Zeilinger, Anton

2012-02-01

The Ince-Gauss modes represent a new addition to the standard solutions to the paraxial wave equation. Parametrized by the ellipticity of the beam, they span the solution space between the Hermite-Gauss and the Laguerre-Gauss modes. These beams may be decomposed in either basis, and single photons in the Ince-Gauss modes exist naturally as superpositions of either Laguerre-Gauss or Hermite-Gauss modes. We present the fully quantum theory of the orbital angular momentum of these beams. Interesting features that arise are: stable beams with fractional orbital angular momentum, non-monotonic behavior of the OAM with respect to ellipticity, and the possibility of orthogonal modes possessing the same OAM. We believe that these modes may open up a fully new parameter space for quantum informatics and communication, and thus are worthy of thorough study.

Atlas-Centaur AC-18 performance evaluation for Applications Technology Satellite ATS-5 mission

NASA Technical Reports Server (NTRS)

1971-01-01

The Atlas-Centaur with the ATS-5 spacecraft was successfully launched from Eastern Test Range on August 12, 1969, and the ATS-5 was placed in the required highly elliptical transfer orbit with apogee near synchronous altitude. From this orbit the ATS-5, using its apogee motor, achieved the desired near-synchronous circular equatorial orbit. All launch vehicle systems performed satisfactorily.

Introduction to Astrodynamic Reentry

DTIC Science & Technology

2009-09-09

be used in most instances throughout this text. Two elements (semimajor axis a and eccentricity e ) describe the size and shape of the orbit ...Figure 2-3 already shows how the semimajor axis defines the size or the orbit . The eccentricity describes the shape: 0e  is circular, 0 1e  is...elliptical, 1e  is parabolic, and 1e  is hyperbolic. Orbital inclination i and right ascension of the ascending node  define how the orbit

A simple method to design non-collision relative orbits for close spacecraft formation flying

NASA Astrophysics Data System (ADS)

Jiang, Wei; Li, JunFeng; Jiang, FangHua; Bernelli-Zazzera, Franco

2018-05-01

A set of linearized relative motion equations of spacecraft flying on unperturbed elliptical orbits are specialized for particular cases, where the leader orbit is circular or equatorial. Based on these extended equations, we are able to analyze the relative motion regulation between a pair of spacecraft flying on arbitrary unperturbed orbits with the same semi-major axis in close formation. Given the initial orbital elements of the leader, this paper presents a simple way to design initial relative orbital elements of close spacecraft with the same semi-major axis, thus preventing collision under non-perturbed conditions. Considering the mean influence of J 2 perturbation, namely secular J 2 perturbation, we derive the mean derivatives of orbital element differences, and then expand them to first order. Thus the first order expansion of orbital element differences can be added to the relative motion equations for further analysis. For a pair of spacecraft that will never collide under non-perturbed situations, we present a simple method to determine whether a collision will occur when J 2 perturbation is considered. Examples are given to prove the validity of the extended relative motion equations and to illustrate how the methods presented can be used. The simple method for designing initial relative orbital elements proposed here could be helpful to the preliminary design of the relative orbital elements between spacecraft in a close formation, when collision avoidance is necessary.

Hubble Views a Galactic Mega-merger

NASA Image and Video Library

2016-01-15

The subject of this NASA/ESA Hubble Space Telescope image is known as NGC 3597. It is the product of a collision between two good-sized galaxies, and is slowly evolving to become a giant elliptical galaxy. This type of galaxy has grown more and more common as the universe has evolved, with initially small galaxies merging and progressively building up into larger galactic structures over time. NGC 3597 is located approximately 150 million light-years away in the constellation of Crater (The Cup). Astronomers study NGC 3597 to learn more about how elliptical galaxies form — many ellipticals began their lives far earlier in the history of the universe. Older ellipticals are nicknamed “red and dead” by astronomers because these bloated galaxies are not anymore producing new, bluer stars, and are thus packed full of old and redder stellar populations. Before infirmity sets in, some freshly formed elliptical galaxies experience a final flush of youth, as is the case with NGC 3597. Galaxies smashing together pool their available gas and dust, triggering new rounds of star birth. Some of this material ends up in dense pockets initially called proto-globular clusters, dozens of which festoon NGC 3597. These pockets will go on to collapse and form fully-fledged globular clusters, large spheres that orbit the centers of galaxies like satellites, packed tightly full of millions of stars. Image credit: ESA/Hubble & NASA, Acknowledgement: Judy Schmidt 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

Trajectories of ballistic impact ejecta on a rotating Earth

NASA Technical Reports Server (NTRS)

Alvarez, W.

1994-01-01

On an airless, slowly rotating planetary body like the Moon, ejecta particles from an impact follow simple ballistic trajectories. If gaseous interactions in the fireball are ignored, ejecta particles follow elliptical orbits with the center of the planetary body at one focus until they encounter the surface at the point of reimpact. The partial elliptical orbit of the ejecta particle lies in a plane in inertial (galactic) coordinates. Because of the slow rotation rate (for example, 360 degrees/28 days for the Moon), the intersection of the orbital plane and the surface remains nearly a great circle during the flight time of the ejecta. For this reason, lunar rays, representing concentrations of ejecta with the same azimuth but different velocities and/or ejecta angles, lie essentially along great circles. Ejecta from airless but more rapidly rotating bodies will follow more complicated, curving trajectories when plotted in the coordinate frame of the rotating planet or viewed as rays on the planetary surface. The curvature of trajectories of ejecta particles can be treated as a manifestation of the Coriolis effect, with the particles being accelerated by Coriolis pseudoforces. However, it is more straightforward to calculate the elliptical orbit in inertial space and then determine how far the planet rotates beneath the orbiting ejecta particle before reimpact. The Earth's eastward rotation affects ballistic ejecta in two ways: (1) the eastward velocity component increases the velocity of eastbound ejecta and reduces the velocity of westbound ejecta; and (2) the Earth turns underneath inflight ejecta, so that although the latitude of reimpact is not changed, the longitude is displaced westward, with the displacement increasing as a function of the time the ejecta remains aloft.

Minimum fuel coplanar aeroassisted orbital transfer using collocation and nonlinear programming

NASA Technical Reports Server (NTRS)

Shi, Yun Yuan; Young, D. H.

1991-01-01

The fuel optimal control problem arising in coplanar orbital transfer employing aeroassisted technology is addressed. The mission involves the transfer from high energy orbit (HEO) to low energy orbit (LEO) without plane change. The basic approach here is to employ a combination of propulsive maneuvers in space and aerodynamic maneuvers in the atmosphere. The basic sequence of events for the coplanar aeroassisted HEO to LEO orbit transfer consists of three phases. In the first phase, the transfer begins with a deorbit impulse at HEO which injects the vehicle into a elliptic transfer orbit with perigee inside the atmosphere. In the second phase, the vehicle is optimally controlled by lift and drag modulation to satisfy heating constraints and to exit the atmosphere with the desired flight path angle and velocity so that the apogee of the exit orbit is the altitude of the desired LEO. Finally, the second impulse is required to circularize the orbit at LEO. The performance index is maximum final mass. Simulation results show that the coplanar aerocapture is quite different from the case where orbital plane changes are made inside the atmosphere. In the latter case, the vehicle has to penetrate deeper into the atmosphere to perform the desired orbital plane change. For the coplanar case, the vehicle needs only to penetrate the atmosphere deep enough to reduce the exit velocity so the vehicle can be captured at the desired LEO. The peak heating rates are lower and the entry corridor is wider. From the thermal protection point of view, the coplanar transfer may be desirable. Parametric studies also show the maximum peak heating rates and the entry corridor width are functions of maximum lift coefficient. The problem is solved using a direct optimization technique which uses piecewise polynomial representation for the states and controls and collocation to represent the differential equations. This converts the optimal control problem into a nonlinear programming problem which is solved numerically by using a modified version of NPSOL. Solutions were obtained for the described problem for cases with and without heating constraints. The method appears to be more robust than other optimization methods. In addition, the method can handle complex dynamical constraints.

USSR and Eastern Europe Scienitific Abstracts, Geophysics, Astronomy and Space. Number 399

DTIC Science & Technology

1977-06-10

Orbit 47 TASS Announces Launching of "Molniya-3" Communications Satellite 47 Abstracts of Scientific Articles 49 Inhomogeneities of Electron...Directions in Space Technology 52 Motion of Body of Variable Rest Mass in Gravity Field 52 Orbits in Applied Problems of Celestial Mechanics..... 53...Satellite Oscillations in Plane of Elliptical Orbit 53 Submillimeter Radiation of Convective Cloud Systems 54 Combined Braking of Spacecraft in

Source Book of the Solar-Geophysical Environment.

DTIC Science & Technology

1982-08-01

Radio Sun ..... es ...... 96 8.5.3.1 Noise Storms. ........... ......... ....... 97 8.5.3.2 Sweep Radio Bursts........ . ................... 97 8.5.3.3...handler, a que ~ language to allow the data monitor to’interact with the data base, ancl. event analysis software to associate and display the data...elliptical orbit is always possible, but so are other orbits-- circles, parabolas , or hyperbolas. Different orbits can be obtained by altering the

Multisatellite constellation configuration selection for multiregional highly elliptical orbit constellations

NASA Technical Reports Server (NTRS)

Matossian, Mark G.

1994-01-01

The Archimedes Project is a joint effort of the European Space Agency (ESA) and the National Space Development Agency of Japan (NASDA). The primary goal of the Archimedes project is to perform a technical feasibility analysis and preliminary design of a highly inclined multisatellite constellation for direct broadcast and mobile communications services for Europe, Japan and much of North America. This report addresses one aspect of this project, specifically an analysis of continuous satellite coverage using multiregional highly elliptical orbits (M-HEO's). The analysis methodology and ensuing software tool, named SPIFF, were developed specifically for this project by the author during the summer of 1992 under the STA/NSF Summer Institute in Japan Program at Tsukuba Space Center.

Artificial equilibrium points for a generalized sail in the elliptic restricted three-body problem

NASA Astrophysics Data System (ADS)

Aliasi, Generoso; Mengali, Giovanni; Quarta, Alessandro A.

2012-10-01

Different types of propulsion systems with continuous and purely radial thrust, whose modulus depends on the distance from a massive body, may be conveniently described within a single mathematical model by means of the concept of generalized sail. This paper discusses the existence and stability of artificial equilibrium points maintained by a generalized sail within an elliptic restricted three-body problem. Similar to the classical case in the absence of thrust, a generalized sail guarantees the existence of equilibrium points belonging only to the orbital plane of the two primaries. The geometrical loci of existing artificial equilibrium points are shown to coincide with those obtained for the circular three body problem when a non-uniformly rotating and pulsating coordinate system is chosen to describe the spacecraft motion. However, the generalized sail has to provide a periodically variable acceleration to maintain a given artificial equilibrium point. A linear stability analysis of the artificial equilibrium points is provided by means of the Floquet theory.

Optical Chirality in Nonlinear Optics: Application to High Harmonic Generation.

PubMed

Neufeld, Ofer; Cohen, Oren

2018-03-30

Optical chirality (OC)-one of the fundamental quantities of electromagnetic fields-corresponds to the instantaneous chirality of light. It has been utilized for exploring chiral light-matter interactions in linear optics, but has not yet been applied to nonlinear processes. Motivated to explore the role of OC in the generation of helically polarized high-order harmonics and attosecond pulses, we first separate the OC of transversal and paraxial beams to polarization and orbital terms. We find that the polarization-associated OC of attosecond pulses corresponds approximately to that of the pump in the quasimonochromatic case, but not in the multichromatic pump cases. We associate this discrepancy with the fact that the polarization OC of multichromatic pumps vary rapidly in time along the optical cycle. Thus, we propose new quantities, noninstantaneous polarization-associated OC, and time-scale-weighted polarization-associated OC, and show that these quantities link the chirality of multichromatic pumps and their generated attosecond pulses. The presented extension to OC theory should be useful for exploring various nonlinear chiral light-matter interactions. For example, it stimulates us to propose a tricircular pump for generation of highly elliptical attosecond pulses with a tunable ellipticity.

Optical Chirality in Nonlinear Optics: Application to High Harmonic Generation

NASA Astrophysics Data System (ADS)

Neufeld, Ofer; Cohen, Oren

2018-03-01

Optical chirality (OC)—one of the fundamental quantities of electromagnetic fields—corresponds to the instantaneous chirality of light. It has been utilized for exploring chiral light-matter interactions in linear optics, but has not yet been applied to nonlinear processes. Motivated to explore the role of OC in the generation of helically polarized high-order harmonics and attosecond pulses, we first separate the OC of transversal and paraxial beams to polarization and orbital terms. We find that the polarization-associated OC of attosecond pulses corresponds approximately to that of the pump in the quasimonochromatic case, but not in the multichromatic pump cases. We associate this discrepancy with the fact that the polarization OC of multichromatic pumps vary rapidly in time along the optical cycle. Thus, we propose new quantities, noninstantaneous polarization-associated OC, and time-scale-weighted polarization-associated OC, and show that these quantities link the chirality of multichromatic pumps and their generated attosecond pulses. The presented extension to OC theory should be useful for exploring various nonlinear chiral light-matter interactions. For example, it stimulates us to propose a tricircular pump for generation of highly elliptical attosecond pulses with a tunable ellipticity.

An Efficient Method for Studying the Stability and Dynamics of the Rotational Motions of Celestial Bodies

NASA Astrophysics Data System (ADS)

Pavlov, A. I.; Maciejewski, A. J.

2003-08-01

We use the alternative MEGNO (Mean Exponential Growth of Nearby Orbits) technique developed by Cincotta and Simo to study the stability of orbital-rotational motions for plane oscillations and three-dimensional rotations. We present a detailed numerical-analytical study of a rigid body in the case where the proper rotation of the body is synchronized with its orbital motion as 3: 2 (Mercurian-type synchronism). For plane rotations, the loss of stability of the periodic solution that corresponds to a 3: 2 resonance is shown to be soft, which should be taken into account to estimate the upper limit for the ellipticity of Mercury. In studying stable and chaotic translational-rotational motions, we point out that the MEGNO criterion can be effectively used. This criterion gives a clear picture of the resonant structures and allows the calculations to be conveniently presented in the form of the corresponding MEGNO stability maps for multidimensional systems. We developed an appropriate software package.

Diverse Orbits Around Mars Graphic

NASA Image and Video Library

2015-05-04

This graphic depicts the relative shapes and distances from Mars for five active orbiter missions plus the planet's two natural satellites. It illustrates the potential for intersections of the spacecraft orbits. The number of active orbiter missions at Mars increased from three to five in 2014. With the increased traffic, NASA has augmented a process for anticipating orbit intersections and avoiding collisions. NASA's Mars Odyssey and MRO (Mars Reconnaissance Orbiter) travel near-circular orbits. The European Space Agency's Mars Express, NASA's MAVEN (Mars Atmosphere and Volatile Evolution) and India's MOM (Mars Orbiter Mission), travel more elliptical orbits. Phobos and Deimos are the two natural moons of Mars. http://photojournal.jpl.nasa.gov/catalog/PIA19396

Elliptical optical solitary waves in a finite nematic liquid crystal cell

NASA Astrophysics Data System (ADS)

Minzoni, Antonmaria A.; Sciberras, Luke W.; Smyth, Noel F.; Worthy, Annette L.

2015-05-01

The addition of orbital angular momentum has been previously shown to stabilise beams of elliptic cross-section. In this article the evolution of such elliptical beams is explored through the use of an approximate methodology based on modulation theory. An approximate method is used as the equations that govern the optical system have no known exact solitary wave solution. This study brings to light two distinct phases in the evolution of a beam carrying orbital angular momentum. The two phases are determined by the shedding of radiation in the form of mass loss and angular momentum loss. The first phase is dominated by the shedding of angular momentum loss through spiral waves. The second phase is dominated by diffractive radiation loss which drives the elliptical solitary wave to a steady state. In addition to modulation theory, the "chirp" variational method is also used to study this evolution. Due to the significant role radiation loss plays in the evolution of an elliptical solitary wave, an attempt is made to couple radiation loss to the chirp variational method. This attempt furthers understanding as to why radiation loss cannot be coupled to the chirp method. The basic reason for this is that there is no consistent manner to match the chirp trial function to the generated radiating waves which is uniformly valid in time. Finally, full numerical solutions of the governing equations are compared with solutions obtained using the various variational approximations, with the best agreement achieved with modulation theory due to its ability to include both mass and angular momentum losses to shed diffractive radiation.

Remote Sensing of Arctic and Boreal Atmospheric Composition from a Highly Elliptical Orbit

NASA Astrophysics Data System (ADS)

Nassar, Ray; McElroy, C. Tom; Walker, Kaley A.; McLinden, Chris; Sioris, Chris E.; Jones, Dylan B. A.; Martin, Randall V.; Rochon, Yves; Garand, Louis; Trischencko, Alexander P.

2016-04-01

The Polar Communications and Weather (PCW) mission is a proposed Canadian mission that aims to provide continuous meteorological observations and communications capacity over the Arctic and northern latitudes from a pair of satellites in a highly elliptical orbit (HEO) configuration. The Weather, Climate and Air quality (WCA) concept is a mission enhancement that completed a Phase A study through the Polar Highly Elliptical Orbit Science (PHEOS) program. The PHEOS-WCA instrument suite would consist of a high resolution Fourier Transform Spectrometer (FTS) operating in the mid-, near- and shortwave infrared and a UV-Visible grating Spectrometer (UVS), both with 2-dimensional imaging capability. These instruments would enable dense measurements of numerous quantities important for understanding weather (H2O and temperature profiles), climate (column-averaged CO2 and CH4) and air quality (tropospheric O3, CO, NO2, SO2, NH3, HCN, CH3OH, BrO, aerosols, ….) with a pixel size of 10×10 km2 or better and repeat time targeted at 2 hours or less. Our studies have demonstrated that HEO observations of CO2 offer major advantages over those from low earth orbit (LEO) for constraining CO2 surface sources and sinks in the Arctic and boreal regions, especially in the summer when there is the potential for the release of CO2 from permafrost thaw and boreal forest disturbances. This presentation will give an overview of the PHEOS-WCA mission concept, discuss its complementarity with upcoming international missions and provide an update on recent progress and challenges in moving forward.

How to Take 30 Years Off the Life of an Earth-Orbiter Network

NASA Technical Reports Server (NTRS)

Berner, C. D.; Perkins, R. C.; Baker, N.

1995-01-01

In the mid 1960's the NASA/JPL Deep Space Network installed a global 26-meter antenna network to support a large group of Low Earth Orbiters and Highly Elliptical Orbiters. Although this network was equipped with then state-of-the-art equipment, operations were labor- intensive. A study is discussed which takes a close look at re- engineering the 26-meter antenna network from all aspects.

A Classroom Note on: The Average Distance in an Ellipse

ERIC Educational Resources Information Center

Gordon, Sheldon P.

2011-01-01

This article presents an applied calculus exercise that can be easily shared with students. One of Kepler's greatest discoveries was the fact that the planets move in elliptic orbits with the sun at one focus. Astronomers characterize the orbits of particular planets by their minimum and maximum distances to the sun, known respectively as the…

Characteristics of the Earth's orbit by observations of the setting Sun

NASA Astrophysics Data System (ADS)

Sclar, N.

2000-07-01

Measurements of the setting Sun were carried out over a period of 16 months at Aliso Pier in Laguna Beach, CA, USA. The measurements are treated with simple analyses to provide good estimates of the obliquity of the ecliptic, and the eccentricity, velocities and radii of the Earth's elliptical orbit about the Sun.

Dynamics of Galaxies

NASA Astrophysics Data System (ADS)

Bertin, Giuseppe

2000-08-01

Part I. Basic Phenomenology: 1. Scales; 2. Observational windows; 3. Classifications; 4. Photometry, kinematics, dark matter; 5. Basic questions, semi-empirical approach, dynamical window; Part II. Physical Models: 6. Self-gravity and relation with plasma physics; 7. Relaxation times, absence of thermodynamical equilibrium; 8. Models; 9. Equilibrium and stability: symmetry and symmetry breaking; 10. Classical ellipsoids; 11. Introduction to dispersive waves; 12. Jeans instability; Part III. Spiral Galaxies: 13. Orbits; 14. The basic state: vertical and horizontal equilibrium in the disk; 15. Density waves; 16. Role of gas; 17. Global spiral modes; 18. Spiral structure in galaxies; 19. Bending waves; 20. Dark matter in spiral galaxies; Part IV. Elliptical Galaxies: 21. Orbits; 22. Stellar dynamical approach; 23. Stability; 24. Dark matter in elliptical galaxies; Part V. In Perspective: 25. Selected aspects of formation and evolution; Notes; Index.

Effects on the orbital debris environment due to solar activity

NASA Technical Reports Server (NTRS)

Kessler, Donald J.; Anz-Meador, Phillip D.

1990-01-01

The rate that earth-orbiting debris is removed from the environment is dependent on a number of factors which include orbital altitude and solar activity. It is generally believed that at lower altitudes and especially during periods of high solar activity, debris generated in the past will be eliminated from the environment. While some debris is eliminated, most is replaced by old debris from higher altitudes or new debris from recent launches. Some low altitude debris, which would reenter if the debris were in circular orbits, does not reenter because the debris is in higher-energy elliptical orbits.

Vortex dynamics in the wake of a pivoted cylinder undergoing vortex-induced vibrations with elliptic trajectories

NASA Astrophysics Data System (ADS)

Marble, Erik; Morton, Christopher; Yarusevych, Serhiy

2018-05-01

Vortex-induced vibrations of a pivoted cylinder are investigated experimentally at a fixed Reynolds number of 3100, a mass ratio of 10.8, and a range of reduced velocities, 4.42 ≤ U^* ≤ 9.05. For these conditions, the cylinder traces elliptic trajectories, with the experimental conditions producing three out of four possible combinations of orbiting direction and primary axis alignment relative to the incoming flow. The study focuses on the quantitative analysis of wake topology and its relation to this type of structural response. Velocity fields were measured using time-resolved, two-component particle image velocimetry (TR-PIV). These results show that phase-averaged wake topology generally agrees with the Morse and Williamson (J Fluids Struct 25(4):697-712, 2009) shedding map for one-degree-of-freedom vortex-induced vibrations, with 2S, 2{P}o, and 2P shedding patterns observed within the range of reduced velocities studied here. Vortex tracking and vortex strength quantification are used to analyze the vortex shedding process and how it relates to cylinder response. In the case of 2S vortex shedding, vortices are shed when the cylinder is approaching the maximum transverse displacement and reaches the streamwise equilibrium. 2P vortices are shed approximately half a period earlier in the cylinder's elliptic trajectory. Leading vortices shed immediately after the peak in transverse oscillation and trailing vortices shed near the equilibrium of transverse oscillation. The orientation and direction of the cylinder's elliptic trajectory are shown to influence the timing of vortex shedding, inducing changes in the 2P wake topology.

Dynamics Simulation Model for Space Tethers

NASA Technical Reports Server (NTRS)

Levin, E. M.; Pearson, J.; Oldson, J. C.

2006-01-01

This document describes the development of an accurate model for the dynamics of the Momentum Exchange Electrodynamic Reboost (MXER) system. The MXER is a rotating tether about 100-km long in elliptical Earth orbit designed to catch payloads in low Earth orbit and throw them to geosynchronous orbit or to Earth escape. To ensure successful rendezvous between the MXER tip catcher and a payload, a high-fidelity model of the system dynamics is required. The model developed here quantifies the major environmental perturbations, and can predict the MXER tip position to within meters over one orbit.

Oort's cloud evolution under the influence of the galactic field.

NASA Astrophysics Data System (ADS)

Kiryushenkova, N. V.; Chepurova, V. M.; Shershkina, S. L.

By numerical integration (Everhart's method) of the differential equations of cometary movement in Oort's cloud an attempt was made to observe how the galactic gravitational field changes the orbital elements of these comets during three solar revolutions in the Galaxy. It is shown that the cometary orbits are more elongated, even the initially circular orbits become strongly elliptical, in the outer layers of Oort's cloud it is possible for comets to turn into hyperbolic orbits and to leave the solar system. The boundaries of the solar system have been precised.

SSC Tenant Meeting: NASA Near Earth Network (NEN) Overview

NASA Technical Reports Server (NTRS)

Carter, David; Larsen, David; Baldwin, Philip; Wilson, Cristy; Ruley, LaMont

2018-01-01

The Near Earth Network (NEN) consists of globally distributed tracking stations that are strategically located throughout the world which provide Telemetry, Tracking, and Commanding (TTC) services support to a variety of orbital and suborbital flight missions, including Low Earth Orbit (LEO), Geosynchronous Earth Orbit (GEO), highly elliptical, and lunar orbits. Swedish Space Corporation (SSC), which is one of the NEN Commercial Service Provider, has provided the NEN with TTC services support from its Alaska, Hawaii, Chile and Sweden. The presentation will give an overview of the NEN and its support from SSC.

No elliptic islands for the universal area-preserving map

NASA Astrophysics Data System (ADS)

Johnson, Tomas

2011-07-01

A renormalization approach has been used in Eckmann et al (1982) and Eckmann et al (1984) to prove the existence of a universal area-preserving map, a map with hyperbolic orbits of all binary periods. The existence of a horseshoe, with positive Hausdorff dimension, in its domain was demonstrated in Gaidashev and Johnson (2009a). In this paper the coexistence problem is studied, and a computer-aided proof is given that no elliptic islands with period less than 18 exist in the domain. It is also shown that less than 1.5% of the measure of the domain consists of elliptic islands. This is proven by showing that the measure of initial conditions that escape to infinity is at least 98.5% of the measure of the domain, and we conjecture that the escaping set has full measure. This is highly unexpected, since generically it is believed that for conservative systems hyperbolicity and ellipticity coexist.

Stable Satellite Orbits for Global Coverage of the Moon

NASA Technical Reports Server (NTRS)

Ely, Todd; Lieb, Erica

2006-01-01

A document proposes a constellation of spacecraft to be placed in orbit around the Moon to provide navigation and communication services with global coverage required for exploration of the Moon. There would be six spacecraft in inclined elliptical orbits: three in each of two orthogonal orbital planes, suggestive of a linked-chain configuration. The orbits have been chosen to (1) provide 99.999-percent global coverage for ten years and (2) to be stable under perturbation by Earth gravitation and solar-radiation pressure, so that no deterministic firing of thrusters would be needed to maintain the orbits. However, a minor amount of orbit control might be needed to correct for such unmodeled effects as outgassing of the spacecraft.

A Computational Study of the Mechanics of Gravity-induced Torque on Cells

NASA Astrophysics Data System (ADS)

Haranas, Ioannis; Gkigkitis, Ioannis; Zouganelis, George D.

2013-10-01

In this paper, we study the effects of the acceleration gravity on the sedimentation deposition probability, as well as the aerosol deposition rate on the surface of the Earth and Mars, but also aboard a spacecraft in orbit around Earth and Mars as well. For particles with density ?p = 1300 kg/m3, diameters dp = 1, 10, 30 μm and residence times t = 0.0272, 0.2 s respectively, we find that, on the surface of Earth and Mars the deposition probabilities are higher at the poles when compared to the ones at the equator. Similarly, when in orbit around Earth we find that the deposition probabilities exhibit 0.0001 % higher percentage difference in equatorial circular and elliptical orbits when compared to polar ones. For both residence times particles with the diameters considered above in circular and elliptical orbits around Mars, the deposition probabilities appear to be the same for all orbital inclinations. Sedimentation probability increases drastically with particle diameter and orbital eccentricity of the orbiting spacecraft. Finally, as an alternative framework for the study of interaction and the effect of gravity in biology, and in particular gravity and the respiratory system we introduce is the term information in a way Shannon has introduced it, considering the sedimentation probability as a random variable. This can be thought as a way in which gravity enters the cognitive processes of the system (processing of information) in the cybernetic sense.

Flyby of large-size space debris objects and their transition to the disposal orbits in LEO

NASA Astrophysics Data System (ADS)

Baranov, Andrey A.; Grishko, Dmitriy A.; Razoumny, Yury N.; Jun, Li

2017-06-01

The article focuses on the flyby issue involving large-size space debris (LSSD) objects in low Earth orbits. The data on overall sizes of the known upper-stages and last stages of launch-vehicles make it possible to emphasize five compact groups of such objects from the Satellite catalogue in 600-2000 km altitude interval. The flyby maneuvers are executed by a single space vehicle (SV) that transfers the current captured LSSD object to the specially selected circular or elliptical disposal orbit (DO) and after a period of time returns to capture a new one. The flight is always realized when a value of the Right Ascension of the Ascending Node (RAAN) is approximately the same for the current DO and for an orbit of the following LSSD object. Distinctive features of changes in mutual distribution of orbital planes of LSSD within a group are shown on the RAAN deviations' evolution portrait. In case of the first three groups (inclinations 71°, 74° and 81°), the lines describing the relative orientation of orbital planes are quasi-parallel. Such configuration allows easy identification of the flyby order within a group, and calculation of the mission duration and the required total ΔV. In case of the 4th and the 5th groups the RAAN deviations' evolution portrait represents a conjunction of lines chaotically intersecting. The article studies changes in mission duration and in the required ΔV depending on the catalogue number of the first object in the flyby order. The article also contains a comparative efficiency analysis of the two world-wide known schemes applicable to LSSD objects' de-orbiting; the analysis is carried out for all 5 distinguished LSSD groups.

Tidal regime of intact planetoid capture model for the Earth-Moon system: Does it relate to the archean sedimentary rock record?

NASA Technical Reports Server (NTRS)

Malcuit, Robert J.; Winters, Ronald R.

1993-01-01

Regardless of one's favorite model for the origin of the Earth-Moon system (fission, coformation, tidal capture, giant-impact) the early history of lunar orbital evolution would produce significant thermal and earth and ocean tidal effects on the primitive earth. Three of the above lunar origin models (fission, coformation, giant-impact) feature a circular orbit which undergoes a progressive increase in orbital radius from the time of origin to the present time. In contrast, a tidal capture model places the moon in an elliptical orbit undergoing progressive circularization from the time of capture (for model purposes about 3.9 billion years ago) for at least a few 10(exp 8) years following the capture event. Once the orbit is circularized, the subsequent tidal history for a tidal capture scenario is similar to that for other models of lunar origin and features a progressive increase in orbital radius to the current state of the lunar orbit. This elliptical orbit phase, if it occurred, should have left a distinctive signature in the terrestrial and lunar rock records. Depositional events would be associated terrestrial shorelines characterized by abnormally high, but progressively decreasing, ocean tidal amplitudes and ranges associated with such an orbital evolution. Several rock units in the age range 3.6-2.5 billion years before present are reported to have a major tidal component. Examples are the Warrawoona, Fortescue, and Hamersley Groups of Western Australia and the Pangola and Witwatersand Supergroups of South Africa. Detailed study of the features of these tidal sequences may be helpful in deciphering the style of lunar orbital evolution during the Archean Eon.

A New Light Curve and Analysis of the Long Period Eclipsing Binary BF Draconis

NASA Astrophysics Data System (ADS)

Wolf, G. W.; Craig, L. E.; Caffey, J. F.

1999-01-01

The star BF Draconis was found to be an eclipsing binary by Strohmeier, Knigge and Ott (1962) and originally thought to be an Algol-type system with a period of 5.6 days. A spectrographic study by Imbert (1985) showed that the period was actually double this value and that the system consisted of two well-separated, almost-equal F-type stars in elliptical orbit. Diethelm, Wolf and Agerer (1993) later published a preliminary light curve of this system showing minima of unequal depth and width with a displaced secondary, confirming the elliptical orbit but disagreeing with Imbert on the specific orbital parameters. As a part of our long-term program of obtaining improved light curves of double-lined spectroscopic and eclipsing binaries, we have observed BF Draconis for the past four years using the 0.4 meter telescope at the Baker Observatory of Southwest Missouri State University. Complete light curves in the Cousins BVRI passbands have been obtained with our Photometrics CCD system, and a new model and orbital parameters for the binary have been determined using the Wilson-Devinney program. This research has been supported by NSF Grants AST-9315061 and AST-9605822 and NASA Grant NGT5-40060.

Deformation-Induced Precession of a Robot Moving on Curved Space

NASA Astrophysics Data System (ADS)

Li, Shengkai; Aydin, Yasemin; Lofaro, Olivia; Rieser, Jennifer; Goldman, Daniel

Previous studies have demonstrated that passive particles rolling on a deformed surface can mimic aspects of general relativity [Ford et al, AJP, 2015]. However, these systems are dissipative. To explore steady-state dynamics, we study the movement of a self-propelled robot car on a large deformable elastic membrane: a spandex sheet stretched over a metal frame with a diameter of 2.5 m. Two wheels in the rear of the car are differentially-driven by a DC motor, and a caster in the front helps maintain directional stability; in the absence of curvature the car drives straight. A linear actuator attached below the membrane allows for controlled deformation at the center of the membrane. We find that closed elliptic orbits occur when the membrane is highly depressed ( 10 cm). However, when the center is only slightly indented, the elliptical orbits precess at a rate depending on the orbit shape and the depression. Remarkably, this dynamic is well described by the Schwarzschild metric solution, typically used to describe the effects of gravity on bodies orbiting a massive object. Experiments with multiple cars reveal complex interactions that are mediated through car-induced deformations of the membrane.

Aerobraking Magellan

NASA Technical Reports Server (NTRS)

Lyons, Daniel T.; Sjogren, William; Johnson, William T. K.; Schmitt, Durwin; Mcronald, Angus

1992-01-01

While the Magellan spacecraft is currently in an elliptical orbit around Venus, its orbit may be circularized by means of an aerobraking maneuver during which a minor amount of aerodynamic drag is applied to 1000-2000 orbits. An evaluation is presently undertaken of the thermal-control and operational problems arising from such a maneuver, in virtue of its not having been considered among the design requirements of the spacecraft. Attention is given to atmospheric erosion and contamination problems to which the spacecraft surfaces could be exposed.

Wireless OAM transmission system based on elliptical microstrip patch antenna.

PubMed

Chen, Jia Jia; Lu, Qian Nan; Dong, Fei Fei; Yang, Jing Jing; Huang, Ming

2016-05-30

The multiplexing transmission has always been a focus of attention for communication technology. In this paper, the radiation characteristics of circular microstrip patch antenna was firstly analyzed based on cavity model theory, and then spiral beams carrying orbital angular momentum (OAM) were generated, using elliptical microstrip patch antenna, with a single feed probe instead of a standard circular patch with two feedpoints. Moreover, by combining the proposed elliptic microstrip patch antenna with Universal Software Radio Peripheral (USRP), a wireless OAM transmission system was established and the real-time transmission of text, image and video in a real channel environment was realized. Since the wireless OAM transmission has the advantage of good safety and high spectrum utilization efficiency, this work has theoretical significance and potential application.

Why has the bohr-sommerfeld model of the atom been ignoredby general chemistry textbooks?

PubMed

Niaz, Mansoor; Cardellini, Liberato

2011-12-01

Bohr's model of the atom is considered to be important by general chemistry textbooks. A major shortcoming of this model was that it could not explain the spectra of atoms containing more than one electron. In order to increase the explanatory power of the model, Sommerfeld hypothesized the existence of elliptical orbits. This study has the following objectives: 1) Formulation of criteria based on a history and philosophy of science framework; and 2) Evaluation of university-level general chemistry textbooks based on the criteria, published in Italy and U.S.A. Presentation of a textbook was considered to be "satisfactory" if it included a description of the Bohr-Sommerfeld model along with diagrams of the elliptical orbits. Of the 28 textbooks published in Italy that were analyzed, only five were classified as "satisfactory". Of the 46 textbooks published in U.S.A., only three were classified as "satisfactory". This study has the following educational implications: a) Sommerfeld's innovation (auxiliary hypothesis) by introducing elliptical orbits, helped to restore the viability of Bohr's model; b) Bohr-Sommerfeld's model went no further than the alkali metals, which led scientists to look for other models; c) This clearly shows that scientific models are tentative in nature; d) Textbook authors and chemistry teachers do not consider the tentative nature of scientific knowledge to be important; e) Inclusion of the Bohr-Sommerfeld model in textbooks can help our students to understand how science progresses.

Trajectory Design for the Phobos and Deimos & Mars Environment Spacecraft

NASA Technical Reports Server (NTRS)

Genova, Anthony L.; Korsmeyer, David J.; Loucks, Michel E.; Yang, Fan Yang; Lee, Pascal

2016-01-01

The presented trajectory design and analysis was performed for the Phobos and Deimos & Mars Environment (PADME) mission concept as part of a NASA proposal submission managed by NASA Ames Research Center in the 2014-2015 timeframe. The PADME spacecraft would be a derivative of the successfully flown Lunar Atmosphere & Dust Environment Explorer (LADEE) spacecraft. While LADEE was designed to enter low-lunar orbit, the PADME spacecraft would instead enter an elliptical Mars orbit of 2-week period. This Mars orbit would pass by Phobos near periapsis on successive orbits and then raise periapsis to yield close approaches of Deimos every orbit thereafter.

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.

Stability of orbits around planetary satellites considering a disturbing body in an elliptical orbit: Applications to Europa and Ganymede

NASA Astrophysics Data System (ADS)

Cardoso dos Santos, Josué; Carvalho, Jean Paulo; Vilhena de Moraes, Rodolpho

Europa and Ganymede are two of the four Jupiter’s moons which compose the Galilean satellite. These ones are planetary satellites of greater interest at the present moment among the scientific community. There are some missions being planned to visit them and and the Jovian system. One of them is the cooperation between NASA and ESA for the Europa Jupiter System Mission (EJSM). In this mission are planned the insertion of the spacecrafts JEO (Jupiter Europa Orbiter) and JGO (Jupiter Ganymede Orbiter) into Europa and Ganymede’s orbit. Thus, there is a great necessity for having a better comprehension of the dynamics of the orbits around this planetary satellite. This comprehension is essential for the success of this type of mission. In this context, this work aims to perform a search for low-altitude orbits around these planetary satellites. An emphasis is given in polar orbits. These orbits can be useful in the planning of aerospace activities to be conducted around this planetary satellite, with respect to the stability of orbits of artificial satellites. The study considers orbits of an artificial satellite around Europa and Ganymede under the influence of the third-body perturbation (the gravitational attraction of Jupiter) and the polygenic perturbations. These last ones occur due to forces such as the non-uniform distribution of mass (J2 and J3) of the main (central) body. A simplified dynamic model for polygenic perturbations is used. A new model for the third-body disturbance is presented considering it in an elliptical orbit. The Lagrange planetary equations, which compose a system of nonlinear differential equations, are used to describe the orbital motion of the artificial satellite around Ganymede. The equations showed here are developed in closed form to avoid expansions in inclination and eccentricity.

LLOFX earth orbit to lunar orbit delta V estimation program user and technical documentation

NASA Technical Reports Server (NTRS)

1988-01-01

The LLOFX computer program calculates in-plane trajectories from an Earth-orbiting space station to Lunar orbit in such a way that the journey requires only two delta V burns (one to leave Earth circular orbit and one to circularize into Lunar orbit). The program requires the user to supply the Space Station altitude and Lunar orbit altitude (in km above the surface), and the desired time of flight for the transfer (in hours). It then determines and displays the trans-Lunar injection (TLI) delta V required to achieve the transfer, the Lunar orbit insertion (LOI) delta V required to circularize the orbit around the Moon, the actual time of flight, and whether the transfer orbit is elliptical or hyperbolic. Return information is also displayed. Finally, a plot of the transfer orbit is displayed.

NASA launches dual Dynamics Explorer spacecraft

NASA Technical Reports Server (NTRS)

1981-01-01

A Delta launch vehicle was used to insert Dynamics Explorer A into a highly elliptical polar orbit, ranging from 675 to 24,945 km, and Dynamics Explorer B satellite into a low polar orbit, ranging from 306 to 1,300 km. The two spacecraft are designed to provide specific knowledge about the interaction of energy, electric currents, electric fields, and plasmas between the magnetosphere, the ionosphere, and the atmosphere.

Mercury Orbiter: Report of the Science Working Team

NASA Technical Reports Server (NTRS)

Belcher, John W.; Slavin, James A.; Armstrong, Thomas P.; Farquhar, Robert W.; Akasofu, Syun I.; Baker, Daniel N.; Cattell, Cynthia A.; Cheng, Andrew F.; Chupp, Edward L.; Clark, Pamela E.

1991-01-01

The results are presented of the Mercury Orbiter Science Working Team which held three workshops in 1988 to 1989 under the auspices of the Space Physics and Planetary Exploration Divisions of NASA Headquarters. Spacecraft engineering and mission design studies at the Jet Propulsion Lab were conducted in parallel with this effort and are detailed elsewhere. The findings of the engineering study, summarized herein, indicate that spin stabilized spacecraft carrying comprehensive particles and fields experiments and key planetology instruments in high elliptical orbits can survive and function in Mercury orbit without costly sun shields and active cooling systems.

Particle-Gas Temperature Differentials Resulting from Time-Dependent Radiative-Conductive Heat Flux Divergences in the Tenuous Dust-Laden Atmosphere of Mars.

DTIC Science & Technology

1987-01-01

The obliquity (inclination of the Martian equator to the Martian orbital plane) is 23059, very close to Earth’s value of 230271. The orbit of Mars...is inclined 1051’ to the ecliptic . The eccer.;ricity of the orbit (the ratio of the -iistanc, Detween the foci of the elliptical orbit 04.. I A m 1~0...and the major axis of the ellipse) is 0.0934, more .’ than five times the value for Earth (0.0167) (Pasachoff, 1979). The obliquity varies by 13

Fifth FLTSATCOM to be launched

NASA Technical Reports Server (NTRS)

1981-01-01

Launch of the FLTSATOOM-E, into an elliptical orbit by the Atlas Centaur launch vehicle is announced. The launch and relevant launch operations are described. A chart of the launch sequence for FLTSATCOM-E communication satellite is given.

A Semi-Analytical Orbit Propagator Program for Highly Elliptical Orbits

NASA Astrophysics Data System (ADS)

Lara, M.; San-Juan, J. F.; Hautesserres, D.

2016-05-01

A semi-analytical orbit propagator to study the long-term evolution of spacecraft in Highly Elliptical Orbits is presented. The perturbation model taken into account includes the gravitational effects produced by the first nine zonal harmonics and the main tesseral harmonics affecting to the 2:1 resonance, which has an impact on Molniya orbit-types, of Earth's gravitational potential, the mass-point approximation for third body perturbations, which on ly include the Legendre polynomial of second order for the sun and the polynomials from second order to sixth order for the moon, solar radiation pressure and atmospheric drag. Hamiltonian formalism is used to model the forces of gravitational nature so as to avoid time-dependence issues the problem is formulated in the extended phase space. The solar radiation pressure is modeled as a potential and included in the Hamiltonian, whereas the atmospheric drag is added as a generalized force. The semi-analytical theory is developed using perturbation techniques based on Lie transforms. Deprit's perturbation algorithm is applied up to the second order of the second zonal harmonics, J2, including Kozay-type terms in the mean elements Hamiltonian to get "centered" elements. The transformation is developed in closed-form of the eccentricity except for tesseral resonances and the coupling between J_2 and the moon's disturbing effects are neglected. This paper describes the semi-analytical theory, the semi-analytical orbit propagator program and some of the numerical validations.

Tsien's method for generating non-Keplerian trajectories. Part 2: The question of thrust to orbit a sphere and the restricted three-body problem

NASA Technical Reports Server (NTRS)

Murad, P. A.

1993-01-01

Tsien's method is extended to treat the orbital motion of a body undergoing accelerations and decelerations. A generalized solution is discussed for the generalized case where a body undergoes azimuthal and radial thrust and the problem is further simplified for azimuthal thrust alone. Judicious selection of thrust could generate either an elliptic or hyperbolic trajectory. This is unexpected especially when the body has only enough energy for a lower state trajectory. The methodology is extended treating the problem of vehicle thrust for orbiting a sphere and vehicle thrust within the classical restricted three-body problem. Results for the latter situation can produce hyperbolic trajectories through eigen value decomposition. Since eigen values for no-thrust can be imaginary, thrust can generate real eigen values to describe hyperbolic trajectories. Keplerian dynamics appears to represent but a small subset of a much larger non-Keplerian domain especially when thrust effects are considered. The need for high thrust long duration space-based propulsion systems for changing a trajectory's canonical form is clearly demonstrated.

Tether System for Exchanging Payloads Between the International Space Station and the Lunar Surface

NASA Technical Reports Server (NTRS)

Hoyt, Robert P.

1998-01-01

Systems composed of several rotating and/or hanging tethers may provide a means of exchanging supplies between low Earth orbit facilities and lunar bases without requiring the use of propellant. This work develops methods for designing a tether system capable of repeatedly exchanging payloads between a LEO facility such as the International Space Station or a Space Business Park and a base on the lunar surface. In this system, a hanging tether extended upwards from the LEO facility, places a payload into a slightly elliptical orbit, where it is caught by a rotating tether in a higher elliptical orbit. This rotating tether then tosses the payload to the moon. At the moon, a long rotating "Lunavator" tether catches the payload and deposits it on the surface of the moon. By transporting an equal mass of lunar materials such as oxygen back down to the LEO facility through the tether transport system, the momentum and energy of the system is conserved, allowing frequent traffic between LEO and the lunar surface with minimal propellant requirements.

Designing Delta-DOR acquisition strategies to determine highly elliptical earth orbits

NASA Technical Reports Server (NTRS)

Frauenholz, R. B.

1986-01-01

Delta-DOR acquisition strategies are designed for use in determining highly elliptical earth orbits. The requirements for a possible flight demonstration are evaluated for the Charged Composition Explorer spacecraft of the Active Magnetospheric Particle Tracer Explorers. The best-performing strategy uses data spanning the view periods of two orthogonal baselines near the same orbit periapse. The rapidly changing viewing geometry yields both angular position and velocity information, but each observation may require a different reference quasar. The Delta-DOR data noise is highly dependent on acquisition geometry, varying several orders of magnitude across the baseline view periods. Strategies are selected to minimize the measurement noise predicted by a theoretical model. Although the CCE transponder is limited by S-band and a small bandwidth, the addition of Delta-DOR to coherent Doppler and range improves the one-sigma apogee position accuracy by more than an order of magnitude. Additional Delta-DOR accuracy improvements possible using dual-frequency (S/X) calibration, increased spanned bandwidth, and water-vapor radiometry are presented for comparison. With these benefits, the residual Delta-DOR data noise is primarily due to quasar position uncertainties.

Predator prey oscillations in a simple cascade model of drift wave turbulence

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

Berionni, V.; Guercan, Oe. D.

2011-11-15

A reduced three shell limit of a simple cascade model of drift wave turbulence, which emphasizes nonlocal interactions with a large scale mode, is considered. It is shown to describe both the well known predator prey dynamics between the drift waves and zonal flows and to reduce to the standard three wave interaction equations. Here, this model is considered as a dynamical system whose characteristics are investigated. The analytical solutions for the purely nonlinear limit are given in terms of the Jacobi elliptic functions. An approximate analytical solution involving Jacobi elliptic functions and exponential growth is computed using scale separationmore » for the case of unstable solutions that are observed when the energy injection rate is high. The fixed points of the system are determined, and the behavior around these fixed points is studied. The system is shown to display periodic solutions corresponding to limit cycle oscillations, apparently chaotic phase space orbits, as well as unstable solutions that grow slowly while oscillating rapidly. The period doubling route to transition to chaos is examined.« less

The divine clockwork: Bohr's correspondence principle and Nelson's stochastic mechanics for the atomic elliptic state

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

Durran, Richard; Neate, Andrew; Truman, Aubrey

2008-03-15

We consider the Bohr correspondence limit of the Schroedinger wave function for an atomic elliptic state. We analyze this limit in the context of Nelson's stochastic mechanics, exposing an underlying deterministic dynamical system in which trajectories converge to Keplerian motion on an ellipse. This solves the long standing problem of obtaining Kepler's laws of planetary motion in a quantum mechanical setting. In this quantum mechanical setting, local mild instabilities occur in the Keplerian orbit for eccentricities greater than (1/{radical}(2)) which do not occur classically.

Characterization of elliptic dark hollow beams

NASA Astrophysics Data System (ADS)

Gutiérrez-Vega, Julio C.

2008-08-01

A dark hollow beam (DHB) is designed in general as a ringed shaped light beam with a null intensity center on the beam axis. DHBs have interesting physical properties such as a helical wavefront, a center vortex singularity, doughnut-shaped transverse intensity distribution, they may carry and transfer orbital and spin angular momentum, and may also exhibit a nondiffracting behavior upon propagation. Most of the known theoretical models to describe DHBs consider axially symmetric transverse intensity distributions. However, in recent years there has been an increasing interest in developing models to describe DHBs with elliptic symmetry. DHBs with elliptic symmetry can be regarded as transition beams between circular and rectangular DHBs. For example, the high-order modes emitted from resonators with neither completely rectangular nor completely circular symmetry, but in between them, cannot be described by the known HermiteGaussian or LaguerreGaussian beams. In this work, we review the current state of research on elliptic DHBs, with particular emphasis in Mathieu and Ince-Gauss beams.

Squeezing and Stretching Titan Author Concept

NASA Image and Video Library

2012-06-28

This artist concept shows tides on Titan raised by Saturn gravity, as detected by NASA Cassini spacecraft. Saturn gravitational pull on Titan, its largest moon, varies as Titan orbits along an elliptical path around the planet every 16 days.

Secular motion around synchronously orbiting planetary satellites.

PubMed

Lara, Martin; San-Juan, Juan F; Ferrer, Sebastián

2005-12-01

We investigate the secular motion of a spacecraft around the natural satellite of a planet. The satellite rotates synchronously with its mean motion around the planet. Our model takes into account the gravitational potential of the satellite up to the second order, and the third-body perturbation in Hill's approximation. Close to the satellite, the ratio of rotation rate of the satellite to mean motion of the orbiter is small. When considering this ratio as a small parameter, the Coriolis effect is a first-order perturbation, while the third-body tidal attraction, the ellipticity effect, and the oblateness perturbation remain at higher orders. Then, we apply perturbation theory and find that a third-order approach is enough to show the influence of the satellite's ellipticity in the pericenter dynamics. Finally, we discuss the averaged system in the three-dimensional parametric space, and provide a global description of the flow.

Variation of parameters using Battin's universal functions

NASA Astrophysics Data System (ADS)

Burton, James R., III; Melton, Robert G.

This paper presents a variation of parameters analysis, suitable for use in situations involving small perturbations to the two-body problem, using Battin's universal functions. Unlike the universal variable formulation, this approach avoids the need to switch among different functional representations if the orbit transitions from elliptical, through parabolic, to hyperbolic state, making it attractive for use in simulating low-thrust trajectories ascending to escape or capturing into orbit.

On the problem of meteor shower's radiants displacement

NASA Astrophysics Data System (ADS)

Tikhomirova, E. N.

2011-06-01

In the context of the perturbed two-body problem a method to evaluate radiant shift for a meteor shower is suggested. We consider the evolution of a meteoroid particle which after every complete revolution "migrates" from one elliptic orbit to another with slightly changed orbital parameters. The obtained analytical solutions of the equations of particle's motion take into account radiation pressure, Poynting-Robertson effect and its corpuscular part.

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

NASA Astrophysics Data System (ADS)

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

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

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

NASA Technical Reports Server (NTRS)

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

1992-01-01

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

Lunar Volatile System Dynamics: Observations Enabled by the Deep Space Gateway

NASA Astrophysics Data System (ADS)

Honniball, C. I.; Lucey, P. G.; Petro, N.; Hurley, D.; Farrell, W.

2018-02-01

A UV spectrometer-imager and IR spectrometer are proposed to solve questions regarding the lunar volatile system. The instrument takes advantage of highly elliptical orbits and the thermal management system of the Deep Space Gateway.

Characteristics of phase-correcting fresnel zone plates and elliptical waveguides

NASA Astrophysics Data System (ADS)

Wiltse, James C.

1994-02-01

The primary area of activity has been concentrated on the investigations relating to Fresnel zone plate antennas. A secondary effort has dealt with the characteristics of propagation in waveguides of elliptical cross section. In both cases, applications at microwave and millimeter-wavelengths have been emphasized. Thorough literature searches were conducted, and the results are given in Appendices A and B. The zone plate work has dealt with both transmission and reflection types, and has included considering the off-axis-fed cases. In the latter case, the plate may consist of elliptical zones, rather than the usual circular configuration. In general, the characteristics studied include far-field patterns, focal region fields, off-axis performance, bandwidth, and aberrations. In the case of propagation in elliptical waveguides, the attenuation and modal properties were studied for enclosed metal waveguides, coaxial transmission lines, and various surface waveguides.

Hubble Views 'Third Kind' of Galaxy

NASA Image and Video Library

2017-12-08

The subject of this image is NGC 6861, a galaxy discovered in 1826 by the Scottish astronomer James Dunlop. Almost two centuries later we now know that NGC 6861 is the second brightest member of a group of at least a dozen galaxies called the Telescopium Group — otherwise known as the NGC 6868 Group — in the small constellation of Telescopium (The Telescope). This NASA/ESA Hubble Space Telescope view shows some important details of NGC 6861. One of the most prominent features is the disk of dark bands circling the centre of the galaxy. These dust lanes are a result of large clouds of dust particles obscuring the light emitted by the stars behind them. Dust lanes are very useful for working out whether we are seeing the galaxy disk edge-on, face-on or, as is the case for NGC 6861, somewhat in the middle. Dust lanes like these are typical of a spiral galaxy. The dust lanes are embedded in a white oval shape, which is made up of huge numbers of stars orbiting the center of the galaxy. This oval is, rather puzzlingly, typical of an elliptical galaxy. So which is it — spiral or elliptical? The answer is neither! NGC 6861 does not belong to either the spiral or the elliptical family of galaxies. It is a lenticular galaxy, a family which has features of both spirals and ellipticals. The relationships between these three kinds of galaxies are not yet well understood. A lenticular galaxy could be a faded spiral that has run out of gas and lost its arms, or the result of two galaxies merging. Being part of a group increases the chances for galactic mergers, so this could be the case for NGC 6861. Credit: ESA/Hubble & NASA; acknowledgement: J. Barrington 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

g Dependent particle concentration due to sedimentation

NASA Astrophysics Data System (ADS)

Haranas, Ioannis; Gkigkitzis, Ioannis; Zouganelis, George D.

2012-11-01

Sedimentation of particles in a fluid has long been used to characterize particle size distribution. Stokes' law is used to determine an unknown distribution of spherical particle sizes by measuring the time required for the particles to settle a known distance in a fluid of known viscosity and density. In this paper, we study the effects of gravity on sedimentation by examining the resulting particle concentration distributed in an equilibrium profile of concentration C m, n above the bottom of a container. This is for an experiment on the surface of the Earth and therefore the acceleration of gravity had been corrected for the oblateness of the Earth and its rotation. Next, at the orbital altitude of the spacecraft in orbit around Earth the acceleration due to the central field is corrected for the oblateness of the Earth. Our results show that for experiments taking place in circular or elliptical orbits of various inclinations around the Earth the concentration ratio C m, n / C m, ave , the inclination seems to be the most ineffective in affecting the concentration among all the orbital elements. For orbital experiment that use particles of diameter d p =0.001 μm the concentration ratios for circular and slightly elliptical orbits in the range e=0-0.1 exhibit a 0.009 % difference. The concentration ratio increases with the increase of eccentricity, which increases more for particles of larger diameters. Finally, for particles of the same diameter concentration ratios between Earth and Mars surface experiments are related in the following way C_{(m,n)_{mathit{Earth}}} = 0.99962 C_{(m,n)_{mathit{Mars}}}.

Intelsat satellite scheduled for launch

NASA Technical Reports Server (NTRS)

1981-01-01

The launch schedule for Intelsat 5-B, the prime Intelsat satellite to provide communications services between the Americas, Europe, the Middle East, and Africa, is presented. The planned placement of the satellite into an elliptical transfer orbit, and circularization of the orbit at geosynchronous altitude over the equator are described. Characteristics of the Atlas Centaur launch vehicle, AC-56, are given. The launch operation is summarized and the launch sequence presented. The Intelsat team and contractors are listed.

Shape of the orbital opening: individual characterization and analysis of variability in modern humans, Gorilla gorilla, and Pan troglodytes.

PubMed

Schmittbuhl, M; Le Minor, J M; Allenbach, B; Schaaf, A

1999-05-01

The description of the human orbital shape is principally qualitative in the classical literature, and characterised by adjectives such as circular, rectangular or quadrangular. In order to provide a precise quantification and interpretation of this shape, a study based on automatic image analysis and Fourier analysis was carried out on 45 human skulls (30 males, 15 females), and for comparison on 61 skulls of Gorilla gorilla (40 males, 21 females), and 34 skulls of Pan troglodytes (20 males, 14 females). Sexual dimorphism in the shape of the orbital opening was not demonstrated. Its dominant morphological features could be characterized by Fourier analysis; elliptical elongation and quadrangularity were dominant morphological features of the shape of the orbital opening in the three species. Elliptical elongation was more marked in humans and Pan, whereas quadrangularity was particularly emphasized in Gorilla. An intraspecific variability of the shape of the orbital opening existed in humans, Gorilla and Pan, and seemed close in the three species. Interspecific partition between humans, Gorilla and Pan was demonstrated despite the variability observed in the three species studied. Interspecific differences between Gorilla and the Pan-humans group were principally explained by the differences in quadrangularity, and by differences in orientation of triangularity and pentagonality. Differences in the shape of the orbital opening between humans and Pan were principally explained by differences in hexagonality, and by differences in orientation of quadrangularity. A closeness of shape between some humans and some individuals in Pan and, to a lesser degree, with some individuals in Gorilla was observed, demonstrating the existence of a morphological continuum of the shape of the orbital opening in hominoids.

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

NASA Astrophysics Data System (ADS)

Chakraborty, A.; Narayan, A.

2018-03-01

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

Supersonic full-potential methods for missile body analysis

NASA Technical Reports Server (NTRS)

Pittman, James L.

1992-01-01

Accounts are presented of representative applications to missile bodies of arbitrary shape of methods based on the steady form of the full potential equation. The NCOREL and SIMP full-potential codes are compared, and their results are evaluated for the cases of an arrow wing and a wing-body configuration. Attention is given to the effect of cross-sectional and longitudinal geometries. Comparisons of surface pressure and longitudinal force and moment data for circular and elliptic bodies have shown that the full-potential methods yielded excellent results in attached-flow conditions. Results are presented for a conical star body, waveriders, the Shuttle Orbiter, and a highly swept wing-body cruising at Mach 4.

Quantum mechanics of hyperbolic orbits in the Kepler problem

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

Rauh, Alexander; Parisi, Juergen

2011-04-15

The problem of deriving macroscopic properties from the Hamiltonian of the hydrogen atom is resumed by extending previous results in the literature, which predicted elliptic orbits, into the region of hyperbolic orbits. As a main tool, coherent states of the harmonic oscillator are used which are continued to imaginary frequencies. The Kustaanheimo-Stiefel (KS) map is applied to transform the original configuration space into the product space of four harmonic oscillators with a constraint. The relation derived between real time and oscillator (pseudo) time includes quantum corrections. In the limit ({h_bar}/2{pi}){yields}0, the time-dependent mean values of position and velocity describe themore » classical motion on a hyperbola and a circular hodograph, respectively. Moreover, the connection between pseudotime and real time comes out in analogy to Kepler's equation for elliptic orbits. The mean-square-root deviations of position and velocity components behave similarly in time to the corresponding ones of a spreading Gaussian wave packet in free space. To check the approximate treatment of the constraint, its contribution to the mean energy is determined with the result that it is negligible except for energy values close to the parabolic orbit with eccentricity equal to 1. It is inevitable to introduce a suitable scalar product in R{sup 4} which makes both the transformed Hamiltonian and the velocity operators Hermitian. An elementary necessary criterion is given for the energy interval where the constraint can be approximated by averaging.« less

Application of conformal transformation to elliptic geometry for electric impedance tomography.

PubMed

Yilmaz, Atila; Akdoğan, Kurtuluş E; Saka, Birsen

2008-03-01

Electrical impedance tomography (EIT) is a medical imaging modality that is used to compute the conductivity distribution through measurements on the cross-section of a body part. An elliptic geometry model, which defines a more general frame, ensures more accurate results in reconstruction and assessment of inhomogeneities inside. This study provides a link between the analytical solutions defined in circular and elliptical geometries on the basis of the computation of conformal mapping. The results defined as voltage distributions for the homogeneous case in elliptic and circular geometries have been compared with those obtained by the use of conformal transformation between elliptical and well-known circular geometry. The study also includes the results of the finite element method (FEM) as another approach for more complex geometries for the comparison of performance in other complex scenarios for eccentric inhomogeneities. The study emphasizes that for the elliptic case the analytical solution with conformal transformation is a reliable and useful tool for developing insight into more complex forms including eccentric inhomogeneities.

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.

Orbital Transfer Techniques for Round-Trip Mars Missions

NASA Technical Reports Server (NTRS)

Landau, Damon

2013-01-01

The human exploration of Phobos and Deimos or the retrieval of a surface sample launched to low-Mars orbit presents a highly constrained orbital transfer problem. In general, the plane of the target orbit will not be accessible from the arrival or departure interplanetary trajectories with an (energetically optimal) tangential burn at periapsis. The orbital design is further complicated by the addition of a high-energy parking orbit for the relatively massive Deep Space Vehicle to reduce propellant expenditure, while the crew transfers to and from the target orbit in a smaller Space Exploration Vehicle. The proposed strategy shifts the arrival and departure maneuvers away from periapsis so that the apsidal line of the parking orbit lies in the plane of the target orbit, permitting highly efficient plane change maneuvers at apoapsis of the elliptical parking orbit. An apsidal shift during the arrival or departure maneuver is approximately five times as efficient as maneuvering while in Mars orbit, thus significantly reducing the propellant necessary to transfer between the arrival, target, and departure orbits.

Martian Meteorology: Determination of Large Scale Weather Patterns from Surface Measurements

NASA Technical Reports Server (NTRS)

Murphy, James R.; Haberle, Robert M.; Bridger, Alison F. C.

1998-01-01

We employed numerical modelling of the martian atmosphere, and our expertise in understanding martian atmospheric processes, to better understand the coupling between lower and upper atmosphere processes. One practical application of this work has been our involvement with the ongoing atmospheric aerobraking which the Mars Global Surveyor (MGS) spacecraft is currently undergoing at Mars. Dr. Murphy is currently a member of the Mars Global Surveyor (MGS) Aerobraking Atmospheric Advisory Group (AAG). He was asked to participate in this activity based upon his knowledge of martian atmospheric dynamical processes. Aerobraking is a process whereby a spacecraft, in an elliptical orbit, passes through the upper layers of the atmosphere (in this instance Mars). This passage through the atmosphere 'drags'upon the spacecraft, gradually reducing its orbital velocity. This has the effect, over time, of converting the elliptical orbit to a circular orbit, which is the desired mapping orbit for MGS. Carrying out aerobraking eliminates the need for carrying large amounts of fuel on the spacecraft to execute an engine burn to achieve the desired orbit. Eliminating the mass of the fuel reduces the cost of launch. Damage to one of MGS's solar panels shortly after launch has resulted in a less aggressive extended in time aerobraking phase which will not end until March, 1999. Phase I extended from Sept. 1997 through March 1998. During this time period, Dr. Murphy participated almost daily in the AAG meetings, and beginning in December 1997 lead the meeting several times per week. The leader of each of the daily AAG meetings took the results of that meeting (current state of the atmosphere, identification of any time trends or spatial patterns in upper atmosphere densities, etc.) forward to the Aerobraking Planning Group (APG) meeting, at which time the decision was made to not change MGS orbit, to lower the orbit to reach higher densities (greater 'drag'), or raise the orbit to avoid experiencing excessive, possibly damaging densities.

Probing the statistics of transport in the Hénon Map

NASA Astrophysics Data System (ADS)

Alus, O.; Fishman, S.; Meiss, J. D.

2016-09-01

The phase space of an area-preserving map typically contains infinitely many elliptic islands embedded in a chaotic sea. Orbits near the boundary of a chaotic region have been observed to stick for long times, strongly influencing their transport properties. The boundary is composed of invariant "boundary circles." We briefly report recent results of the distribution of rotation numbers of boundary circles for the Hénon quadratic map and show that the probability of occurrence of small integer entries of their continued fraction expansions is larger than would be expected for a number chosen at random. However, large integer entries occur with probabilities distributed proportionally to the random case. The probability distributions of ratios of fluxes through island chains is reported as well. These island chains are neighbours in the sense of the Meiss-Ott Markov-tree model. Two distinct universality families are found. The distributions of the ratio between the flux and orbital period are also presented. All of these results have implications for models of transport in mixed phase space.

Estimation of Untracked Geosynchronous Population from Short-Arc Angles-Only Observations

NASA Technical Reports Server (NTRS)

Healy, Liam; Matney, Mark

2017-01-01

Telescope observations of the geosynchronous regime will observe two basic types of objects --- objects related to geosynchronous earth orbit (GEO) satellites, and objects in highly elliptical geosynchronous transfer orbits (GTO). Because telescopes only measure angular rates, the GTO can occasionally mimic the motion of GEO objects over short arcs. A GEO census based solely on short arc telescope observations may be affected by these ``interlopers''. A census that includes multiple angular rates can get an accurate statistical estimate of the GTO population, and that then can be used to correct the estimate of the geosynchronous earth orbit population.

The Orbital precession around oblate spheroids

NASA Astrophysics Data System (ADS)

Montanus, J. M. C.

2006-07-01

An exact series will be given for the gravitational potential generated by an oblate gravitating source. To this end the corresponding Epstein-Hubbell type elliptic integral is evaluated. The procedure is based on the Legendre polynomial expansion method and on combinatorial techniques. The result is of interest for gravitational models based on the linearity of the gravitational potential. The series approximation for such potentials is of use for the analysis of orbital motions around a nonspherical source. It can be considered advantageous that the analysis is purely algebraic. Numerical approximations are not required. As an important example, the expression for the orbital precession will be derived for an object orbiting around an oblate homogeneous spheroid.

The Lunar IceCube Mission Challenge: Attaining Science Orbit Parameters from a Constrained Approach Trajectory

NASA Technical Reports Server (NTRS)

Folta, David C.; Bosanac, Natasha; Cox, Andrew; Howell, Kathleen C.

2017-01-01

The challenges of targeting specific lunar science orbit parameters from a concomitant Sun-EarthMoon system trajectory are examined. While the concept of ballistic lunar capture is well-studied, achieving and controlling the time evolution of the orbital elements to satisfy mission constraints is especially problematic when the spacecraft is equipped with a low-thrust propulsion system. Satisfying these requirements on the lunar approach and capture segments is critical to the success of the Lunar IceCube mission, a 6U CubeSat that will prospect for water in solid (ice), liquid, and vapor forms and other lunar volatiles from a low-periapsis, highly inclined elliptical lunar orbit.

The Lunar IceCube Mission Challenge: Attaining Science Orbit Parameters from a Constrained Approach Trajectory

NASA Technical Reports Server (NTRS)

Folta, David C.; Bosanac, Natasha; Cox, Andrew; Howell, Kathleen C.

2017-01-01

The challenges of targeting specific lunar science orbit parameters from a concomitant Sun-Earth/Moon system trajectory are examined. While the concept of ballistic lunar capture is well-studied, achieving and controlling the time evolution of the orbital elements to satisfy mission constraints is especially problematic when the spacecraft is equipped with a low-thrust propulsion system. Satisfying these requirements on the lunar approach and capture segments is critical to the success of the Lunar IceCube mission, a 6U CubeSat that will prospect for water in solid (ice), liquid, and vapor forms and other lunar volatiles from a low-periapsis, highly inclined elliptical lunar orbit.

Measurements of the linear energy transfer spectra on the Mir orbital station and comparison with radiation transport models

NASA Technical Reports Server (NTRS)

Badhwar, G. D.; Konradi, A.; Atwell, W.; Golightly, M. J.; Cucinotta, F. A.; Wilson, J. W.; Petrov, V. M.; Tchernykh, I. V.; Shurshakov, V. A.; Lobakov, A. P.

1996-01-01

A tissue equivalent proportional counter designed to measure the linear energy transfer spectra (LET) in the range 0.2-1250 keV/micrometer was flown in the Kvant module on the Mir orbital station during September 1994. The spacecraft was in a 51.65 degrees inclination, elliptical (390 x 402 km) orbit. This is nearly the lower limit of its flight altitude. The total absorbed dose rate measured was 411.3 +/- 4.41 microGy/day with an average quality factor of 2.44. The galactic cosmic radiation (GCR) dose rate was 133.6 microGy/day with a quality factor of 3.35. The trapped radiation belt dose rate was 277.7 microGy/day with an average quality factor of 1.94. The peak rate through the South Atlantic Anomaly was approximately 12 microGy/min and nearly constant from one pass to another. A detailed comparison of the measured LET spectra has been made with radiation transport models. The GCR results are in good agreement with model calculations; however, this is not the case for radiation belt particles and again points to the need for improving the AP8 omni-directional trapped proton models.

Sitnikov problem in the square configuration: elliptic case

NASA Astrophysics Data System (ADS)

Shahbaz Ullah, M.

2016-05-01

This paper is extension to the classical Sitnikov problem, when the four primaries of equal masses lie at the vertices of a square for all time and moving in elliptic orbits around their center of mass of the system, the distances between the primaries vary with time but always in such a way that their mutual distances remain in the same ratio. First we have established averaged equation of motion of the Sitnikov five-body problem in the light of Jalali and Pourtakdoust (Celest. Mech. Dyn. Astron. 68:151-162, 1997), by applying the Van der Pol transformation and averaging technique of Guckenheimer and Holmes (Nonlinear oscillations, dynamical system bifurcations of vector fields, Springer, Berlin, 1983). Next the Hamiltonian equation of motion has been solved with the help of action angle variables I and φ. Finally the periodicity and stability of the Sitnikov five-body problem have been examined with the help of Poincare surfaces of section (PSS). It is shown that chaotic region emerging from the destroyed islands, can easily be seen by increasing the eccentricity of the primaries to e = 0.21. It is valid for bounded small amplitude solutions z_{max} ( z_{max} = 0.65 ) and 0 ≤ e < 0.3.

The mechanics and origin of cometaria

NASA Astrophysics Data System (ADS)

Beech, Martin

2002-12-01

The cometarium, literally a mechanical device for describing the orbit of a comet, had its genesis as a machine for illustrating the observable consequences of Kepler's second law of planetary motion. The device that became known as the cometarium was originally constructed by J.T. Desaguliers in 1732 to demonstrate, in a sensible fashion, the perihelion to aphelion change in velocity of the planet Mercury. It was only with the imminent, first predicted, return of Halley's comet in 1758 that the name cometarium was coined, and subsequent devices so named. Most early cometaria used a pair of elliptical formers joined via a figure-of-eight cord to translate uniform drive motion into the non-uniform motion of an object moving along an elliptic track. It is shown in a series of calculations, however, that two elliptical former cometaria do not actually provide a correct demonstration of Keplerian velocity variations and nor do they actually demonstrate Kepler's second law of planetary motion.

Physics Notes.

ERIC Educational Resources Information Center

School Science Review, 1982

1982-01-01

Discusses determination of elliptical path of a satellite caught into orbit by the sun or earth; using microcomputer as signal generator (includes program listing); collision process; simple hysteresis loop using double beam CRO; method of demonstrating parallelogram of forces; measuring radius of electron beam curvature; and half-life of thorium…

Propagation dynamics of Helical Hermite-Gaussian beams

NASA Astrophysics Data System (ADS)

López-Mariscal, Carlos; Gutiérrez-Vega, Julio C.

2007-09-01

We investigate theoretically and experimentally the propagation characteristics of the Helical Hermite-Gauss beams corresponding to the helical Ince-Gauss beams in the limit of infinite ellipticity. Particular attention is paid to the transverse irradiance structure, the orbital angular momentum density, and the vortex distribution.

Electromagnetic fields and Green's functions in elliptical vacuum chambers

NASA Astrophysics Data System (ADS)

Persichelli, S.; Biancacci, N.; Migliorati, M.; Palumbo, L.; Vaccaro, V. G.

2017-10-01

In this paper, we discuss the electromagnetic interaction between a point charge travelling inside a waveguide of elliptical cross section, and the waveguide itself. By using a convenient expansion of the Mathieu functions, useful in particular for treating a variety of problems in applied mathematics and physics with elliptic geometry, we first obtain the longitudinal electromagnetic field of a point charge (Green's function) in free space in terms of elliptical coordinates. This expression allows, then, to calculate the scattered field due to the boundary conditions in our geometry. By summing the contribution of the direct or primary field and the indirect field scattered by the boundary, after a careful choice of some expansion expressions, we derive a novel formula of the longitudinal electric field, in any transverse position of the elliptical cross section, generated by the charge moving along the longitudinal axis of the waveguide. The obtained expression is represented in a closed form, it can be differentiated and integrated, it can be used to fully describe the radiation process of a particle beam travelling inside a waveguide of elliptical cross section, and it is valid for any elliptic geometry. The equations are used to evaluate the coupling impedance due to indirect space charge in case of elliptical geometry. In addition, they are useful as preliminary studies for the determination of the coupling impedance in different cases involving elliptic vacuum chambers, as, for example, the effect of the finite conductivity of the beam pipe wall or the geometrical variation of the vacuum chamber due to elliptic step transitions existing in some accelerators.

Electromagnetic fields and Green’s functions in elliptical vacuum chambers

DOE PAGES

Persichelli, S.; Biancacci, N.; Migliorati, M.; ...

2017-10-23

In this paper, we discuss the electromagnetic interaction between a point charge travelling inside a waveguide of elliptical cross section, and the waveguide itself. By using a convenient expansion of the Mathieu functions, useful in particular for treating a variety of problems in applied mathematics and physics with elliptic geometry, we first obtain the longitudinal electromagnetic field of a point charge (Green's function) in free space in terms of elliptical coordinates. This expression allows, then, to calculate the scattered field due to the boundary conditions in our geometry. By summing the contribution of the direct or primary field and themore » indirect field scattered by the boundary, after a careful choice of some expansion expressions, we derive a novel formula of the longitudinal electric field, in any transverse position of the elliptical cross section, generated by the charge moving along the longitudinal axis of the waveguide. The obtained expression is represented in a closed form, it can be differentiated and integrated, it can be used to fully describe the radiation process of a particle beam travelling inside a waveguide of elliptical cross section, and it is valid for any elliptic geometry. The equations are used to evaluate the coupling impedance due to indirect space charge in case of elliptical geometry. In addition, they are useful as preliminary studies for the determination of the coupling impedance in different cases involving elliptic vacuum chambers, as, for example, the effect of the finite conductivity of the beam pipe wall or the geometrical variation of the vacuum chamber due to elliptic step transitions existing in some accelerators.« less

Electromagnetic fields and Green’s functions in elliptical vacuum chambers

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

Persichelli, S.; Biancacci, N.; Migliorati, M.

In this paper, we discuss the electromagnetic interaction between a point charge travelling inside a waveguide of elliptical cross section, and the waveguide itself. By using a convenient expansion of the Mathieu functions, useful in particular for treating a variety of problems in applied mathematics and physics with elliptic geometry, we first obtain the longitudinal electromagnetic field of a point charge (Green's function) in free space in terms of elliptical coordinates. This expression allows, then, to calculate the scattered field due to the boundary conditions in our geometry. By summing the contribution of the direct or primary field and themore » indirect field scattered by the boundary, after a careful choice of some expansion expressions, we derive a novel formula of the longitudinal electric field, in any transverse position of the elliptical cross section, generated by the charge moving along the longitudinal axis of the waveguide. The obtained expression is represented in a closed form, it can be differentiated and integrated, it can be used to fully describe the radiation process of a particle beam travelling inside a waveguide of elliptical cross section, and it is valid for any elliptic geometry. The equations are used to evaluate the coupling impedance due to indirect space charge in case of elliptical geometry. In addition, they are useful as preliminary studies for the determination of the coupling impedance in different cases involving elliptic vacuum chambers, as, for example, the effect of the finite conductivity of the beam pipe wall or the geometrical variation of the vacuum chamber due to elliptic step transitions existing in some accelerators.« less

EG Andromedae: A New Orbit and Additional Evidence for a Photoionized Wind

NASA Astrophysics Data System (ADS)

Kenyon, Scott J.; Garcia, Michael R.

2016-07-01

We analyze a roughly 20 yr set of spectroscopic observations for the symbiotic binary EG And. Radial velocities derived from echelle spectra are best fit with a circular orbit having an orbital period of P = 483.3 ± 1.6 days and semi-amplitude K = 7.34 ± 0.07 km s-1. Combined with previous data, these observations rule out an elliptical orbit at the 10σ level. Equivalent widths of H I Balmer emission lines and various absorption features vary in phase with the orbital period. Relative to the radius of the red giant primary, the apparent size of the H II region is consistent with a model where a hot secondary star with effective temperature T h ≈ 75,000 K ionizes the wind from the red giant.

TRAP/SEE Code Users Manual for Predicting Trapped Radiation Environments

NASA Technical Reports Server (NTRS)

Armstrong, T. W.; Colborn, B. L.

2000-01-01

TRAP/SEE is a PC-based computer code with a user-friendly interface which predicts the ionizing radiation exposure of spacecraft having orbits in the Earth's trapped radiation belts. The code incorporates the standard AP8 and AE8 trapped proton and electron models but also allows application of an improved database interpolation method. The code treats low-Earth as well as highly-elliptical Earth orbits, taking into account trajectory perturbations due to gravitational forces from the Moon and Sun, atmospheric drag, and solar radiation pressure. Orbit-average spectra, peak spectra per orbit, and instantaneous spectra at points along the orbit trajectory are calculated. Described in this report are the features, models, model limitations and uncertainties, input and output descriptions, and example calculations and applications for the TRAP/SEE code.

A preliminary analysis of the orbit of the Mars Trojan asteroid (5261) Eureka

NASA Technical Reports Server (NTRS)

Mikkola, Seppo; Innanen, Kimmo; Muinonen, Karri; Bowell, Edward

1994-01-01

Observations and results of orbit determination of the first known Mars Trojan asteroid (5261) Eureka are presented. We have numerically calculated the evolution of the orbital elements, and have analyzed the behavior of the motion during the next 2 Myr. Strong perturbations by planets other than Mars seem to stabilize the eccentricity of the asteroid by stirring the high order resonances present in the elliptic restricted problem. As a result, the orbit appears stable at least on megayear timescales. The difference of the mean longitudes of Mars and Eureka and the semimajor axis of the asteroid form a pair of variables that essentially behave in an adiabatic manner, while the evolution of the other orbital elements is largely determined by the pertubations due to other planets.

Taking the Measure of the Universe: Precision Astrometry with SIM Planetquest (Preprint)

DTIC Science & Technology

2006-10-09

the orbits of nearby galaxies and groups going out to the distance of the Virgo Cluster . The orbits are in comoving coordinates. This is just a...single solution of a set of several solutions using present 3-d positions as inputs. The four massive objects ( Virgo Cluster , Coma Group, CenA Group, and... Virgo Cluster from a Numerical Action Method calculation with parameters M/L = 90 for spirals and 155 for ellipticals, Ωm = 0.24, ΩΛ = 0.76. The axes are

Relative Orbit Elements for Satellites in Elliptical Orbits

DTIC Science & Technology

2010-03-01

studied subject; many important contributions to the study were made before and during the dawn of the Space Age . In fact, the most celebrated...accomplishments of the Space Age would not have been possible without a good understanding of relative satellite motion. The Apollo astronauts could not... secular terms (containing t and 2t ) in the y-direction and mixed- secular terms (of the form  1 2 3sint t   ) in all three directions. In 1999

Hamilton-Jacobi modelling of relative motion for formation flying.

PubMed

Kolemen, Egemen; Kasdin, N Jeremy; Gurfil, Pini

2005-12-01

A precise analytic model for the relative motion of a group of satellites in slightly elliptic orbits is introduced. With this aim, we describe the relative motion of an object relative to a circular or slightly elliptic reference orbit in the rotating Hill frame via a low-order Hamiltonian, and solve the Hamilton-Jacobi equation. This results in a first-order solution to the relative motion identical to the Clohessy-Wiltshire approach; here, however, rather than using initial conditions as our constants of the motion, we utilize the canonical momenta and coordinates. This allows us to treat perturbations in an identical manner, as in the classical Delaunay formulation of the two-body problem. A precise analytical model for the base orbit is chosen with the included effect of zonal harmonics (J(2), J(3), J(4)). A Hamiltonian describing the real relative motion is formed and by differing this from the nominal Hamiltonian, the perturbing Hamiltonian is obtained. Using the Hamilton equations, the variational equations for the new constants are found. In a manner analogous to the center manifold reduction procedure, the non-periodic part of the motion is canceled through a magnitude analysis leading to simple boundedness conditions that cancel the drift terms due to the higher order perturbations. Using this condition, the variational equations are integrated to give periodic solutions that closely approximate the results from numerical integration (1 mm/per orbit for higher order and eccentricity perturbations and 30 cm/per orbit for zonal perturbations). This procedure provides a compact and insightful analytic description of the resulting relative motion.

An intrinsic approach in the curved n-body problem: The negative curvature case

NASA Astrophysics Data System (ADS)

Diacu, Florin; Pérez-Chavela, Ernesto; Reyes Victoria, J. Guadalupe

We consider the motion of n point particles of positive masses that interact gravitationally on the 2-dimensional hyperbolic sphere, which has negative constant Gaussian curvature. Using the stereographic projection, we derive the equations of motion of this curved n-body problem in the Poincaré disk, where we study the elliptic relative equilibria. Then we obtain the equations of motion in the Poincaré upper half plane in order to analyze the hyperbolic and parabolic relative equilibria. Using techniques of Riemannian geometry, we characterize each of the above classes of periodic orbits. For n=2 and n=3 we recover some previously known results and find new qualitative results about relative equilibria that were not apparent in an extrinsic setting.

Dynamics of a Probable Earth-mass Planet in the GJ 832 System

NASA Astrophysics Data System (ADS)

Satyal, S.; Griffith, J.; Musielak, Z. E.

2017-08-01

The stability of planetary orbits around the GJ 832 star system, which contains inner (GJ 832c) and outer (GJ 832b) planets, is investigated numerically and a detailed phase-space analysis is performed. Special attention is given to the existence of stable orbits for a planet less than 15 M ⊕ that is injected between the inner and outer planets. Thus, numerical simulations are performed for three and four bodies in elliptical orbits (or circular for special cases) by using a large number of initial conditions that cover the selected phase-spaces of the planet’s orbital parameters. The results presented in the phase-space maps for GJ 832c indicate the least deviation of eccentricity from its nominal value, which is then used to determine its inclination regime relative to the star-outer planet plane. Also, the injected planet is found to display stable orbital configurations for at least one billion years. Then, the radial velocity curves based on the signature from the Keplerian motion are generated for the injected planets with masses 1 M ⊕ to 15 M ⊕ in order to estimate their semimajor axes and mass limits. The synthetic RV signal suggests that an additional planet of mass ≤15 M ⊕ with a dynamically stable configuration may be residing between 0.25 and 2.0 au from the star. We have provided an estimated number of RV observations for the additional planet that is required for further observational verification.

Consideration of lifetime limitation for spent stages in GTO

NASA Astrophysics Data System (ADS)

Sharma, R.; Bandyopadhyay, P.; Adimurthy, V.

It is well known that the time of launch during a day can have substantial effect in determining the orbital life of an object placed in a highly elliptic orbit like GTO (Ref.1). One of the proposed criteria to ensure stable space debris environment is to place the objects in orbits with limited lifetime of up to 25 years. This paper presents the investigations made in this connection for the Launch of GSLV-D1 on April 18, 2001. The decay of objects from elliptic orbits of moderate eccentricity is well understood in the literature where the apogee height decreases fast resulting in the circularization of orbits, which decays gradually under the effect of drag till the reentry. The evolution of objects in GTO orbits, whose perigee altitude falls between 180 km to 650 km and apogee is near the geo-stationary altitudes (35000 km to 36000 km), is determined by a complex interplay of different kind of forces, like upper atmospheric drag and luni-solar gravitation. These orbits are characterized by periodic changes in the altitude of the perigee caused by gravitational perturbations of the moon and the sun. The initial orientation of the orbit just after the launch with respect to the sun and the moon predominantly determines the subsequent histories of the orbital evolution. Therefore, the launch time plays an important role. The long time evolution of objects in GTO orbits can fall into two broad categories; (a) Decay predominantly by luni-solar gravity effect and (b) Decay by combination of atmospheric drag and luni-solar perturbations. In the former case, the perigee is driven below the decay altitude and circularization of the orbit does not take place before the reentry. In the later case, the evolution has phases of complex interplay of drag and luni-solar perturbations. Atmospheric drag generates a retarding force on the space object, but the effects of the sun and the moon on the object are more complex and can result in either increase or decrease in perigee altitude. It is interesting to understand the basic physics of the luni-solar perturbations. A few typical examples presented here illustrate this effect very clearly. It is interesting to note that in GTO orbits the interplay of drag and luni- solar gravity effects can give rise to situations where more drag get translated into more lifetime. Orbital evolution study of the third stage of GSLV-D1, which falls into the second category described above, provides us with a few interesting observations (Ref.2). The orbital lifetime can vary from around 7 months to well beyond 50 years depending on the launch time during the day of launch. A study with respect to few other days during the year to find the effect of sun and moon initial locations on orbital life is also included. For the present launch, the orbital life is around 600 days, which is well within the widely accepted criterion on the lifetime of any manmade space object. It is noted that the osculating perigee altitude decreases and apogee altitude increases when the object comes near the perigee due to oblate earth effects. The decrease in perigee is about 3.5 km and the increase in apogee is 160 km. Utilizing 175 Two Line Element (TLE) sets of the object available in the first 100 days of its life, the suitable ballistic coefficient is estimated and simulations up to re-entry are done. The re-entry is predicted between 7 Nov 2002 and 29 Dec 2002. A continuous monitoring with the available orbital data shows that the predictions continue to be within the above bounds. Ref.1. King-Hele, D.G., "Lifetime Predictions for Satellites in Low inclination Transfer Orbits", Journal of the British Interplanetary Society, Vol.35, pp.339-344, 1982 Ref.2. Priyankar Bandhopadhyay, Sharma, R.K., Adimurthy,V., " The Orbiting Third Stage of GSLV-D1 as Space Debris", VSSC/AERO/TR-001/2001, Vikram Sarabhai Space Centre, Trivandrum, 2001

Secular dynamics of multiplanetary circumbinary systems: stationary solutions and binary-planet secular resonance

NASA Astrophysics Data System (ADS)

Andrade-Ines, Eduardo; Robutel, Philippe

2018-01-01

We present an analytical formalism to study the secular dynamics of a system consisting of N-2 planets orbiting a binary star in outer orbits. We introduce a canonical coordinate system and expand the disturbing function in terms of canonical elliptic elements, combining both Legendre polynomials and Laplace coefficients, to obtain a general formalism for the secular description of this type of configuration. With a quadratic approximation of the development, we present a simplified analytical solution for the planetary orbits for both the single planet and the two-planet cases. From the two-planet model, we show that the inner planet accelerates the precession rate of the binary pericenter, which, in turn, may enter in resonance with the secular frequency of the outer planet, characterizing a secular resonance. We calculate an analytical expression for the approximate location of this resonance and apply it to known circumbinary systems, where we show that it can occur at relatively close orbits, for example at 2.4 au for the Kepler-38 system. With a more refined model, we analyse the dynamics of this secular resonance and we show that a bifurcation of the corresponding fixed points can affect the long- term evolution and stability of planetary systems. By comparing our results with complete integrations of the exact equations of motion, we verified the accuracy of our analytical model.

Starspots found on the ellipsoidal variable V350 lacertae = HR 8575

NASA Technical Reports Server (NTRS)

Crews, Lionel J.; Hall, Douglas S.; Henry, Gregory W.; Lines, Richard D.; Lines, Helen C.; Fried, Robert E.

1995-01-01

It has been a puzzle why this chromospherically active, strong-dynamo K2 IV-III star is not known to have the large starspots characteristic of other such stars. Published individual radial velocities, which had never been analyzed, are used to derive an orbital solution. Combined with the one older existing orbital solution, this yields an improved orbital ephemeris: time of conjunction (K star behind) = JD 2445255.47 +/- 0.11 days and period = 17.75346 +/- 0.00016 days. All available photoelectric photometry, from 1970.9 to 1992.5, is collected A cos 2 theta fit of the ellipticity effect yields JD 2445255.60 +/- 0.06 days for a time of conjunction, 17.7523 +/- 0.0005 days for the period, and 0.084 mins for the peak-to-peak amplitude in V. With the ellipticity effect removed, the light curve does show measurable starspot variability in 15 of 16 data groups, the starspot wave amplitudes ranging between 0.03 mins and 0.08 mins. Ten starspots are identified and their rotation periods determined, the mean being 17.70 +/- 0.03 days (confirming synchronous rotation) and the range being Delta P/P = 0.017 +/- 0.006 (indicating differential rotation). There is a slow variation in mean brightness, almost 0.1 min in range and at least 2 decades in length.

3-D orbital evolution model of outer asteroid belt

NASA Technical Reports Server (NTRS)

Solovaya, Nina A.; Gerasimov, Igor A.; Pittich, Eduard M.

1992-01-01

The evolution of minor planets in the outer part of the asteroid belt is considered. In the framework of the semi-averaged elliptic restricted three-dimensional three-body model, the boundary of regions of the Hill's stability is found. As was shown in our work, the Jacobian integral exists.

Imaging Near-Earth Electron Densities Using Thomson Scattering

DTIC Science & Technology

2009-01-15

geocentric solar magnetospheric (GSM) coordinates1. TECs were initially computed from a viewing loca- tion at the Sun-Earth L1 Lagrange point2 for both...further find that an elliptical Earth orbit (apogee ~30 RE) is a suitable lower- cost option for a demonstration mission. 5. SIMULATED OBSERVATIONS We

The Mars Reconnaissance Orbiter Mission: From Launch to the Primary Science Orbit

NASA Technical Reports Server (NTRS)

Johnston, Martin D.; Graf, James E.; Zurek, Richard W.; Eisen, Howard J.; Jai, Benhan; Erickson, James K.

2007-01-01

The Mars Reconnaissance Orbiter (MRO) was launched from Cape Canaveral Air Force Station, Florida, USA, aboard an Atlas V-401 launch vehicle on August 12, 2005. The MRO spacecraft carries a very sophisticated scientific payload. Its primary science mission is to to provide global, regional survey, and targeted observations from a low altitude orbit for one Martian year (687 Earth days). After a seven month interplanetary transit, the spacecraft fired its six main engines and established a highly elliptical capture orbit at Mars. During the post-MOI early check-out period, four instruments acquired engineering-quality data. This was followed by five months of aerobraking operations. After aerobraking was terminated, a series of propulsive maneuvers were used to establish the desired low altitude science orbit. As the spacecraft is readied for its primary science mission, spacecraft and instrument checkout and deployment activities have continued.

Autonomous orbital navigation using Kepler's equation

NASA Technical Reports Server (NTRS)

Boltz, F. W.

1974-01-01

A simple method of determining the six elements of elliptic satellite orbits has been developed for use aboard manned and unmanned spacecraft orbiting the earth, moon, or any planet. The system requires the use of a horizon sensor or other device for determining the local vertical, a precision clock or timing device, and Apollo-type navigation equipment including an inertial measurement unit (IMU), a digital computer, and a coupling data unit. The three elements defining the in-plane motion are obtained from simultaneous measurements of central angle traversed around the planet and elapsed flight time using a linearization of Kepler's equation about a reference orbit. It is shown how Kalman filter theory may also be used to determine the in-plane orbital elements. The three elements defining the orbit orientation are obtained from position angles in celestial coordinates derived from the IMU with the spacecraft vertically oriented after alignment of the IMU to a known inertial coordinate frame.

A retrograde object near Jupiter's orbit

NASA Astrophysics Data System (ADS)

Connors, M.; Wiegert, P.

2018-02-01

Asteroid 2007 VW266 is among the rare objects with a heliocentric retrograde orbit, and its semimajor axis is within a Hill sphere radius of that of Jupiter. This raised the interesting possibility that it could be in co-orbital retrograde resonance with Jupiter, a second "counter-orbital" object in addition to recently discovered 2015 BZ509. We find instead that the object is in 13/14 retrograde mean motion resonance (also referred to as 13/-14). The object is shown to have entered its present orbit about 1700 years ago, and it will leave it in about 8000 years, both through close approach to Jupiter. Entry and exit states both avoid 1:1 retrograde resonance, but the retrograde nature is preserved. The temporary stable state is due to an elliptic orbit with high inclination keeping nodal passages far from the associated planet. We discuss the motion of this unusual object based on modeling and theory, and its observational prospects.

Feasibility study of a single, elliptical heliocentric Earth-Mars trajectory

NASA Technical Reports Server (NTRS)

Blake, M.; Fulgham, K.; Westrup, S.

1989-01-01

The initial intent of this design project was to evaluate the existence and feasibility of a single elliptical heliocentric Earth/Mars trajectory. This trajectory was constrained to encounter Mars twice in its orbit, within a time interval of 15 to 180 Earth days between encounters. The single ellipse restriction was soon found to be prohibitive for reasons shown later. Therefore, the approach taken in the design of the round-trip mission to Mars was to construct single-leg trajectories which connected two planets on two prescribed dates. Three methods of trajectory design were developed. Method 1 is an eclectic approach and employs Gaussian Orbit Determination (Method 1A) and Lambert-Euler Preliminary Orbit Determination (Method 1B) in conjunction with each other. Method 2 is an additional version of Lambert's Solution to orbit determination, and both a coplanar and a noncoplanar solution were developed within Method 2. In each of these methods, the fundamental variables are two position vectors and the time between the position vectors. In all methods, the motion was considered Keplerian motion and the reference frame origin was located at the sun. Perturbative effects were not considered in Method 1. The feasibility study of round-trip Earth/Mars trajectories maintains generality by considering only heliocentric trajectory parameters and planetary approach conditions. The coordinates and velocity components of the planets, for the standard epoch J2000, were computed from an approximate set of osculating elements by the procedure outlined in an ephemeris of coordinates.

Two-Body Orbit Expansion Due to Time-Dependent Relative Acceleration Rate of the Cosmological Scale Factor

NASA Astrophysics Data System (ADS)

Iorio, Lorenzo

2014-01-01

By phenomenologically assuming a slow temporal variation of the percent acceleration rate S̈S -1 of the cosmic scale factor S(t), it is shown that the orbit of a local binary undergoes a secular expansion. To first order in the power expansion of S̈S -1 around the present epoch t0, a non-vanishing shift per orbit (Δr) of the two-body relative distance r occurs for eccentric trajectories. A general relativistic expression, which turns out to be cubic in the Hubble parameter H0 at the present epoch, is explicitly calculated for it in the case of matter-dominated epochs with Dark Energy. For a highly eccentric Oort comet orbit with period Pb ≈ 31 Myr, the general relativistic distance shift per orbit turns out to be of the order of (Δr) ≈ 70 km. For the Large Magellanic Cloud, assumed on a bound elliptic orbit around the Milky Way, the shift per orbit is of the order of (Δr) ≈ 2-4 pc. Our result has a general validity since it holds in any cosmological model admitting the Hubble law and a slowly varying S̈S-1(t). More generally, it is valid for an arbitrary Hooke-like extra-acceleration whose "elastic" parameter κ is slowly time-dependent, irrespectively of the physical mechanism which may lead to it. The coefficient κ1 of the first-order term of the power expansion of κ(t) can be preliminarily constrained in a model-independent way down to a κ1 ≤ 2 x 10-13 year-3 level from latest Solar System's planetary observations. The radial velocities of the double lined spectroscopic binary ALPHA Cen AB yield κ1 ≤ 10-8 year-3.

Analysis of error in TOMS total ozone as a function of orbit and attitude parameters

NASA Technical Reports Server (NTRS)

Gregg, W. W.; Ardanuy, P. E.; Braun, W. C.; Vallette, B. J.; Bhartia, P. K.; Ray, S. N.

1991-01-01

Computer simulations of orbital scenarios were performed to examine the effects of orbital altitude, equator crossing time, attitude uncertainty, and orbital eccentricity on ozone observations by future satellites. These effects were assessed by determining changes in solar and viewing geometry and earth daytime coverage loss. The importance of these changes on ozone retrieval was determined by simulating uncertainties in the TOMS ozone retrieval algorithm. The major findings are as follows: (1) Drift of equator crossing time from local noon would have the largest effect on the quality of ozone derived from TOMS. The most significant effect of this drift is the loss of earth daytime coverage in the winter hemisphere. The loss in coverage increases from 1 degree latitude for + or - 1 hour from noon, 6 degrees for + or - 3 hours from noon, to 53 degrees for + or - 6 hours from noon. An additional effect is the increase in ozone retrieval errors due to high solar zenith angles. (2) To maintain contiguous earth coverage, the maximum scan angle of the sensor must be increased with decreasing orbital altitude. The maximum scan angle required for full coverage at the equator varies from 60 degrees at 600 km altitude to 45 degrees at 1200 km. This produces an increase in spacecraft zenith angle, theta, which decreases the ozone retrieval accuracy. The range in theta was approximately 72 degrees for 600 km to approximately 57 degrees at 1200 km. (3) The effect of elliptical orbits is to create gaps in coverage along the subsatellite track. An elliptical orbit with a 200 km perigee and 1200 km apogee produced a maximum earth coverage gap of about 45 km at the perigee at nadir. (4) An attitude uncertainty of 0.1 degree in each axis (pitch, roll, yaw) produced a maximum scan angle to view the pole, and maximum solar zenith angle).

Vortex survival in 3D self-gravitating accretion discs

NASA Astrophysics Data System (ADS)

Lin, Min-Kai; Pierens, Arnaud

2018-07-01

Large-scale, dust-trapping vortices may account for observations of asymmetric protoplanetary discs. Disc vortices are also potential sites for accelerated planetesimal formation by concentrating dust grains. However, in 3D discs vortices are subject to destructive `elliptic instabilities', which reduces their viability as dust traps. The survival of vortices in 3D accretion discs is thus an important issue to address. In this work, we perform shearing box simulations to show that disc self-gravity enhances the survival of 3D vortices, even when self-gravity is weak in the classic sense (e.g. with a Toomre Q ≃ 5). We find a 3D self-gravitating vortex can grow on secular time-scales in spite of the elliptic instability. The vortex aspect ratio decreases as it strengthens, which feeds the elliptic instability. The result is a 3D vortex with a turbulent core that persists for ˜103 orbits. We find when gravitational and hydrodynamic stresses become comparable, the vortex may undergo episodic bursts, which we interpret as an interaction between elliptic and gravitational instabilities. We estimate the distribution of dust particles in self-gravitating, turbulent vortices. Our results suggest large-scale vortices in protoplanetary discs are more easily observed at large radii.

Vortex survival in 3D self-gravitating accretion discs

NASA Astrophysics Data System (ADS)

Lin, Min-Kai; Pierens, Arnaud

2018-04-01

Large-scale, dust-trapping vortices may account for observations of asymmetric protoplanetary discs. Disc vortices are also potential sites for accelerated planetesimal formation by concentrating dust grains. However, in 3D discs vortices are subject to destructive `elliptic instabilities', which reduces their viability as dust traps. The survival of vortices in 3D accretion discs is thus an important issue to address. In this work, we perform shearing box simulations to show that disc self-gravity enhances the survival of 3D vortices, even when self-gravity is weak in the classic sense (e.g. with a Toomre Q ≃ 5). We find a 3D, self-gravitating vortex can grow on secular timescales in spite of the elliptic instability. The vortex aspect-ratio decreases as it strengthens, which feeds the elliptic instability. The result is a 3D vortex with a turbulent core that persists for ˜103 orbits. We find when gravitational and hydrodynamic stresses become comparable, the vortex may undergo episodic bursts, which we interpret as interaction between elliptic and gravitational instabilities. We estimate the distribution of dust particles in self-gravitating, turbulent vortices. Our results suggest large-scale vortices in protoplanetary discs are more easily observed at large radii.

Uranus and Neptune orbiter missions via solar electric propulsion

NASA Technical Reports Server (NTRS)

Friedlander, A. L.; Brandenburg, R. K.

1971-01-01

The characteristics and capabilities of solar electric propulsion for performing orbiter missions at the planets Uranus and Neptune are described. An assessment of the scientific objectives and instrumentation requirements, their relation to orbit size selection, and parametric analysis of solar electric propulsion trajectory/payload performance are included. Utilizing the Titan 3D/Centaur launch vehicle, minimum flight times of about 3400 days to Uranus and 5300 days to Neptune are required to place the TOPS spacecraft into the nominal orbits. It has been shown that solar electric propulsion can be used effectively to accomplish elliptical orbiter missions at Uranus and Neptune. However, because of the very long flight time required, these mission profiles are not too attractive. Previous studies have shown that nuclear electric propulsion, if developed, would allow much faster trips; 5 years to Uranus and 8 years to Neptune.

Dynamics of groups around interacting double ellipticals: Measuring dark matter haloes

NASA Technical Reports Server (NTRS)

Quintana, H.

1990-01-01

Binary galaxies, as binary stars, are important to measure masses, as suggested by Page (1952). Because three orbit parameters are measurable for galaxies at one instant of time, severe uncertainties remain in the orbit and mass determinations. These uncertainties can partly be overcome by statistical studies of selected samples and/or n-body simulations. Close double galaxies (and isolated galaxies) could also be useful to estimate dynamical masses if we can find test particles around them. Interacting elliptical pairs or dumb-bell galaxies are found with a large range, between 0-1200 km s(exp -1), of relative radial velocities. Standard 2-body orbit calculations, highly uncertain due to projection factors, suggest for the largest velocity differences very large galaxy masses, if the systems are bound and stationary. However, recent n-body simulations model these binaries as galaxies captured from hyperbolic orbits, requiring masses of order a few times 10(exp 11) solar maximum (Borne et al. 1988), but producing systems that are short lived. A different picture appears when we study observationally the dynamical mass of interacting double ellipticals using faint satellite galaxies. These satellites contribute little luminosity and, presumably, little mass to the system. The authors present results of two such groups, basically forming systems of test particles, around the dumb-bells NGC 4782/3 and IC 5049. They also briefly discuss the satellite group around the central dumb-bell in the cluster Sersic 40/6. Apparently, they detect large quantities of dark matter in the vicinity of these dumb-bell galaxies, because the system masses of approx. 4.5 times 10(exp 13) solar mass and 8 times 10(exp 13) solar mass for NGC 4782/3 and IC 5049, respectively, are quite high. Likewise, the mass of the Sersic 40/6 inner core is 7 times 10(exp 13) solar mass. The possibility that a common massive dark matter halo increases the merging times of these types of galaxies is suggested. Here, the authors assume H sub o = 100 km s (exp -1) Mpc(exp -1).

Lossy compression of weak lensing data

DOE PAGES

Vanderveld, R. Ali; Bernstein, Gary M.; Stoughton, Chris; ...

2011-07-12

Future orbiting observatories will survey large areas of sky in order to constrain the physics of dark matter and dark energy using weak gravitational lensing and other methods. Lossy compression of the resultant data will improve the cost and feasibility of transmitting the images through the space communication network. We evaluate the consequences of the lossy compression algorithm of Bernstein et al. (2010) for the high-precision measurement of weak-lensing galaxy ellipticities. This square-root algorithm compresses each pixel independently, and the information discarded is by construction less than the Poisson error from photon shot noise. For simulated space-based images (without cosmicmore » rays) digitized to the typical 16 bits per pixel, application of the lossy compression followed by image-wise lossless compression yields images with only 2.4 bits per pixel, a factor of 6.7 compression. We demonstrate that this compression introduces no bias in the sky background. The compression introduces a small amount of additional digitization noise to the images, and we demonstrate a corresponding small increase in ellipticity measurement noise. The ellipticity measurement method is biased by the addition of noise, so the additional digitization noise is expected to induce a multiplicative bias on the galaxies measured ellipticities. After correcting for this known noise-induced bias, we find a residual multiplicative ellipticity bias of m {approx} -4 x 10 -4. This bias is small when compared to the many other issues that precision weak lensing surveys must confront, and furthermore we expect it to be reduced further with better calibration of ellipticity measurement methods.« less

Basic Geometric Support of Systems for Earth Observation from Geostationary and Highly Elliptical Orbits

NASA Astrophysics Data System (ADS)

Gektin, Yu. M.; Egoshkin, N. A.; Eremeev, V. V.; Kuznecov, A. E.; Moskatinyev, I. V.; Smelyanskiy, M. B.

2017-12-01

A set of standardized models and algorithms for geometric normalization and georeferencing images from geostationary and highly elliptical Earth observation systems is considered. The algorithms can process information from modern scanning multispectral sensors with two-coordinate scanning and represent normalized images in optimal projection. Problems of the high-precision ground calibration of the imaging equipment using reference objects, as well as issues of the flight calibration and refinement of geometric models using the absolute and relative reference points, are considered. Practical testing of the models, algorithms, and technologies is performed in the calibration of sensors for spacecrafts of the Electro-L series and during the simulation of the Arktika prospective system.

A transmission line model for propagation in elliptical core optical fibers

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

Georgantzos, E.; Boucouvalas, A. C.; Papageorgiou, C.

The calculation of mode propagation constants of elliptical core fibers has been the purpose of extended research leading to many notable methods, with the classic step index solution based on Mathieu functions. This paper seeks to derive a new innovative method for the determination of mode propagation constants in single mode fibers with elliptic core by modeling the elliptical fiber as a series of connected coupled transmission line elements. We develop a matrix formulation of the transmission line and the resonance of the circuits is used to calculate the mode propagation constants. The technique, used with success in the casemore » of cylindrical fibers, is now being extended for the case of fibers with elliptical cross section. The advantage of this approach is that it is very well suited to be able to calculate the mode dispersion of arbitrary refractive index profile elliptical waveguides. The analysis begins with the deployment Maxwell’s equations adjusted for elliptical coordinates. Further algebraic analysis leads to a set of equations where we are faced with the appearance of harmonics. Taking into consideration predefined fixed number of harmonics simplifies the problem and enables the use of the resonant circuits approach. According to each case, programs have been created in Matlab, providing with a series of results (mode propagation constants) that are further compared with corresponding results from the ready known Mathieu functions method.« less

Two-photon polymerization of a three dimensional structure using beams with orbital angular momentum

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

Zhang, Shi-Jie; Li, Yan, E-mail: li@pku.edu.cn; Liu, Zhao-Pei

The focus of a beam with orbital angular momentum exhibits internal structure instead of an elliptical intensity distribution of a Gaussian beam, and the superposition of Gauss-Laguerre beams realized by two-dimensional phase modulation can generate a complex three-dimensional (3D) focus. By taking advantage of the flexibility of this 3D focus tailoring, we have fabricated a 3D microstructure with high resolution by two-photon polymerization with a single exposure. Furthermore, we have polymerized an array of double-helix structures that demonstrates optical chirality.

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.

Applications technology satellites advanced mission study

NASA Technical Reports Server (NTRS)

Gould, L. M.

1972-01-01

Three spacecraft configurations were designed for operation as a high powered synchronous communications satellite. Each spacecraft includes a 1 kw TWT and a 2 kw Klystron power amplifier feeding an antenna with multiple shaped beams. One of the spacecraft is designed to be boosted by a Thor-Delta launch vehicle and raised to synchronous orbit with electric propulsion. The other two are inserted into a elliptical transfer orbit with an Atlas Centaur and injected into final orbit with an apogee kick motor. Advanced technologies employed in the several configurations include tubes with multiple stage collectors radiating directly to space, multiple-contoured beam antennas, high voltage rollout solar cell arrays with integral power conditioning, electric propulsion for orbit raising and on-station attitude control and station-keeping, and liquid metal slip rings.

Changing Speed of Comets

ERIC Educational Resources Information Center

Follows, Mike

2003-01-01

It is shown that highly elliptical orbits, such as those of comets, can be explained well in terms of energy rather than forces. The principle of conservation of energy allows a comet's velocity to be calculated at aphelion and perihelion. An example asks students to calculate whether they can run fast enough to escape from a small asteroid.…

Evolution of starspots in the long-period RS CVN binary V1817 Cygni = HR 7428

NASA Technical Reports Server (NTRS)

Hall, Douglas S.; Gessner, Susan E.; Lines, Helen C.; Lines, Richard D.

1990-01-01

Photometry between 1982 and 1989, published and unpublished, is analyzed. The ellipticity effect produces variability with a full amplitude of 0.033 m in V. A recent time of light minimum (JD 2445988.0 + or - 0.3 d) combined with an old spectroscopic time of conjunction from the 1920's yields a much improved orbital period (108.854 + or - 0.003). Removal of the ellipticity effect reveals starspot variability. Four different spots were observed at various times, two of them present simultaneously in the light curve during 1985. Mean spot lifetimes were around 2 years and the largest amplitude attributed to starspots was 0.04 m in V during 1986. Derived rotation periods for two spots were 5.3 + or - 1.2 percent slower than synchronous and 3.0 + or - 0.4 percent faster. The differential rotation coefficient for the K2 giant is k = 0.25 + or - 0.04, compared to k = 0.186 for the sun. V1817 Cygni has the longest orbital period of any binary known to execute synchronous rotation.

Formation Flying Control Implementation in Highly Elliptical Orbits

NASA Technical Reports Server (NTRS)

Capo-Lugo, Pedro A.; Bainum, Peter M.

2009-01-01

The Tschauner-Hempel equations are widely used to correct the separation distance drifts between a pair of satellites within a constellation in highly elliptical orbits [1]. This set of equations was discretized in the true anomaly angle [1] to be used in a digital steady-state hierarchical controller [2]. This controller [2] performed the drift correction between a pair of satellites within the constellation. The objective of a discretized system is to develop a simple algorithm to be implemented in the computer onboard the satellite. The main advantage of the discrete systems is that the computational time can be reduced by selecting a suitable sampling interval. For this digital system, the amount of data will depend on the sampling interval in the true anomaly angle [3]. The purpose of this paper is to implement the discrete Tschauner-Hempel equations and the steady-state hierarchical controller in the computer onboard the satellite. This set of equations is expressed in the true anomaly angle in which a relation will be formulated between the time and the true anomaly angle domains.

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.

Mesa = Table

NASA Technical Reports Server (NTRS)

2006-01-01

10 August 2006 This Mars Global Surveyor (MGS) Mars Orbiter Camera (MOC) image shows two mesas on the northern plains of Mars. 'Mesa' is the Spanish word for 'table,' and that is a very good description of the two elliptical features captured in this MOC image. In both cases, the mesa tops and the material beneath them, down to the level of the surrounding, rugged plain, are remnants of a once more extensive layer (or layers) of material that has been largely eroded away. The circular feature near the center of the larger mesa is the site of a filled and buried impact crater.

Location near: 53.5oN, 153.5oW Image width: 3 km (1.9 mi) Illumination from: lower left Season: Northern Spring

Satellite orbits in Levi-Civita space

NASA Astrophysics Data System (ADS)

Humi, Mayer

2018-03-01

In this paper we consider satellite orbits in central force field with quadratic drag using two formalisms. The first using polar coordinates in which the satellite angular momentum plays a dominant role. The second is in Levi-Civita coordinates in which the energy plays a central role. We then merge these two formalisms by introducing polar coordinates in Levi-Civita space and derive a new equation for satellite orbits which unifies these two paradigms. In this equation energy and angular momentum appear on equal footing and thus characterize the orbit by its two invariants. Using this formalism we show that equatorial orbits around oblate spheroids can be expressed analytically in terms of Elliptic functions. In the second part of the paper we derive in Levi-Civita coordinates a linearized equation for the relative motion of two spacecrafts whose trajectories are in the same plane. We carry out also a numerical verification of these equations.

Launching rockets and small satellites from the lunar surface

NASA Technical Reports Server (NTRS)

Anderson, K. A.; Dougherty, W. M.; Pankow, D. H.

1985-01-01

Scientific payloads and their propulsion systems optimized for launch from the lunar surface differ considerably from their counterparts for use on earth. For spin-stabilized payloads, the preferred shape is a large diameter-to-length ratio to provide stability during the thrust phase. The rocket motor required for a 50-kg payload to reach an altitude of one lunar radius would have a mass of about 41 kg. To place spin-stabilized vehicles into low altitude circular orbits, they are first launched into an elliptical orbit with altitude about 840 km at aposelene. When the spacecraft crosses the desired circular orbit, small retro-rockets are fired to attain the appropriate direction and speed. Values of the launch angle, velocity increments, and other parameters for circular orbits of several altitudes are tabulated. To boost a 50-kg payload into a 100-km altitude circular orbit requires a total rocket motor mass of about 90 kg.

Launching rockets and small satellites from the lunar surface

NASA Astrophysics Data System (ADS)

Anderson, K. A.; Dougherty, W. M.; Pankow, D. H.

Scientific payloads and their propulsion systems optimized for launch from the lunar surface differ considerably from their counterparts for use on earth. For spin-stabilized payloads, the preferred shape is a large diameter-to-length ratio to provide stability during the thrust phase. The rocket motor required for a 50-kg payload to reach an altitude of one lunar radius would have a mass of about 41 kg. To place spin-stabilized vehicles into low altitude circular orbits, they are first launched into an elliptical orbit with altitude about 840 km at aposelene. When the spacecraft crosses the desired circular orbit, small retro-rockets are fired to attain the appropriate direction and speed. Values of the launch angle, velocity increments, and other parameters for circular orbits of several altitudes are tabulated. To boost a 50-kg payload into a 100-km altitude circular orbit requires a total rocket motor mass of about 90 kg.

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.

EG ANDROMEDAE: A NEW ORBIT AND ADDITIONAL EVIDENCE FOR A PHOTOIONIZED WIND

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

Kenyon, Scott J.; Garcia, Michael R., E-mail: skenyon@cfa.harvard.edu, E-mail: michael.r.garcia@nasa.gov

We analyze a roughly 20 yr set of spectroscopic observations for the symbiotic binary EG And. Radial velocities derived from echelle spectra are best fit with a circular orbit having an orbital period of P = 483.3 ± 1.6 days and semi-amplitude K = 7.34 ± 0.07 km s{sup −1}. Combined with previous data, these observations rule out an elliptical orbit at the 10 σ level. Equivalent widths of H i Balmer emission lines and various absorption features vary in phase with the orbital period. Relative to the radius of the red giant primary, the apparent size of the H ii region is consistent withmore » a model where a hot secondary star with effective temperature T{sub h} ≈ 75,000 K ionizes the wind from the red giant.« less

Simulation of interference between Earth stations and Earth-orbiting satellites

NASA Technical Reports Server (NTRS)

Bishop, D. F.

1994-01-01

It is often desirable to determine the potential for radio frequency interference between earth stations and orbiting spacecraft. This information can be used to select frequencies for radio systems to avoid interference or it can be used to determine if coordination between radio systems is necessary. A model is developed that will determine the statistics of interference between earth stations and elliptical orbiting spacecraft. The model uses orbital dynamics, detailed antenna patterns, and spectral characteristics to obtain accurate levels of interference at the victim receiver. The model is programmed into a computer simulation to obtain long-term statistics of interference. Two specific examples are shown to demonstrate the model. The first example is a simulation of interference from a fixed-satellite earth station to an orbiting scatterometer receiver. The second example is a simulation of interference from earth-exploration satellites to a deep-space earth station.

Orbital motions of bubbles in an acoustic field

NASA Astrophysics Data System (ADS)

Shirota, Minori; Yamashita, Ko; Inamura, Takao

2012-09-01

This experimental study aims to clarify the mechanism of orbital motion of two oscillating bubbles in an acoustic field. Trajectory of the orbital motion on the wall of a spherical levitator was observed using a high-speed video camera. Because of a good repeatability in volume oscillation of bubbles, we were also able to observe the radial motion driven at 24 kHz by stroboscopic like imaging technique. The orbital motions of bubbles raging from 0.13 to 0.18 mm were examined with different forcing amplitude and in different viscous oils. As a result, we found that pairs of bubbles revolve along an elliptic orbit around the center of mass of the bubbles. We also found that the two bubbles perform anti-phase radial oscillation. Although this radial oscillation should result in a repulsive secondary Bjerknes force, the bubbles kept a constant separate distance of about 1 mm, which indicates the existence of centripetal primary Bjerknes force.

Shallow structure of the InSight 2018 landing site in Elysium Planitia, Mars, from ambient vibration Rayleigh wave ellipticity: A modeling study

NASA Astrophysics Data System (ADS)

Knapmeyer-Endrun, B.; Golombek, M.; Ohrnberger, M. M.

2016-12-01

The SEIS (Seismic Experiment for Interior Structure) instrument onboard NASA's InSight mission, scheduled to land in November 2018, will be the first seismometer directly deployed on the surface of Mars. From studies on both the Earth and the Moon, it is well known that site amplification in low-velocity sediments, e.g. regolith, on top of more competent rocks has a strong influence on seismic signals, but can also be used to constrain the subsurface structure. Based on orbital data, lab measurements and terrestrial analogues, we construct a model of the shallow sub-surface at the landing site in western Elysium Planitia and simulate the ambient vibration wavefield. We show how Rayleigh wave ellipticity can be extracted from these data and inverted for shallow structure. Using reasonable variations in regolith properties, we do not expect any influence of site resonances on teleseismic quakes recorded by InSight, but recordings of local events will likely be affected. We find that higher mode ellipticity information might be extracted from the data, significantly reducing uncertainties in the inversion. Though the data are most sensitive to properties of the upper-most layer and show a strong trade-off between layer depth and velocity, it is possible to estimate the velocity and thickness of the sub-regolith layer and distinguish between different models by using reasonable constraints on regolith properties. Model parameters are best constrained if either higher mode data can be used or additional constraints on regolith properties, e.g. from analysis of hammer strokes of the HP3 heat flow probe or orbital mapping of regolith thickness from the onset diameter of rocky ejecta craters, are available. In addition, Rayleigh wave ellipticity can differentiate between models with a constant regolith velocity and models with increasing velocity with depth. We also discuss the influence of lander and leveling system mechanical noise on the identification of site resonances.

Enhanced gauge symmetry in type II and F-theory compactifications: Dynkin diagrams from polyhedra

NASA Astrophysics Data System (ADS)

Perevalov, Eugene; Skarke, Harald

1997-02-01

We explain the observation by Candelas and Font that the Dynkin diagrams of non-abelian gauge groups occurring in type IIA and F-theory can be read off from the polyhedron Δ ∗ that provides the toric description of the Calabi-Yau manifold used for compactification. We show how the intersection pattern of toric divisors corresponding to the degeneration of elliptic fibers follows the ADE classification of singularities and the Kodaira classification of degenerations. We treat in detail the cases of elliptic K3 surfaces and K3 fibered threefolds where the fiber is again elliptic. We also explain how even the occurrence of monodromy and non-simply laced groups in the latter case is visible in the toric picture. These methods also work in the fourfold case.

Elliptical polarization of near-resonant linearly polarized probe light in optically pumped alkali metal vapor

PubMed Central

Li, Yingying; Wang, Zhiguo; Jin, Shilong; Yuan, Jie; Luo, Hui

2017-01-01

Optically pumped alkali metal atoms currently provide a sensitive solution for magnetic microscopic measurements. As the most practicable plan, Faraday rotation of linearly polarized light is extensively used in spin polarization measurements of alkali metal atoms. In some cases, near-resonant Faraday rotation is applied to improve the sensitivity. However, the near-resonant linearly polarized probe light is elliptically polarized after passing through optically pumped alkali metal vapor. The ellipticity of transmitted near-resonant probe light is numerically calculated and experimentally measured. In addition, we also analyze the negative impact of elliptical polarization on Faraday rotation measurements. From our theoretical estimate and experimental results, the elliptical polarization forms an inevitable error in spin polarization measurements. PMID:28216649

Parallelization of elliptic solver for solving 1D Boussinesq model

NASA Astrophysics Data System (ADS)

Tarwidi, D.; Adytia, D.

2018-03-01

In this paper, a parallel implementation of an elliptic solver in solving 1D Boussinesq model is presented. Numerical solution of Boussinesq model is obtained by implementing a staggered grid scheme to continuity, momentum, and elliptic equation of Boussinesq model. Tridiagonal system emerging from numerical scheme of elliptic equation is solved by cyclic reduction algorithm. The parallel implementation of cyclic reduction is executed on multicore processors with shared memory architectures using OpenMP. To measure the performance of parallel program, large number of grids is varied from 28 to 214. Two test cases of numerical experiment, i.e. propagation of solitary and standing wave, are proposed to evaluate the parallel program. The numerical results are verified with analytical solution of solitary and standing wave. The best speedup of solitary and standing wave test cases is about 2.07 with 214 of grids and 1.86 with 213 of grids, respectively, which are executed by using 8 threads. Moreover, the best efficiency of parallel program is 76.2% and 73.5% for solitary and standing wave test cases, respectively.

Lunar Reconnaissance Orbiter Orbit Determination Accuracy Analysis

NASA Technical Reports Server (NTRS)

Slojkowski, Steven E.

2014-01-01

Results from operational OD produced by the NASA Goddard Flight Dynamics Facility for the LRO nominal and extended mission are presented. During the LRO nominal mission, when LRO flew in a low circular orbit, orbit determination requirements were met nearly 100% of the time. When the extended mission began, LRO returned to a more elliptical frozen orbit where gravity and other modeling errors caused numerous violations of mission accuracy requirements. Prediction accuracy is particularly challenged during periods when LRO is in full-Sun. A series of improvements to LRO orbit determination are presented, including implementation of new lunar gravity models, improved spacecraft solar radiation pressure modeling using a dynamic multi-plate area model, a shorter orbit determination arc length, and a constrained plane method for estimation. The analysis presented in this paper shows that updated lunar gravity models improved accuracy in the frozen orbit, and a multiplate dynamic area model improves prediction accuracy during full-Sun orbit periods. Implementation of a 36-hour tracking data arc and plane constraints during edge-on orbit geometry also provide benefits. A comparison of the operational solutions to precision orbit determination solutions shows agreement on a 100- to 250-meter level in definitive accuracy.

Contraction of high eccentricity satellite orbits using uniformly regular KS canonical elements with oblate diurnally varying atmosphere.

NASA Astrophysics Data System (ADS)

Raj, Xavier James

2016-07-01

Accurate orbit prediction of an artificial satellite under the influence of air drag is one of the most difficult and untraceable problem in orbital dynamics. The orbital decay of these satellites is mainly controlled by the atmospheric drag effects. The effects of the atmosphere are difficult to determine, since the atmospheric density undergoes large fluctuations. The classical Newtonian equations of motion, which is non linear is not suitable for long-term integration. Many transformations have emerged in the literature to stabilize the equations of motion either to reduce the accumulation of local numerical errors or allowing the use of large integration step sizes, or both in the transformed space. One such transformation is known as KS transformation by Kustaanheimo and Stiefel, who regularized the nonlinear Kepler equations of motion and reduced it into linear differential equations of a harmonic oscillator of constant frequency. The method of KS total energy element equations has been found to be a very powerful method for obtaining numerical as well as analytical solution with respect to any type of perturbing forces, as the equations are less sensitive to round off and truncation errors. The uniformly regular KS canonical equations are a particular canonical form of the KS differential equations, where all the ten KS Canonical elements αi and βi are constant for unperturbed motion. These equations permit the uniform formulation of the basic laws of elliptic, parabolic and hyperbolic motion. Using these equations, developed analytical solution for short term orbit predictions with respect to Earth's zonal harmonic terms J2, J3, J4. Further, these equations were utilized to include the canonical forces and analytical theories with air drag were developed for low eccentricity orbits (e < 0.2) with different atmospheric models. Using uniformly regular KS canonical elements developed analytical theory for high eccentricity (e > 0.2) orbits by assuming the atmosphere to be oblate only. In this paper a new non-singular analytical theory is developed for the motion of high eccentricity satellite orbits with oblate diurnally varying atmosphere in terms of the uniformly regular KS canonical elements. The analytical solutions are generated up to fourth-order terms using a new independent variable and c (a small parameter dependent on the flattening of the atmosphere). Due to symmetry, only two of the nine equations need to be solved analytically to compute the state vector and change in energy at the end of each revolution. The theory is developed on the assumption that density is constant on the surfaces of spheroids of fixed ellipticity ɛ (equal to the Earth's ellipticity, 0.00335) whose axes coincide with the Earth's axis. Numerical experimentation with the analytical solution for a wide range of perigee height, eccentricity, and orbital inclination has been carried out up to 100 revolutions. Comparisons are made with numerically integrated values and found that they match quite well. Effectiveness of the present analytical solutions will be demonstrated by comparing the results with other analytical solutions in the literature.

Orbit-induced localized spin angular momentum in strong focusing of optical vectorial vortex beams

NASA Astrophysics Data System (ADS)

Li, Manman; Cai, Yanan; Yan, Shaohui; Liang, Yansheng; Zhang, Peng; Yao, Baoli

2018-05-01

Light beams may carry optical spin or orbital angular momentum, or both. The spin and orbital parts manifest themselves by the ellipticity of the state of polarization and the vortex structure of phase of light beams, separately. Optical spin and orbit interaction, arising from the interaction between the polarization and the spatial structure of light beams, has attracted enormous interest recently. The optical spin-to-orbital angular momentum conversion under strong focusing is well known, while the converse process, orbital-to-spin conversion, has not been reported so far. In this paper, we predict in theory that the orbital angular momentum can induce a localized spin angular momentum in strong focusing of a spin-free azimuthal polarization vortex beam. This localized longitudinal spin of the focused field can drive the trapped particle to spin around its own axis. This investigation provides a new degree of freedom for spinning particles by using a vortex phase, which may have considerable potentials in optical spin and orbit interaction, light-beam shaping, or optical manipulation.

Intelsat communications satellite scheduled for launch

NASA Technical Reports Server (NTRS)

1983-01-01

To be placed into a highly elliptical transfer orbit by the Atlas Centaur (AC-61) launch vehicle, the INTELSAT V-F satellite has 12,000 voice circuits and 2 color television channels and incorporates a maritime communication system for ship to shore communications. The stages of the launch vehicle and the launch operations are described. A table shows the launch sequence.

Concept of Operations for the Dust Dispenser Spacecraft for Active Orbital Debris Removal

DTIC Science & Technology

2014-03-25

the fragments, liquid , and gas from the microcrater into vacuum as a recoil jet that imparts negative thrust to the debris mass. The dust vaporizes...approximately 1,100 km and maneuvers occur to lower the altitude to perhaps 200 km circular or 200 x 1,100 km elliptical , thrusters are activated

Dynamics of test particles in thin-shell wormhole spacetimes

NASA Astrophysics Data System (ADS)

Diemer, Valeria; Smolarek, Elena

2013-09-01

Geodesic motion in traversable Schwarzschild and Kerr thin-shell wormholes constructed by the cut-and-paste method introduced by Visser (1989 Nucl. Phys. B 328 203; 1995 Wormholes: from Einstein to Hawking (Woodbury, MN: American Institute of Physics)) is studied. The orbits are calculated exactly in terms of elliptic functions and visualized with the help of embedding diagrams.

Induced Ellipticity for Inspiraling Binary Systems

NASA Astrophysics Data System (ADS)

Randall, Lisa; Xianyu, Zhong-Zhi

2018-01-01

Although gravitational waves tend to erase eccentricity of an inspiraling binary system, ellipticity can be generated in the presence of surrounding matter. We present a semianalytical method for understanding the eccentricity distribution of binary black holes (BHs) in the presence of a supermassive BH in a galactic center. Given a matter distribution, we show how to determine the resultant eccentricity analytically in the presence of both tidal forces and evaporation up to one cutoff and one matter-distribution-independent function, paving the way for understanding the environment of detected inspiraling BHs. We furthermore generalize Kozai–Lidov dynamics to situations where perturbation theory breaks down for short time intervals, allowing more general angular momentum exchange, such that eccentricity is generated even when all bodies orbit in the same plane.

Flat Plate Wake Velocity Statistics Obtained With Circular And Elliptic Trailing Edges

NASA Technical Reports Server (NTRS)

Rai, Man Mohan

2016-01-01

The near wake of a flat plate with circular and elliptic trailing edges is investigated with data from direct numerical simulations. The plate length and thickness are the same in both cases. The separating boundary layers are turbulent and statistically identical. Therefore the wake is symmetric in the two cases. The emphasis in this study is on a comparison of the wake-distributions of velocity components, normal intensity and fluctuating shear stress obtained in the two cases.

Nonlinear dynamics of an elliptic vortex embedded in an oscillatory shear flow.

PubMed

Ryzhov, Eugene A

2017-11-01

The nonlinear dynamics of an elliptic vortex subjected to a time-periodic linear external shear flow is studied numerically. Making use of the ideas from the theory of nonlinear resonance overlaps, the study focuses on the appearance of chaotic regimes in the ellipse dynamics. When the superimposed flow is stationary, two general types of the steady-state phase portrait are considered: one that features a homoclinic separatrix delineating bounded and unbounded phase trajectories and one without a separatrix (all the phase trajectories are bounded in a periodic domain). When the external flow is time-periodic, the ensuing nonlinear dynamics differs significantly in both cases. For the case with a separatrix and two distinct types of phase trajectories: bounded and unbounded, the effect of the most influential nonlinear resonance with the winding number of 1:1 is analyzed in detail. Namely, the process of occupying the central stability region associated with the steady-state elliptic critical point by the stability region associated with the nonlinear resonance of 1:1 as the perturbation frequency gradually varies is investigated. A stark increase in the persistence of the central regular dynamics region against perturbation when the resonance of 1:1 associated stability region occupies the region associated with the steady-state elliptic critical point is observed. An analogous persistence of the regular motion occurs for higher perturbation frequencies when the corresponding stability islands reach the central stability region associated with the steady-state elliptic point. An analysis for the case with the resonance of 1:2 is presented. For the second case with only bounded phase trajectories and, therefore, no separatrix, the appearance of much bigger stability islands associated with nonlinear resonances compared with the case with a separatrix is reported.

Effects of solar radiation on the orbits of small particles

NASA Technical Reports Server (NTRS)

Lyttleton, R. A.

1976-01-01

A modification of the Robertson (1937) equations of particle motion in the presence of solar radiation is developed which allows for partial reflection of sunlight as a result of rapid and varying particle rotations caused by interaction with the solar wind. The coefficients and forces in earlier forms of the equations are compared with those in the present equations, and secular rates of change of particle orbital elements are determined. Orbital dimensions are calculated in terms of time, probable sizes and densities of meteoric and cometary particles are estimated, and times of infall to the sun are computed for a particle moving in an almost circular orbit and a particle moving in an elliptical orbit of high eccentricity. Changes in orbital elements are also determined for particles from a long-period sun-grazing comet. The results show that the time of infall to the sun from a highly eccentric orbit is substantially shorter than from a circular orbit with a radius equal to the mean distance in the eccentric orbit. The possibility is considered that the free orbital kinetic energy of particles drawn into the sun may be the energy source for the solar corona.

Tidal Excitation of the Core Dynamo of Mars

NASA Astrophysics Data System (ADS)

Seyed-Mahmoud, B.; Arkani-Hamed, J.; Aldridge, K.

2007-05-01

The lack of magnetic anomalies inside the giant impact basins Hellas, Isidis, Utopia and Argyre, inside the northern low lands, over the Tharsis bulge, and over the Tharsis and Olympus mounts suggests that the core field of Mars ceased to exist by about 4 Gyr ago, almost when the giant basins were formed. On the other hand, the giant basins are located on a great circle, implying that the basins were likely produced by fragments of a large asteroid that broke apart as it entered the Roche limit of Mars. This scenario offers a causative relationship for the apparent coincidence of the formation of the giant basins and the cessation of the core dynamo. We suggest that the core dynamo was excited by tidally driven elliptical instability in the Martian core. The breaking of the asteroid and its final impact on Mars eliminated the excitation and thus killed the dynamo. We show that a retrograde asteroid captured in a Keplerian orbit around Mars at a distance of about 50,000-100,000 km could orbit Mars for several hundreds of millions of years before impacting the planet due to the tidal coupling of the asteroid and Mars. Because of relatively very short growth time of the elliptical instability, less than 50,000 years, the asteroid was capable of retaining the elliptical instability and energizing the core dynamo for a geologically long period prior to 4 Ga. Our laboratory observations of a parametric instability of a rotating incompressible fluid, contained in a flexible-walled spherical cavity, confirm the possibility that an early Martian dynamo could have been powered by tidal straining.

Gravity Recovery and Interior Laboratory (GRAIL) Mission: Status at the Initiation of the Science Mapping Phase

NASA Technical Reports Server (NTRS)

Zuber, Maria T.; Smith, David E.; Asmar, Sami W.; Alomon; Konopliv, Alexander S.; Lemoine, Frank G.; Melosh, H. Jay; Neumann, Gregory A.; Phillips. Roger J.; Solomon, Sean C.;

WMAP Observatory Thermal Design and On-Orbit Thermal Performance

NASA Technical Reports Server (NTRS)

Glazer, Stuart D.; Brown, Kimberly D.; Michalek, Theodore J.; Ancarrow, Walter C.

2003-01-01

The Wilkinson Microwave Anisotropy Probe (WMAP) observatory, launched June 30, 2001, is designed to measure the cosmic microwave background radiation with unprecedented precision and accuracy while orbiting the second Lagrange point (L2). The instrument cold stage must be cooled passively to <95K, and systematic thermal variations in selected instrument components controlled to less than 0.5 mK (rms) per spin period. This paper describes the thermal design and testing of the WMAP spacecraft and instrument. Flight thermal data for key spacecraft and instrument components are presented from launch through the first year of mission operations. Effects of solar flux variation due to the Earth's elliptical orbit about the sun, surface thermo-optical property degradations, and solar flares on instrument thermal stability are discussed.

Martian bow shock: Phobos observations

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

Schwingenschuh, K.; Riedler, W.; Lichtenegger, H.

1990-05-01

Data obtained with the MAGMA magnetometer on the subsolar passes of the Phobos spacecraft during its 3 elliptic orbits reveals a turbulent bow shock with a strong foot consistent with the reflection of solar wind protons. The bow shock lies at a subsolar distance of 1.47 {plus minus} .03 R{sub M}. The circular orbit phase of the mission reveals a bow shock with a highly varying location. The median terminator crossing lies at 2.72 Mars radii. The location of the bow shock in the terminator plane is sensitive to neither the EUV flux nor to planetary longitude.

International Ultraviolet Explorer (IUE) satellite mission analysis

NASA Technical Reports Server (NTRS)

Cook, R. A.; Griffin, J. H.

1975-01-01

The results are presented of the mission analysis performed by Computer Sciences Corporation (CSC) in support of the International Ultraviolet Explorer (IUE) satellite. The launch window is open for three separate periods (for a total time of 7 months) during the year extending from July 20, 1977, to July 20, 1978. The synchronous orbit shadow constraint limits the launch window to approximately 88 minutes per day. Apogee boost motor fuel was computed to be 455 pounds (206 kilograms) and on-station weight was 931 pounds (422 kilograms). The target orbit is elliptical synchronous, with eccentricity 0.272 and 24 hour period.

Shuttle/IUS performance for planetary missions. [Interim Upper Stage

NASA Technical Reports Server (NTRS)

Cork, M. J.; Driver, J. M.; Wright, J. L.

1975-01-01

Potential requirements for planetary missions in the 1980s, capabilities of the Interim Upper Stage (IUS) candidates to perform those missions, and Shuttle/IUS mission profile options for performance enhancement are examined. The most demanding planetary missions are the Pioneer Saturn/Uranus/Titan Probe and the Mariner-class orbiters of Mercury, Jupiter, and Saturn. Options available to designers of these missions will depend on the specific IUS selected for development and the programmatic phasing of the IUS and the NASA Tug. Use of Shuttle elliptic orbits as initial conditions for IUS ignition offers significant performance improvements; specific values are mission dependent.

KSC-2014-3457

NASA Image and Video Library

2014-08-10

CAPE CANAVERAL, Fla. – A “supermoon” breaks through the clouds over Launch Complex 39 at NASA’s Kennedy Space Center in Florida. The scientific term for the supermoon phenomenon is "perigee moon." Full moons vary in size because of the oval shape of the moon's orbit. The moon follows an elliptical path around Earth with one side about 50,000 kilometers closer than the other. Full moons that occur on the perigee side of the moon's orbit seem extra big and bright. For additional information, visit http://science.nasa.gov/science-news/science-at-nasa/2014/10jul_supermoons/. Photo credit: NASA/Ben Smegelsky

Magnetospheric Multiscale Mission Navigation Performance During Apogee-Raising and Beyond

NASA Technical Reports Server (NTRS)

Farahmand, Mitra; Long, Anne; Hollister, Jacob; Rose, Julie; Godine, Dominic

2017-01-01

The primary objective of the Magnetospheric Multiscale (MMS) Mission is to study the magnetic reconnection phenomena in the Earths magnetosphere. The MMS mission consists of four identical spinning spacecraft with the science objectives requiring a tetrahedral formation in highly elliptical orbits. The MMS spacecraft are equipped with onboard orbit and time determination software, provided by a weak-signal Global Positioning System (GPS) Navigator receiver hosting the Goddard Enhanced Onboard Navigation System (GEONS). This paper presents the results of MMS navigation performance analysis during the Phase 2a apogee-raising campaign and Phase 2b science segment of the mission.

Linear and nonlinear stability of periodic orbits in annular billiards.

PubMed

Dettmann, Carl P; Fain, Vitaly

2017-04-01

An annular billiard is a dynamical system in which a particle moves freely in a disk except for elastic collisions with the boundary and also a circular scatterer in the interior of the disk. We investigate the stability properties of some periodic orbits in annular billiards in which the scatterer is touching or close to the boundary. We analytically show that there exist linearly stable periodic orbits of an arbitrary period for scatterers with decreasing radii that are located near the boundary of the disk. As the position of the scatterer moves away from a symmetry line of a periodic orbit, the stability of periodic orbits changes from elliptic to hyperbolic, corresponding to a saddle-center bifurcation. When the scatterer is tangent to the boundary, the periodic orbit is parabolic. We prove that slightly changing the reflection angle of the orbit in the tangential situation leads to the existence of Kolmogorov-Arnold-Moser islands. Thus, we show that there exists a decreasing to zero sequence of open intervals of scatterer radii, along which the billiard table is not ergodic.

Linear and nonlinear stability of periodic orbits in annular billiards

NASA Astrophysics Data System (ADS)

Dettmann, Carl P.; Fain, Vitaly

2017-04-01

An annular billiard is a dynamical system in which a particle moves freely in a disk except for elastic collisions with the boundary and also a circular scatterer in the interior of the disk. We investigate the stability properties of some periodic orbits in annular billiards in which the scatterer is touching or close to the boundary. We analytically show that there exist linearly stable periodic orbits of an arbitrary period for scatterers with decreasing radii that are located near the boundary of the disk. As the position of the scatterer moves away from a symmetry line of a periodic orbit, the stability of periodic orbits changes from elliptic to hyperbolic, corresponding to a saddle-center bifurcation. When the scatterer is tangent to the boundary, the periodic orbit is parabolic. We prove that slightly changing the reflection angle of the orbit in the tangential situation leads to the existence of Kolmogorov-Arnold-Moser islands. Thus, we show that there exists a decreasing to zero sequence of open intervals of scatterer radii, along which the billiard table is not ergodic.

How One Teacher, Two Students with Visual Impairments, and a Three-Year R & D Project Could Change How All Students Learn Science

ERIC Educational Resources Information Center

Urquhart, Vicki

2012-01-01

You probably recognize this standard definition of a comet: "a relatively small extraterrestrial body consisting of a frozen mass that travels around the sun in a highly elliptical orbit." Add an accompanying photograph or diagram, and students "get" what a comet is, right? Science textbook publishers expect students to…

Utopia Cracks and Polygons

NASA Technical Reports Server (NTRS)

2003-01-01

MGS MOC Release No. MOC2-339, 23 April 2003

This Mars Global Surveyor (MGS) Mars Orbiter Camera (MOC) image shows a pattern of polygonal cracks and aligned, elliptical pits in western Utopia Planitia. The picture covers an area about 3 km (about 1.9 mi) wide near 44.9oN, 274.7oW. Sunlight illuminates the scene from the left.

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.

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

Geier, S.; Edelmann, H.; Heber, U.

Substellar objects, like planets and brown dwarfs orbiting stars, are by-products of the star formation process. The evolution of their host stars may have an enormous impact on these small companions. Vice versa a planet might also influence stellar evolution as has recently been argued. Here, we report the discovery of an 8-23 Jupiter-mass substellar object orbiting the hot subdwarf HD 149382 in 2.391 d at a distance of only about five solar radii. Obviously, the companion must have survived engulfment in the red giant envelope. Moreover, the substellar companion has triggered envelope ejection and enabled the sdB star tomore » form. Hot subdwarf stars have been identified as the sources of the unexpected ultraviolet (UV) emission in elliptical galaxies, but the formation of these stars is not fully understood. Being the brightest star of its class, HD 149382 offers the best conditions to detect the substellar companion. Hence, undisclosed substellar companions offer a natural solution for the long-standing formation problem of apparently single hot subdwarf stars. Planets and brown dwarfs may therefore alter the evolution of old stellar populations and may also significantly affect the UV emission of elliptical galaxies.« less

Nonstationary EO/IR Clutter Suppression and Dim Object Tracking

NASA Astrophysics Data System (ADS)

Tartakovsky, A.; Brown, A.; Brown, J.

2010-09-01

We develop and evaluate the performance of advanced algorithms which provide significantly improved capabilities for automated detection and tracking of ballistic and flying dim objects in the presence of highly structured intense clutter. Applications include ballistic missile early warning, midcourse tracking, trajectory prediction, and resident space object detection and tracking. The set of algorithms include, in particular, adaptive spatiotemporal clutter estimation-suppression and nonlinear filtering-based multiple-object track-before-detect. These algorithms are suitable for integration into geostationary, highly elliptical, or low earth orbit scanning or staring sensor suites, and are based on data-driven processing that adapts to real-world clutter backgrounds, including celestial, earth limb, or terrestrial clutter. In many scenarios of interest, e.g., for highly elliptic and, especially, low earth orbits, the resulting clutter is highly nonstationary, providing a significant challenge for clutter suppression to or below sensor noise levels, which is essential for dim object detection and tracking. We demonstrate the success of the developed algorithms using semi-synthetic and real data. In particular, our algorithms are shown to be capable of detecting and tracking point objects with signal-to-clutter levels down to 1/1000 and signal-to-noise levels down to 1/4.

Tidal excitation of elliptical instability in the Martian core: Possible mechanism for generating the core dynamo

NASA Astrophysics Data System (ADS)

Arkani-Hamed, J.; Seyed-Mahmoud, B.; Aldridge, K. D.; Baker, R. E.

2008-06-01

We propose a causal relationship between the creation of the giant impact basins on Mars by a large asteroid, ruptured when it entered the Roche limit, and the excitation of the Martian core dynamo. Our laboratory experiments indicate that the elliptical instability of the Martian core can be excited if the asteroid continually exerts tidal forces on Mars for ~20,000 years. Our numerical experiments suggest that the growth-time of the instability was 5,000-15,000 years when the asteroid was at a distance of 50,000-75,000 km. We demonstrate the stability of the orbital motion of an asteroid captured by Mars at a distance of 100,000 km in the presence of the Sun and Jupiter. We also present our results for the tidal interaction of the asteroid with Mars. An asteroid captured by Mars in prograde fashion can survive and excite the elliptical instability of the core for only a few million years, whereas a captured retrograde asteroid can excite the elliptical instability for hundreds of millions of years before colliding with Mars. The rate at which tidal energy dissipates in Mars during this period is over two orders of magnitude greater than the rate at which magnetic energy dissipates. If only 1% of the tidal energy dissipation is partitioned to the core, sufficient energy would be available to maintain the core dynamo. Accordingly, a retrograde asteroid is quite capable of exciting an elliptical instability in the Martian core, thus providing a candidate process to drive a core dynamo.

Squashed Toric Sigma Models and Mock Modular Forms

NASA Astrophysics Data System (ADS)

Gupta, Rajesh Kumar; Murthy, Sameer

2018-05-01

We study a class of two-dimensional N}=(2,2)} sigma models called squashed toric sigma models, using their Gauged Linear Sigma Models (GLSM) description. These models are obtained by gauging the global {U(1)} symmetries of toric GLSMs and introducing a set of corresponding compensator superfields. The geometry of the resulting vacuum manifold is a deformation of the corresponding toric manifold in which the torus fibration maintains a constant size in the interior of the manifold, thus producing a neck-like region. We compute the elliptic genus of these models, using localization, in the case when the unsquashed vacuum manifolds obey the Calabi-Yau condition. The elliptic genera have a non-holomorphic dependence on the modular parameter {τ} coming from the continuum produced by the neck. In the simplest case corresponding to squashed {C / Z_{2 the elliptic genus is a mixed mock Jacobi form which coincides with the elliptic genus of the {N=(2,2)} {SL(2,R) / U(1)} cigar coset.

Accurate analytical periodic solution of the elliptical Kepler equation using the Adomian decomposition method

NASA Astrophysics Data System (ADS)

Alshaery, Aisha; Ebaid, Abdelhalim

2017-11-01

Kepler's equation is one of the fundamental equations in orbital mechanics. It is a transcendental equation in terms of the eccentric anomaly of a planet which orbits the Sun. Determining the position of a planet in its orbit around the Sun at a given time depends upon the solution of Kepler's equation, which we will solve in this paper by the Adomian decomposition method (ADM). Several properties of the periodicity of the obtained approximate solutions have been proved in lemmas. Our calculations demonstrated a rapid convergence of the obtained approximate solutions which are displayed in tables and graphs. Also, it has been shown in this paper that only a few terms of the Adomian decomposition series are sufficient to achieve highly accurate numerical results for any number of revolutions of the Earth around the Sun as a consequence of the periodicity property. Numerically, the four-term approximate solution coincides with the Bessel-Fourier series solution in the literature up to seven decimal places at some values of the time parameter and nine decimal places at other values. Moreover, the absolute error approaches zero using the nine term approximate Adomian solution. In addition, the approximate Adomian solutions for the eccentric anomaly have been used to show the convergence of the approximate radial distances of the Earth from the Sun for any number of revolutions. The minimal distance (perihelion) and maximal distance (aphelion) approach 147 million kilometers and 152.505 million kilometers, respectively, and these coincide with the well known results in astronomical physics. Therefore, the Adomian decomposition method is validated as an effective tool to solve Kepler's equation for elliptical orbits.

Light equation in eclipsing binary CV Boo: third body candidate in elliptical orbit

NASA Astrophysics Data System (ADS)

Bogomazov, A. I.; Kozyreva, V. S.; Satovskii, B. L.; Krushevska, V. N.; Kuznyetsova, Y. G.; Ehgamberdiev, S. A.; Karimov, R. G.; Khalikova, A. V.; Ibrahimov, M. A.; Irsmambetova, T. R.; Tutukov, A. V.

2016-12-01

A short period eclipsing binary star CV Boo is tested for the possible existence of additional bodies in the system with a help of the light equation method. We use data on the moments of minima from the literature as well as from our observations during 2014 May-July. A variation of the CV Boo's orbital period is found with a period of {≈}75 d. This variation can be explained by the influence of a third star with a mass of {≈}0.4 M_{⊙} in an eccentric orbit with e≈0.9. A possibility that the orbital period changes on long time scales is discussed. The suggested tertiary companion is near the chaotic zone around the central binary, so CV Boo represents an interesting example to test its dynamical evolution. A list of 14 minima moments of the binary obtained from our observations is presented.

Application of Monte-Carlo Analyses for the Microwave Anisotropy Probe (MAP) Mission

NASA Technical Reports Server (NTRS)

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

2001-01-01

The Microwave Anisotropy Probe (MAP) is the third launch in the National Aeronautics and Space Administration's (NASA's) a Medium Class Explorers (MIDEX) program. MAP will measure, in greater detail, the cosmic microwave background radiation from an orbit about the Sun-Earth-Moon L2 Lagrangian point. Maneuvers will be required to transition MAP from it's initial highly elliptical orbit to a lunar encounter which will provide the remaining energy to send MAP out to a lissajous orbit about L2. Monte-Carlo analysis methods were used to evaluate the potential maneuver error sources and determine their effect of the fixed MAP propellant budget. This paper will discuss the results of the analyses on three separate phases of the MAP mission - recovering from launch vehicle errors, responding to phasing loop maneuver errors, and evaluating the effect of maneuver execution errors and orbit determination errors on stationkeeping maneuvers at L2.

Mars NanoOrbiter: A CubeSat for Mars System Science

NASA Astrophysics Data System (ADS)

Ehlmann, Bethany; Klesh, Andrew; Alsedairy, Talal

2017-10-01

The Mars NanoOrbiter mission consists of two identical 12U spacecraft, launched simultaneously as secondary payloads on a larger planetary mission launch, and deployed to Earth-escape, as early as with Mars 2020. The nominal mission will last for 1 year, during which time the craft will independently navigate to Mars, enter into elliptical orbit, and achieve close flybys of Phobos and Deimos, obtaining unprecedented coverage of each moon. The craft will additionally provide high temporal resolution data of Mars clouds and atmospheric phenomena at multiple times of day. Two spacecraft provide redundancy to reduce the risk in meeting the science objectives at the Mars moons and enhanced coverage of the dynamic Mars atmosphere. This technology is enabled by recent advances in CubeSat propulsion technology, attitude control systems, guidance, navigation and control. NanoOrbiter builds directly on the systems heritage of the MarCO mission, scheduled to launch with the 2018 Discovery mission Insight.

Mars Molniya Orbit Atmospheric Resource Mining

NASA Technical Reports Server (NTRS)

Mueller, Robert P.; Braun, Robert D.; Sibille, Laurent; Sforzo, Brandon; Gonyea, Keir; Ali, Hisham

2016-01-01

This NIAC (NASA Advanced Innovative Concepts) work will focus on Mars and will build on previous efforts at analyzing atmospheric mining at Earth and the outer solar system. Spacecraft systems concepts will be evaluated and traded, to assess feasibility. However the study will primarily examine the architecture and associated missions to explore the closure, constraints and critical parameters through sensitivity studies. The Mars atmosphere consists of 95.5 percent CO2 gas which can be converted to methane fuel (CH4) and Oxidizer (O2) for chemical rocket propulsion, if hydrogen is transported from electrolyzed water on the Mars surface or from Earth. By using a highly elliptical Mars Molniya style orbit, the CO2 atmosphere can be scooped, ram-compressed and stored while the spacecraft dips into the Mars atmosphere at periapsis. Successive orbits result in additional scooping of CO2 gas, which also serves to aerobrake the spacecraft, resulting in a decaying Molniya orbit.

Extrasolar planets.

PubMed

Lissauer, J J; Marcy, G W; Ida, S

2000-11-07

The first known extrasolar planet in orbit around a Sun-like star was discovered in 1995. This object, as well as over two dozen subsequently detected extrasolar planets, were all identified by observing periodic variations of the Doppler shift of light emitted by the stars to which they are bound. All of these extrasolar planets are more massive than Saturn is, and most are more massive than Jupiter. All orbit closer to their stars than do the giant planets in our Solar System, and most of those that do not orbit closer to their star than Mercury is to the Sun travel on highly elliptical paths. Prevailing theories of star and planet formation, which are based on observations of the Solar System and of young stars and their environments, predict that planets should form in orbit about most single stars. However, these models require some modifications to explain the properties of the observed extrasolar planetary systems.

Extrasolar planets

PubMed Central

Lissauer, Jack J.; Marcy, Geoffrey W.; Ida, Shigeru

2000-01-01

The first known extrasolar planet in orbit around a Sun-like star was discovered in 1995. This object, as well as over two dozen subsequently detected extrasolar planets, were all identified by observing periodic variations of the Doppler shift of light emitted by the stars to which they are bound. All of these extrasolar planets are more massive than Saturn is, and most are more massive than Jupiter. All orbit closer to their stars than do the giant planets in our Solar System, and most of those that do not orbit closer to their star than Mercury is to the Sun travel on highly elliptical paths. Prevailing theories of star and planet formation, which are based on observations of the Solar System and of young stars and their environments, predict that planets should form in orbit about most single stars. However, these models require some modifications to explain the properties of the observed extrasolar planetary systems. PMID:11035782

Scatter of elastic waves by a thin flat elliptical inhomogeneity

NASA Technical Reports Server (NTRS)

Fu, L. S.

1983-01-01

Elastodynamic fields of a single, flat, elliptical inhomogeneity embedded in an infinite elastic medium subjected to plane time harmonic waves are studied. Scattered displacement amplitudes and stress intensities are obtained in series form for an incident wave in an arbitrary direction. The cases of a penny shaped crack and an elliptical crack are given as examples. The analysis is valid for alpha a up to about two, where alpha is longitudinal wave number and a is a typical geometric parameter.

The VLBI time delay function for synchronous orbits

NASA Technical Reports Server (NTRS)

Rosenbaum, B.

1972-01-01

The VLBI is a satellite tracking technique that to date was applied largely to the tracking of synchronous orbits. These orbits are favorable for VLBI in that the remote satellite range allows continuous viewing from widely separated stations. The primary observable, geometric time delay is the time difference for signal propagation between satellite and baseline terminals. Extraordinary accuracy in angular position data on the satellite can be obtained by observation from baselines of continental dimensions. In satellite tracking though the common objective is to derive orbital elements. A question arises as to how the baseline vector bears on the accuracy of determining the elements. Our approach to this question is to derive an analytic expression for the time delay function in terms of Kepler elements and station coordinates. The analysis, which is for simplicity based on elliptic motion, shows that the resolution for the inclination of the orbital plane depends on the magnitude of the baseline polar component and the resolution for in-plane elements depends on the magnitude of a projected equatorial baseline component.

NASA Human Spaceflight Architecture Team Cis-Lunar Analysis

NASA Technical Reports Server (NTRS)

Lupisella, M.; Bobskill, M. R.

2012-01-01

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

Properties of Earth's temporarily-captured flybys

NASA Astrophysics Data System (ADS)

Fedorets, Grigori; Granvik, Mikael

2014-11-01

In addition to the Moon, a population of small temporarily-captured NEOs is predicted to orbit the Earth. The definition of a natural Earth satellite is that it is on an elliptic geocentric orbit within 0.03 au from the Earth. The population is further divided into temporarily-captured orbiters (TCOs, or minimoons, making at least one full revolution around the Earth in a coordinate system co-rotating with the Sun) and temporarily-captured flybys (TCFs) which fail to make a full revolution, but are temporarily on an elliptic orbit around the Earth. Only one minimoon has been discovered to date, but it is expected that next generation surveys will be able to detect these objects regularly.Granvik et al. (2012) performed an extensive analysis of the behaviour of these temporarily-captured objects. One of the main results was that at any given moment there is at least one 1-meter-diameter minimoon in orbit around the Earth. However, the results of Granvik et al. (2012) raised questions considering the NES population such as the bimodality of the capture duration distribution and a distinctive lack of test particles within Earth's Hill sphere, which requires investigating the statistical properties also of the TCF population.In this work we confirm the population characteristics for minimoons described by Granvik et al. (2012), and extend the analysis to TCFs. For the calculations we use a Bulirsch-Stoer integrator implemented in the OpenOrb software package (Granvik et al. 2009). We study, e.g., the capture statistics, residence-time distributions, and steady-state properties of TCFs. Our preliminary results indicate that TCFs may be suitable targets for asteroid-redirect missions. More detailed knowledge of the TCF population will also improve our understanding of the link between temporarily-captured objects and NEOs in general.References: Granvik et al. (2009) MPS 44(12), 1853-1861; Granvik et al. (2012) Icarus 218, 262-277.

Analytical formulation of impulsive collision avoidance dynamics

NASA Astrophysics Data System (ADS)

Bombardelli, Claudio

2014-02-01

The paper deals with the problem of impulsive collision avoidance between two colliding objects in three dimensions and assuming elliptical Keplerian orbits. Closed-form analytical expressions are provided that accurately predict the relative dynamics of the two bodies in the encounter b-plane following an impulsive delta-V manoeuvre performed by one object at a given orbit location prior to the impact and with a generic three-dimensional orientation. After verifying the accuracy of the analytical expressions for different orbital eccentricities and encounter geometries the manoeuvre direction that maximises the miss distance is obtained numerically as a function of the arc length separation between the manoeuvre point and the predicted collision point. The provided formulas can be used for high-accuracy instantaneous estimation of the outcome of a generic impulsive collision avoidance manoeuvre and its optimisation.

The Kaguya Mission: Present Status and its Lunar Science.

NASA Astrophysics Data System (ADS)

Kato, M.; Takizawa, Y.; Sasaki, S.; Kaguya Team

2009-04-01

Lunar orbiter Kaguya(SELENE) has been successfully launched on September 14, 2007. After insertion into lunar orbit　on October 4 , release of two subsatellites into the elliptical orbits of 100 km perilune, and 2400 km and 800 km apolune, reach the nominal observation orbit with 100 km circular and polar on October 18, and the extension of four sounder antennas with 15 m length and the 12 m mast for magnetometer, and deployment of plasma imager, Kaguya has started nominal observation for ten months on December 21. Most of science instruments show excellent performance for ten months, and continue to acquire their data in extention mission term using saved fuel. New information and insights have been brought to lunar sciences in topography, gravimetry, geology, mineralogy, lithology, plasma physics.

Correlating Solar Wind Modulation with Ionospheric Variability at Mars from MEX and MAVEN Observations

NASA Astrophysics Data System (ADS)

Kopf, A. J.; Morgan, D. D.; Halekas, J. S.; Ruhunusiri, S.; Gurnett, D. A.; Connerney, J. E. P.

2017-12-01

The synthesis of observations by the Mars Express and Mars Atmosphere and Volatiles Evolution (MAVEN) spacecraft allows for a unique opportunity to study variability in the Martian ionosphere from multiple perspectives. One major source for this variability is the solar wind. Due to its elliptical orbit which precesses over time, MAVEN periodically spends part of its orbit outside the Martian bow shock, allowing for direct measurements of the solar wind impacting the Martian plasma environment. When the Mars Advanced Radar for Subsurface and Ionosphere Sounding (MARSIS) instrument aboard Mars Express is simultaneously sounding the ionosphere, the influence from changes in the solar wind can be observed. Previous studies have suggested a positive correlation, connecting ionospheric density to the solar wind proton flux, but depended on Earth-based measurements for solar wind conditions. More recently, research has indicated that observations of ionospheric variability from these two spacecraft can be connected in special cases, such as shock wave impacts or specific solar wind magnetic field orientations. Here we extend this to more general solar wind conditions and examine how changes in the solar wind properties measured by MAVEN instruments correlate with ionospheric structure and dynamics observed simultaneously in MARSIS remote and local measurements.

Effects of mean-field and softening of equation of state on elliptic flow in Au+Au collisions at \\sqrt{{s}_{\\rm{NN}}}=5\\,{GeV} from the JAM model

NASA Astrophysics Data System (ADS)

Chen, Jiamin; Luo, Xiaofeng; Liu, Feng; Nara, Yasushi

2018-01-01

We perform a systematic study of elliptic flow (v 2) in Au+Au collisions at \\sqrt{{s}NN}}=5 {GeV} by using a microscopic transport model, JAM. The centrality, pseudorapidity, transverse momentum and beam energy dependence of v 2 for charged as well as identified hadrons are studied. We investigate the effects of both the hadronic mean-field and the softening of equation of state (EoS) on elliptic flow. The softening of the EoS is realized by imposing attractive orbits in two body scattering, which can reduce the pressure of the system. We found that the softening of the EoS leads to the enhancement of v 2, while the hadronic mean-field suppresses v 2 relative to the cascade mode. It indicates that elliptic flow at high baryon density regions is highly sensitive to the EoS and the enhancement of v 2 may probe the signature of a first-order phase transition in heavy-ion collisions at beam energies of a strong baryon stopping region. Supported by the MoST of China 973-Project (2015CB856901), NSFC (11575069, 11221504). Y. N. is supported by the Grants-in-Aid for Scientific Research from JSPS (15K05079, 15K05098)

Flight Results of the Chandra X-ray Observatory Inertial Upper Stage Space Mission

NASA Technical Reports Server (NTRS)

Tillotson, R.; Walter, R.

2000-01-01

Under contract to NASA, a specially configured version of the Boeing developed Inertial Upper Stage (IUS) booster was provided by Boeing to deliver NASA's 1.5 billion dollar Chandra X-Ray Observatory satellite into a highly elliptical transfer orbit from a Shuttle provided circular park orbit. Subsequently, the final orbit of the Chandra satellite was to be achieved using the Chandra Integral Propulsion System (IPS) through a series of IPS burns. On 23 July 1999 the Shuttle Columbia (STS-93) was launched with the IUS/Chandra stack in the Shuttle payload bay. Unfortunately, the Shuttle Orbiter was unexpectantly inserted into an off-nominal park orbit due to a Shuttle propulsion anomaly occurring during ascent. Following the IUS/Chandra on-orbit deployment from the Shuttle, at seven hours from liftoff, the flight proven IUS GN&C system successfully injected Chandra into the targeted transfer orbit, in spite of the off-nominal park orbit. This paper describes the IUS GN&C system, discusses the specific IUS GN&C mission data load development, analyses and testing for the Chandra mission, and concludes with a summary of flight results for the IUS part of the Chandra mission.

Effective Power-Law Dependence of Lyapunov Exponents on the Central Mass in Galaxies

NASA Technical Reports Server (NTRS)

Delis, N.; Efthymiopoulos, C.; Kalapotharakos, C.

2015-01-01

Using both numerical and analytical approaches, we demonstrate the existence of an effective power-law relation L alpha m(sup p) between themean Lyapunov exponent L of stellar orbits chaotically scattered by a supermassive black hole (BH) in the centre of a galaxy and the mass parameter m, i.e. ratio of the mass of the BH over the mass of the galaxy. The exponent p is found numerically to obtain values in the range p approximately equals 0.3-0.5. We propose a theoretical interpretation of these exponents, based on estimates of local 'stretching numbers', i.e. local Lyapunov exponents at successive transits of the orbits through the BH's sphere of influence. We thus predict p = 2/3 - q with q approximately equaling 0.1-0.2. Our basic model refers to elliptical galaxy models with a central core. However, we find numerically that an effective power-law scaling of L with m holds also in models with central cusp, beyond a mass scale up to which chaos is dominated by the influence of the cusp itself. We finally show numerically that an analogous law exists also in disc galaxies with rotating bars. In the latter case, chaotic scattering by the BH affects mainly populations of thick tube-like orbits surrounding some low-order branches of the x(sub 1) family of periodic orbits, as well as its bifurcations at low-order resonances, mainly the inner Lindblad resonance and the 4/1 resonance. Implications of the correlations between L and m to determining the rate of secular evolution of galaxies are discussed.

Sedna Orbit Comparisons

NASA Image and Video Library

2004-03-15

These four panels show the location of the newly discovered planet-like object, dubbed "Sedna," which lies in the farthest reaches of our solar system. Each panel, moving counterclockwise from the upper left, successively zooms out to place Sedna in context. The first panel shows the orbits of the inner planets, including Earth, and the asteroid belt that lies between Mars and Jupiter. In the second panel, Sedna is shown well outside the orbits of the outer planets and the more distant Kuiper Belt objects. Sedna's full orbit is illustrated in the third panel along with the object's current location. Sedna is nearing its closest approach to the Sun; its 10,000 year orbit typically takes it to far greater distances. The final panel zooms out much farther, showing that even this large elliptical orbit falls inside what was previously thought to be the inner edge of the Oort cloud. The Oort cloud is a spherical distribution of cold, icy bodies lying at the limits of the Sun's gravitational pull. Sedna's presence suggests that this Oort cloud is much closer than scientists believed. http://photojournal.jpl.nasa.gov/catalog/PIA05569

Sedna Orbit Comparisons

NASA Technical Reports Server (NTRS)

2004-01-01

These four panels show the location of the newly discovered planet-like object, dubbed 'Sedna,' which lies in the farthest reaches of our solar system. Each panel, moving counterclockwise from the upper left, successively zooms out to place Sedna in context. The first panel shows the orbits of the inner planets, including Earth, and the asteroid belt that lies between Mars and Jupiter. In the second panel, Sedna is shown well outside the orbits of the outer planets and the more distant Kuiper Belt objects. Sedna's full orbit is illustrated in the third panel along with the object's current location. Sedna is nearing its closest approach to the Sun; its 10,000 year orbit typically takes it to far greater distances. The final panel zooms out much farther, showing that even this large elliptical orbit falls inside what was previously thought to be the inner edge of the Oort cloud. The Oort cloud is a spherical distribution of cold, icy bodies lying at the limits of the Sun's gravitational pull. Sedna's presence suggests that this Oort cloud is much closer than scientists believed.

Navigation Challenges in the MAVEN Science Phase

NASA Technical Reports Server (NTRS)

Demcak, Stuart; Young, Brian; Lam, Try; Trawny, Nikolas; Lee, Clifford; Anderson, Rodney; Broschart, Stephen; Ballard, Christopher; Folta, David C.

2012-01-01

The MAVEN spacecraft will explore Mars' upper atmosphere. The primary science phase will last one (Earth) year, during which the spacecraft will be in an elliptical 4.5 hour orbit at an inclination of 75 degrees. The 75 degree inclination results in the orbit periapsis oscillating between +/-75 degrees latitude, thus naturally covering most Mars latitudes during the primary mission. The orbit will be controlled via maneuvers so that the maximum orbit density remains in a density corridor. This results in the MAVEN science phase being in a light aerobraking type orbit of around 160 km for an extended period. In addition, the mission has significantly less tracking data than aerobraking phases of other missions, and even less than other NASA Mars orbiter primary phases. This results in significant challenges for the Navigation Team. They can be summarized as a difficulty in determining the current density profile, which maps into degraded trajectory predictions and less accurate control over the spacecraft location in the targeted density corridor via maneuvers. This paper describes these challenges and the Navigation Team's plans to meet them.

Evolution of the Debris Cloud Generated by the Fengyun-1C Fragmentation Event

NASA Technical Reports Server (NTRS)

Pardini, Carmen; Anselmo, Luciano

2007-01-01

The cloud of cataloged debris produced in low earth orbit by the fragmentation of the Fengyun-1C spacecraft was propagated for 15 years, taking into account all relevant perturbations. Unfortunately, the cloud resulted to be very stable, not suffering substantial debris decay during the time span considered. The only significant short term evolution was the differential spreading of the orbital planes of the fragments, leading to the formation of a debris shell around the earth approximately 7-8 months after the breakup, and the perigee precession of the elliptical orbits. Both effects will render the shell more "isotropic" in the coming years. The immediate consequence of the Chinese anti-satellite test, carried out in an orbital regime populated by many important operational satellites, was to increase significantly the probability of collision with man-made debris. For the two Italian spacecraft launched in the first half of 2007, the collision probability with cataloged objects increased by 12% for AGILE, in equatorial orbit, and by 38% for COSMO-SkyMed 1, in sun-synchronous orbit.

Lifetime maps for orbits around Callisto using a double-averaged model

NASA Astrophysics Data System (ADS)

Cardoso dos Santos, Josué; Carvalho, Jean P. S.; Prado, Antônio F. B. A.; Vilhena de Moraes, Rodolpho

2017-12-01

The present paper studies the lifetime of orbits around a moon that is in orbit around its mother planet. In the context of the inner restricted three-body problem, the dynamical model considered in the present study uses the double-averaged dynamics of a spacecraft moving around a moon under the gravitational pulling of a disturbing third body in an elliptical orbit. The non-uniform distribution of the mass of the moon is also considered. Applications are performed using numerical experiments for the Callisto-spacecraft-Jupiter system, and lifetime maps for different values of the eccentricity of the disturbing body (Jupiter) are presented, in order to investigate the role of this parameter in these maps. The idea is to simulate a system with the same physical parameters as the Jupiter-Callisto system, but with larger eccentricities. These maps are also useful for validation and improvements in the results available in the literature, such as to find conditions to extend the available time for a massless orbiting body to be in highly inclined orbits under gravitational disturbances coming from the other bodies of the system.

A new class of long-term stable lunar resonance orbits: Space weather applications and the Interstellar Boundary Explorer

NASA Astrophysics Data System (ADS)

McComas, D. J.; Carrico, J. P.; Hautamaki, B.; Intelisano, M.; Lebois, R.; Loucks, M.; Policastri, L.; Reno, M.; Scherrer, J.; Schwadron, N. A.; Tapley, M.; Tyler, R.

2011-11-01

NASA's Interstellar Boundary Explorer (IBEX) mission was recently maneuvered into a unique long-term stable Earth orbit, with apogee at ˜50 Earth radii (RE). The Moon's (˜65 RE) gravity disrupts most highly elliptical Earth orbits, leading to (1) chaotic orbital solutions, (2) the inability to predict orbital positions more than a few years into the future, and ultimately (3) mission-ending possibilities of atmospheric reentry or escape from Earth orbit. By synchronizing the satellite's orbital period to integer fractions of the Moon's sidereal period, PM = 27.3 days (e.g., PM/2 = 13.6 days, PM/3 = 9.1 days), and phasing apogee to stay away from the Moon, very long term stability can be achieved. Our analysis indicates orbital stability for well over a decade, and these IBEX-like orbits represent a new class of Earth orbits that are stable far longer than typical satellite lifetimes. These orbits provide cost-effective and nearly ideal locations for long-term space weather observations from spacecraft that can remotely image the Earth's magnetosphere from outside its boundaries while simultaneously providing external (solar wind or magnetosheath) observation over most of their orbits. Utilized with multiple spacecraft, such orbits would allow continuous and simultaneous monitoring of the magnetosphere in order to help predict and mitigate adverse space weather-driven effects.

KSC-2014-3456

NASA Image and Video Library

2014-08-10

CAPE CANAVERAL, Fla. – Clouds over Launch Complex 39 at NASA’s Kennedy Space Center in Florida threaten to obscure the view of the “supermoon” forecast to light up the sky. The scientific term for the supermoon phenomenon is "perigee moon." Full moons vary in size because of the oval shape of the moon's orbit. The moon follows an elliptical path around Earth with one side about 50,000 kilometers closer than the other. Full moons that occur on the perigee side of the moon's orbit seem extra big and bright. For additional information, visit http://science.nasa.gov/science-news/science-at-nasa/2014/10jul_supermoons/. Photo credit: NASA/Ben Smegelsky

KSC-2014-3453

NASA Image and Video Library

2014-08-10

CAPE CANAVERAL, Fla. – Night falls over the turn basin in Launch Complex 39 at NASA’s Kennedy Space Center in Florida, bringing with it expectations of the appearance of a “supermoon.” The scientific term for the supermoon phenomenon is "perigee moon." Full moons vary in size because of the oval shape of the moon's orbit. The moon follows an elliptical path around Earth with one side about 50,000 kilometers closer than the other. Full moons that occur on the perigee side of the moon's orbit seem extra big and bright. For additional information, visit http://science.nasa.gov/science-news/science-at-nasa/2014/10jul_supermoons/. Photo credit: NASA/Ben Smegelsky

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.

Analysis of reentry into the White Sands Missile Range (WSMR) for the LifeSat mission

NASA Technical Reports Server (NTRS)

Hametz, M.; Roszman, L.; Snow, F.; Cooley, J.

1993-01-01

This study investigates the reentry of the LifeSat vehicles into the WSMR. The LifeSat mission consists of two reusable reentry satellites, each carrying a removable payload module, which scientists will use to study long-term effects of microgravity, Van Allen belt radiation, and galactic cosmic rays on living organisms. A series of missions is planned for both low-Earth circular orbits and highly elliptic orbits. To recover the payload module with the specimens intact, a soft parachute landing and recovery at the WSMR is planned. This analysis examines operational issues surrounding the reentry scenario to assess the feasibility of the reentry.

Infrared imaging spectroscopy of the Galactic center - Distribution and motions of the ionized gas

NASA Technical Reports Server (NTRS)

Herbst, T. M.; Beckwith, S. V. W.; Forrest, W. J.; Pipher, J. L.

1993-01-01

High spatial spectral resolution IR images of the Galactic center in the Br-gamma recombination line of hydrogen were taken. A coherent filament of gas extending from north of IRS 1, curving around IRS 16/Sgr A complex, and continuing to the southwest, is seen. Nine stellar sources have associated Br-gamma emission. The total Br-gamma line flux in the filament is approximately 3 x 10 exp -15 W/sq m. The distribution and kinematics of the northern arm suggest orbital motion; the observations are accordingly fit with elliptical orbits in the field of a central point of mass.

LOOPUS Mob-D: System concept for a public mobile satellite system providing integrated digital services for the Northern Hemisphere from an elliptical orbit

NASA Technical Reports Server (NTRS)

Kuhlen, H.; Horn, P.

1990-01-01

A new concept for a satellite based public mobile communications system, LOOPUS Mob-D, is introduced, whereby most of the classical problems in mobile satellite systems are approached in a different way. The LOOPUS system will offer a total capacity of 6000 high rate channels in three service areas (Europe, Asia, and North America), covering the entire Northern Hemisphere with a set of group special mobile (GSM) compatible mobile services, eventually providing the 'office in the car'. Special characteristics of the LOOPUS orbit and the communications network architecture are highlighted.

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

NASA Technical Reports Server (NTRS)

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

2011-01-01

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

Apollonius [Apollonios] of Perga (200-100 BC)

NASA Astrophysics Data System (ADS)

Murdin, P.

2000-11-01

Greek geometer from Perga, now in Turkey, who proposed that the planets revolved around the Sun, and the Sun revolves around the Earth. Apollonius left no astronomical works but is believed to be the inventor of the geometric system of epicycles and eccentric circles, by which perfect circular motions were combined into the actual elliptical orbits of the planets. His work was developed by HIPPAR...

Violent Relaxation, Dynamical Instabilities and the Formation of Elliptical Galaxies

NASA Astrophysics Data System (ADS)

Aguilar, L. A.

1990-11-01

RESUMEN: El problema de la formaci6n de galaxias elfpticas por medjo de colapso gravitacional sin disipaci6n de energfa es estudiado usando un gran numero de simulaciones numericas. Se muestra que este tipo de colapsos, partiendo de condiciones iniciales frfas donde la energfa cinetica inicial representa s6lo un 5%, 0 , de a potencial inicial, produce sistemas relajados de forma triaxial muy similares a las galaxias elfpticas reales en sus formas y perfiles de densidad en proyecci6i . La forina triaxial resulta de la acci6n de una inestabilidad dinamica que aparece en sistemas 'inicos dominados por movimientos radiales, mientras que el perfil de densidad final Cs debido al llamado relajamiento violento que tiende a producir una distribuci6n en espacio fase unica. Estos dos fen6menos tienden a borrar los detalles particulares sobre las condiciones iniciales y dan lugar a una evoluci6n convergente hacia sistemas realistas, esto innecesario el uso de condiciones iniciales especiales (excepto por Ia condici6i de que estas deben ser frfas). Las condiciones iniciales frfas producen los movimientos radiales y fluctuaciones de la energfa potencial requeridos por ambos fen6menos. ABSTRACT: The problem of formation of elliptical galaxies via dissipationless collapse is studied using a large set of numerical simulations. It is shown that dissipationless collapses from cold initial conditions, where the total initial kinetic energy is less than 5% ofthe initial potential energy, lead to relaxed triaxial systems ery similar to real elliptical galaxies ii projected shape and density profiles. The triaxial shape is due to the of a dynamical instability that appears on systems dominated by radial orbits, while final density profile is due to violent relaxation that tends to produce a unique distribution iii space. These two phenomena erase memory of the initial prodtice a convergent evolution toward realistic systems, thus making unnecessary use o[special initial conditions (other than the condition ofbeing cold). Cold initial the radial orbits and large potential energy fluctuations necessary for both and are thus sufficient. KQ words: GALAXIES-DYNAMICS - GALAXIES-ELLIPTICAL - GALAXIES-FORMATION

Current Highlights on ESA's Planetary Technology Reference Studies

NASA Astrophysics Data System (ADS)

Falkner, P.

The concept of Technology Reference Studies has been introduced already at EGU05, where the Venus Entry Probe (VEP), the Jupiter Minisat Explorer (JME), the Deimos Sample Return (DSR) and the Interstellar Heliopause Probe (IHP) have been presented in detail. At the EGU06 the new studies in reaction to the Cosmic Vision exercise have been introduced. The formulation of themes and mapping into potential future missions has been taken as basis in the planning of additional new and adaptation of existing TRS's to cover areas, which have not yet been addressed by any TRS. These new ongoing studies are progressing well and current highlights will be presented in the paper in further detail as well as an overview on supporting technology studies and Concurrent Design Facility (CDF) sessions. The Jupiter System Explorer (JSE) study investigates mission concepts with up to two Magnetospheric Orbiters placed in a highly elliptical Jovian orbit and the possibility to deploy a Jovian Entry Probe. The mission profile is based on a solar powered concept launched on a Soyuz-Fregat launcher. Mission analysis and the application of a new Jovian radiation model are supporting the study activities. The Near-Earth Asteroid Sample Return (NEA-SR) concept explores the possibilities of sample return or in-situ mission profiles with visits to up to two NEA targets. Due to the assumed low cost cap a trade between a sample return and remote/in-situ exploration concept has a high attention in the study. The Cross Scale TRS (CS-TRS) is intended to simultaneously investigate magnetospheric and plasma processes in three spatial scales with a formation flight of up to 12 spacecraft, orbiting on deep elliptical orbits around Earth. One of the major challenges is the launch of that number of spacecraft on a single launcher and the collisionless deployment of the formation at the target orbit. The scope if the GeoSail TRS is to demonstrate deployment, attitude control and navigation concepts for a solar sailing mission as required by Interstellar Heliopause Probe (IHP) or Solar Polar Orbiter (SPO) mission concepts and to investigate the potential influence of the extended sail for science measurements.

Libration Point Navigation Concepts Supporting Exploration Vision

NASA Technical Reports Server (NTRS)

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

2004-01-01

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

The Architectural Design Rules of Solar Systems Based on the New Perspective

NASA Astrophysics Data System (ADS)

Sharma, Bijay Kumar

2011-05-01

In this paper I present a new perspective of the birth and evolution of Planetary Systems. This new perspective presents an all encompassing and self consistent Paradigm of the birth and evolution of the solar systems. In doing so it redefines astronomy and rewrites astronomical principles. Kepler and Newton defined a stable and non-evolving elliptical orbits. While this perspective defines a collapsing or expanding spiral orbit of planets except for Brown Dwarfs. Brown Dwarfs are significant fraction of the central star. Hence they rapidly evolve from non-Keplerian state to the end point which is a Keplerian state where it is in stable elliptical orbits. On the basis of the Lunar Laser Ranging Data released by NASA on the Silver Jubilee Celebration of Man's Landing on Moon on 21st July 1969-1994, theoretical formulation of Earth-Moon tidal interaction was carried out and Planetary Satellite Dynamics was established. It was found that this mathematical analysis could as well be applied to Star and Planets system and since every star could potentially contain an extra-solar system, hence we have a large ensemble of exo-planets to test our new perspective on the birth and evolution of solar systems. Till date 403 exo-planets have been discovered in 390 extra-solar systems by radial velocity method, by transiting planet method, by gravitational lensing method, by direct imaging method and by timing method. I have taken 12 single planet systems, four Brown Dwarf - Star systems and two Brown Dwarf pairs. Following architectural design rules are corroborated through this study of exo-planets. All planets are born at inner Clarke's Orbit what we refer to as inner geo-synchronous orbit in case of Earth-Moon System. The inner Clarke's Orbit is an orbit of unstable equilibrium. By any perturbative force such as cosmic particles or radiation pressure, the planet gets tipped long of aG1 or short of aG1. Here aG1 is inner Clarke's Orbit. If planet is long of aG1 then it is said to be in extra-synchronous orbit. Here Gravitational Sling Shot effect is in play. In gravity assist planet fly-by maneuver in space flights, gravitational sling shot is routinely used to boost the space craft to its destination. The exo-planet can either be launched on death spiral as CLOSE HOT JUPITERS or can be launched on an expanding spiral path as the planets in our Solar System are. In death spiral, exo-planet less than 5 mJ will get pulverized and vaporized in close proximity to the host star. If the mass is between 5 and 7.5 mJ then it will be partially vaporized and partially engulfed by the host star and if it is greater than 7.5 mJ, then it will be completely ingested by the host star. In the process the planet will deposit all its material and angular momentum in the Host Star. This will leave tell-tale imprints of ingestion: in such cases host Star will have higher 7Li, host star will become a rapidly rotating progenitor and the host star will have excess IR. All these have been confirmed by observations of Transiting Planets. It was also found that if the exo-planet are significant fraction of the host star then those exo-planets rapidly migrate from aG1 to aG2 and have very short Time Constant of Evolution as Brown Dwarfs have. But if exo-planets are insignificant fraction of the host star as our terrestrial planets are then they are stay put in their original orbit of birth. By corollary this implies that Giant exo-planets reach nearly Unity Evolution Factor in a fraction of the life span of a solar system. This is particularly true for brown dwarfs orbiting main sequence stars. In this study four star systems hosting Brown Dwarfs, two Brown Dwarf pairs and 12 extrasolar systems hosting Jupiter sized planets are selected. In Brown Dwarfs evolution factor is invariably UNITY or near UNITY irrespective of their respective age and Time Constant of Evolution is very short of the order of year or tens of years. In case of 12 exo-planets system with increasing mass ratio evolution factor increases and time constant of evolution shortens from Gy to My though there are two exceptions. TW Hydrae is a special case. This Solar System is newly born system which is only 9 million years old. Hence its exo-planet has just been born and it is very near its birth place just as predicted by my hypothesis. In fact it is only slightly greater than aG1. This vindicates our basic premise that planets are always born at inner Clarke's Orbit. This study vindicates the design rules which had been postulated at 35th COSPAR Scientific Assembly in 2004 at Paris, France, under the title "New Perspective on the Birth & Evolution of Solar Systems".

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

NASA Astrophysics Data System (ADS)

Zamaro, Mattia; Biggs, James D.

2016-02-01

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

An exact solution for orbit view-periods from a station on a tri-axial ellipsoidal planet

NASA Technical Reports Server (NTRS)

Tang, C. C. H.

1986-01-01

This paper presents the concise exact solution for predicting view-periods to be observed from a masked or unmasked tracking station on a tri-axial ellipsoidal surface. The new exact approach expresses the azimuth and elevation angles of a spacecraft in terms of the station-centered geodetic topocentric coordinates in an elegantly concise manner. A simple and efficient algorithm is developed to avoid costly repetitive computations in searching for neighborhoods near the rise and set times of each satellite orbit for each station. Only one search for each orbit is necessary for each station. Sample results indicate that the use of an assumed spherical earth instead of an 'actual' tri-axial ellipsoidal earth could introduce an error up to a few minutes in a view-period prediction for circular orbits of low or medium altitude. For an elliptical orbit of high eccentricity and long period, the maximum error could be even larger. The analytic treatment and the efficient algorithm are designed for geocentric orbits, but they should be applicable to interplanetary trajectories by an appropriate coordinates transformation at each view-period calculation. This analysis can be accomplished only by not using the classical orbital elements.

Long-term evaluation of orbital dynamics in the Sun-planet system considering axial-tilt

NASA Astrophysics Data System (ADS)

Bakhtiari, Majid; Daneshjou, Kamran

2018-05-01

In this paper, the axial-tilt (obliquity) effect of planets on the motion of planets’ orbiter in prolonged space missions has been investigated in the presence of the Sun gravity. The proposed model is based on non-simplified perturbed dynamic equations of planetary orbiter motion. From a new point of view, in this work, the dynamic equations regarding a disturbing body in elliptic inclined three-dimensional orbit are derived. The accuracy of this non-simplified method is validated with dual-averaged method employed on a generalized Earth-Moon system. It is shown that the neglected short-time oscillations in dual-averaged technique can accumulate and propel to remarkable errors in the prolonged evolution. After validation, the effects of the planet’s axial-tilt on eccentricity, inclination and right ascension of the ascending node of the orbiter are investigated. Moreover, a generalized model is provided to study the effects of third-body inclination and eccentricity on orbit characteristics. It is shown that the planet’s axial-tilt is the key to facilitating some significant changes in orbital elements in long-term mission and short-time oscillations must be considered in accurate prolonged evaluation.

An exact solution for orbit view-periods from a station on a tri-axial ellipsoidal planet

NASA Astrophysics Data System (ADS)

Tang, C. C. H.

1986-08-01

This paper presents the concise exact solution for predicting view-periods to be observed from a masked or unmasked tracking station on a tri-axial ellipsoidal surface. The new exact approach expresses the azimuth and elevation angles of a spacecraft in terms of the station-centered geodetic topocentric coordinates in an elegantly concise manner. A simple and efficient algorithm is developed to avoid costly repetitive computations in searching for neighborhoods near the rise and set times of each satellite orbit for each station. Only one search for each orbit is necessary for each station. Sample results indicate that the use of an assumed spherical earth instead of an 'actual' tri-axial ellipsoidal earth could introduce an error up to a few minutes in a view-period prediction for circular orbits of low or medium altitude. For an elliptical orbit of high eccentricity and long period, the maximum error could be even larger. The analytic treatment and the efficient algorithm are designed for geocentric orbits, but they should be applicable to interplanetary trajectories by an appropriate coordinates transformation at each view-period calculation. This analysis can be accomplished only by not using the classical orbital elements.

Application of the dressed-bound-state molecular strong-field approximation to above-threshold ionization of heteronuclear molecules: NO vs. CO.

PubMed

Busuladžić, M; Hasović, E; Becker, W; Milošević, D B

2012-10-07

We theoretically investigate high-order above-threshold ionization (HATI) of heteronuclear diatomic molecules applying the molecular strong-field approximation which includes dressing of the molecular bound state. We consider HATI of nitrogen monoxide molecules, which are characterized by the π symmetry of their highest occupied molecular orbital. We show that the HATI spectra of NO exhibit characteristic interference structures. We analyze the differences and similarities of the HATI spectra of NO molecules and the spectra of CO (σ symmetry) and O(2) (π(g) symmetry) molecules. The symmetry properties of the molecular HATI spectra governed by linearly and elliptically polarized fields are considered in detail. The yields of high-energy electrons, contributing to the plateau region of the photoelectron spectra, strongly depend on the employed ellipticity.

Stability of triangular lagrangian points in elliptical restricted three body problem under the radiating binary systems

NASA Astrophysics Data System (ADS)

Narayan, A.; Singh, Nutan

2014-10-01

This paper studies the stability of Triangular Lagrangian points in the model of elliptical restricted three body problem, under the assumption that both the primaries are radiating. The model proposed is applicable to the well known binary systems Achird, Luyten, αCen AB, Kruger-60, Xi-Bootis. Conditional stability of the motion around the triangular points exists for 0≤ μ≤ μ ∗, where μ is the mass ratio. The method of averaging due to Grebenikov has been exploited throughout the analysis of stability of the system. The critical mass ratio depends on the combined effects of radiation of both the primaries and eccentricity of this orbit. It is found by adopting the simulation technique that the range of stability decreases as the radiation pressure parameter increases.

System Engineering Issues for Avionics Survival in the Space Environment

NASA Technical Reports Server (NTRS)

Pavelitz, Steven

1999-01-01

This paper examines how the system engineering process influences the design of a spacecraft's avionics by considering the space environment. Avionics are susceptible to the thermal, radiation, plasma, and meteoroids/orbital debris environments. The environment definitions for various spacecraft mission orbits (LEO/low inclination, LEO/Polar, MEO, HEO, GTO, GEO and High ApogeeElliptical) are discussed. NASA models and commercial software used for environment analysis are reviewed. Applicability of technical references, such as NASA TM-4527 "Natural Orbital Environment Guidelines for Use in Aerospace Vehicle Development" is discussed. System engineering references, such as the MSFC System Engineering Handbook, are reviewed to determine how the environments are accounted for in the system engineering process. Tools and databases to assist the system engineer and avionics designer in addressing space environment effects on avionics are described and usefulness assessed.

Spin Relaxation and Manipulation in Spin-orbit Qubits

NASA Astrophysics Data System (ADS)

Borhani, Massoud; Hu, Xuedong

2012-02-01

We derive a generalized form of the Electric Dipole Spin Resonance (EDSR) Hamiltonian in the presence of the spin-orbit interaction for single spins in an elliptic quantum dot (QD) subject to an arbitrary (in both direction and magnitude) applied magnetic field. We predict a nonlinear behavior of the Rabi frequency as a function of the magnetic field for sufficiently large Zeeman energies, and present a microscopic expression for the anisotropic electron g-tensor. Similarly, an EDSR Hamiltonian is devised for two spins confined in a double quantum dot (DQD). Finally, we calculate two-electron-spin relaxation rates due to phonon emission, for both in-plane and perpendicular magnetic fields. Our results have immediate applications to current EDSR experiments on nanowire QDs, g-factor optimization of confined carriers, and spin decay measurements in DQD spin-orbit qubits.

Orbit and uncertainty propagation: a comparison of Gauss-Legendre-, Dormand-Prince-, and Chebyshev-Picard-based approaches

NASA Astrophysics Data System (ADS)

Aristoff, Jeffrey M.; Horwood, Joshua T.; Poore, Aubrey B.

2014-01-01

We present a new variable-step Gauss-Legendre implicit-Runge-Kutta-based approach for orbit and uncertainty propagation, VGL-IRK, which includes adaptive step-size error control and which collectively, rather than individually, propagates nearby sigma points or states. The performance of VGL-IRK is compared to a professional (variable-step) implementation of Dormand-Prince 8(7) (DP8) and to a fixed-step, optimally-tuned, implementation of modified Chebyshev-Picard iteration (MCPI). Both nearly-circular and highly-elliptic orbits are considered using high-fidelity gravity models and realistic integration tolerances. VGL-IRK is shown to be up to eleven times faster than DP8 and up to 45 times faster than MCPI (for the same accuracy), in a serial computing environment. Parallelization of VGL-IRK and MCPI is also discussed.

The Effect of Orifice Eccentricity on Instability of Liquid Jets

NASA Astrophysics Data System (ADS)

Amini, Ghobad; Dolatabadi, Ali

2011-11-01

The hydrodynamic instability of inviscid jets issuing from elliptic orifices is studied. A linear stability analysis is presented for liquid jets that includes the effect of the surrounding gas and an explicit dispersion equation is derived for waves on an infinite uniform jet column. Elliptic configuration has two extreme cases; round jet when ratio of minor to major axis is unity and plane sheet when this ratio approaches zero. Dispersion equation of elliptic jet is approximated for large and small aspect ratios considering asymptotic of the dispersion equation. In case of aspect ratio equal to one, the dispersion equation is analogous to one of the circular jets derived by Yang. In case of aspect ratio approaches zero, the behavior of waves is qualitatively similar to that of long waves on a two dimensional liquid jets and the varicose and sinuous modes are predicted. The growth rate of initial disturbances for various azimuthal modes has been presented in a wide range of disturbances. PhD Candidate.

Mechanical Slosh Models for Rocket-Propelled Spacecraft

NASA Technical Reports Server (NTRS)

Jang, Jiann-Woei; Alaniz, Abram; Yang, Lee; Powers. Joseph; Hall, Charles

2013-01-01

Several analytical mechanical slosh models for a cylindrical tank with flat bottom are reviewed. Even though spacecrafts use cylinder shaped tanks, most of those tanks usually have elliptical domes. To extend the application of the analytical models for a cylindrical tank with elliptical domes, the modified slosh parameter models are proposed in this report by mapping an elliptical dome cylindrical tank to a flat top/bottom cylindrical tank while maintaining the equivalent liquid volume. For the low Bond number case, the low-g slosh models were also studied. Those low-g models can be used for Bond number > 10. The current low-g slosh models were also modified to extend their applications for the case that liquid height is smaller than the tank radius. All modified slosh models are implemented in MATLAB m-functions and are collected in the developed MST (Mechanical Slosh Toolbox).

Is the Capsular Bag Perimeter Round or Elliptical?

PubMed Central

Amigó, Alfredo; Bonaque-González, Sergio

2016-01-01

Purpose: To report findings that could suggest an elliptical shape of the capsular bag. Methods: Five eyes of three patients with axial length greater than 24 mm underwent phacoemulsification cataract surgery with plate-haptic multifocal toric intraocular lens (IOL) implantation oriented in the vertical meridian. Results: In all cases, correct orientation of the IOLs was verified 30 minutes after surgery. After 24 hours, all eyes demonstrated unwanted rotation of the IOLs ranging from 15 to 45 degrees. The IOLs remained stable in the new position in all cases until adhesion of the capsular bag took place. Conclusion: These observations could suggest that the perimeter of the capsular bag has an elliptical shape. Therefore, the IOL tends to become fixated in a meridian of the capsular bag that best fits the diagonal diameter of the IOL. PMID:27413495

Uranus and the shape of elliptical rings

NASA Technical Reports Server (NTRS)

Lucke, R. L.

1978-01-01

It is reported that when the star SAO158687 passed behind the Uranus system, its light was occulted twice by the epsilon (fifth) ring of the planet. The first part of the ring to occult was about 100 km wide and the second part was about 40 km wide. The variable width of the ring is accounted for by differences in the orbital eccentricities of the individual particles composing the ring.

A Framework for Designing Optimal Spacecraft Formations

DTIC Science & Technology

2002-09-01

to the Hill- Clohessy - Wiltshire equations were reproduced. For an example using elliptical reference orbits, Reference 17 outlines a solution with...2001. 15. Clohessy , W.H. and Wiltshire , R. S., “Terminal Guidance System for Satellite Rendezvous,” Journal of the Aerospace Sciences, Vol.27, No...Hill- Clohessy -Wiltshire15 (C-W) equations were chosen as the first model specifically because the solutions were known. This allowed a validation

Stability of triangular points in the elliptic restricted three-body problem with oblateness up to zonal harmonic J4 of both primaries

NASA Astrophysics Data System (ADS)

Singh, Jagadish; Tyokyaa, Richard K.

2016-10-01

In this paper, we study the locations and stability of triangular points in the elliptic restricted three-body problem when both primaries are taken as oblate spheroids with oblateness up to J4. The positions of the triangular points are seen to be affected by oblateness of the primaries and the eccentricity of their orbits. The triangular points are conditionally stable for 0<μ<μc0<μ<μc and unstable for μc≤μ≤12μc≤μ≤12, where μcμc is the critical mass parameter depending on the oblateness coefficients J2iJ2i (i =1,2) and the eccentricity of the orbits. We further observe that both coefficients J2 and J4, semi-major axis and the eccentricity have destabilizing tendencies resulting in a decrease in the size of the region of stability with an increase in the parameters involved. Knowing that, in general, the triangular equilibrium points are stable for 0<μ<μc0<μ<μc, in particular systems (Alpha Centauri, X1X1 Bootis, Sirius and Kruger 60) this does not hold and such points are unstable.

GSC 4232.2850, a new eclipsing binary with elliptical orbit

NASA Astrophysics Data System (ADS)

Goranskij, V.; Shugarov, S.; Kroll, P.; Golovin, A.

2005-04-01

GSC 4232.2830 (20h 01m 28s.407, +61? 10' 17".18, 2000.0, v=12m.1) was suspected to be an eclipsing binary by VPG in the routine overview of photographical plates taken with 40-cm astrograph of SAI Crimean station. To define orbital elements of the binary, we searched for observations in Sonneberg Observatory plate collection, NSVS database (Wozniak et al., 2004), and carried out visual monitoring with a small telescope equipped with an electronic image tube, an analogue of a night vision device. Later, when we had found a preliminary solution, we carried out accurate CCD photometry to improve the orbital elements. We should note, that the depths of eclipses in the NSVS database do not exceed 0m.2, what contradicts to other observations. We suppose that NSVS measurements concern to integral light of two stars, a variable star, and a nearby brighter star, GSC 4232.2395, due to low resolution of this survey, 72". Using all the available observations we found the single orbital solution with an elliptical orbit and the period of 11,6 day. The center of the secondary minimum occurs at the orbital phase 0.69835 or 8.1 day after the primary minimum. The improved ephemeris derived using accurate CCD observations is following: HJD Min I = 2453278,3185(2) + 11.628188 (5) x E. O-C analysis does not show orbital period variations during the time interval of observations, or any evidence of apsidal motion. The observations show that both eclipses have about equal depth 0m.60, but essentially different duration, 0p.028 (7 h.8) for Min I, and 0 p.0175 (4 h.9) for Min II. The eclipses are partial. CCD photometry gives mean colors U-B = -0 m.06, B-V = 0 m.57, and V-R = 0 m.50 without notable color variations in the eclipse phases. Old Sonneberg photographic observations indicate that the eclipses were shallower in the middle of the past century than in the present time! Such contradictions may suggest that the depth of eclipses varied, as in the well-known system SSLac (Mossakovskaja, 1993; Milone et al, 2000; Torres and Stefanic, 2001). The eclipse depth variations should be verified with more precise observations taken during the longer time interval.

Demonstration of an Aerocapture GN and C System Through Hardware-in-the-Loop Simulations

NASA Technical Reports Server (NTRS)

Masciarelli, James; Deppen, Jennifer; Bladt, Jeff; Fleck, Jeff; Lawson, Dave

2010-01-01

Aerocapture is an orbit insertion maneuver in which a spacecraft flies through a planetary atmosphere one time using drag force to decelerate and effect a hyperbolic to elliptical orbit change. Aerocapture employs a feedback Guidance, Navigation, and Control (GN&C) system to deliver the spacecraft into a precise postatmospheric orbit despite the uncertainties inherent in planetary atmosphere knowledge, entry targeting and aerodynamic predictions. Only small amounts of propellant are required for attitude control and orbit adjustments, thereby providing mass savings of hundreds to thousands of kilograms over conventional all-propulsive techniques. The Analytic Predictor Corrector (APC) guidance algorithm has been developed to steer the vehicle through the aerocapture maneuver using bank angle control. Through funding provided by NASA's In-Space Propulsion Technology Program, the operation of an aerocapture GN&C system has been demonstrated in high-fidelity simulations that include real-time hardware in the loop, thus increasing the Technology Readiness Level (TRL) of aerocapture GN&C. First, a non-real-time (NRT), 6-DOF trajectory simulation was developed for the aerocapture trajectory. The simulation included vehicle dynamics, gravity model, atmosphere model, aerodynamics model, inertial measurement unit (IMU) model, attitude control thruster torque models, and GN&C algorithms (including the APC aerocapture guidance). The simulation used the vehicle and mission parameters from the ST-9 mission. A 2000 case Monte Carlo simulation was performed and results show an aerocapture success rate of greater than 99.7%, greater than 95% of total delta-V required for orbit insertion is provided by aerodynamic drag, and post-aerocapture orbit plane wedge angle error is less than 0.5 deg (3-sigma). Then a real-time (RT), 6-DOF simulation for the aerocapture trajectory was developed which demonstrated the guidance software executing on a flight-like computer, interfacing with a simulated IMU and simulated thrusters, with vehicle dynamics provided by an external simulator. Five cases from the NRT simulations were run in the RT simulation environment. The results compare well to those of the NRT simulation thus verifying the RT simulation configuration. The results of the above described simulations show the aerocapture maneuver using the APC algorithm can be accomplished reliably and the algorithm is now at TRL-6. Flight validation is the next step for aerocapture technology development.

Computer program for calculating supersonic flow about circular, elliptic, and bielliptic cones by the method of lines

NASA Technical Reports Server (NTRS)

Klunker, E. B.; South, J. C., Jr.; Davis, R. M.

1972-01-01

A user's manual for a computer program which calculates the supersonic flow about circular, elliptic, and bielliptic cones at incidence and elliptic cones at yaw by the method of lines is presented. The program is automated to compute a case from known or easily calculated solution by changing the parameters through a sequence of steps. It provides information including the shock shape, flow field, isentropic surface properties, entropy layer, and force coefficients. A description of the program operation, sample computations, and a FORTRAN 4 listing are presented.

Elliptical concentrators.

PubMed

Garcia-Botella, Angel; Fernandez-Balbuena, Antonio Alvarez; Bernabeu, Eusebio

2006-10-10

Nonimaging optics is a field devoted to the design of optical components for applications such as solar concentration or illumination. In this field, many different techniques have been used to produce optical devices, including the use of reflective and refractive components or inverse engineering techniques. However, many of these optical components are based on translational symmetries, rotational symmetries, or free-form surfaces. We study a new family of nonimaging concentrators called elliptical concentrators. This new family of concentrators provides new capabilities and can have different configurations, either homofocal or nonhomofocal. Translational and rotational concentrators can be considered as particular cases of elliptical concentrators.

Elliptical flux vortices in YBa2Cu3O7

NASA Technical Reports Server (NTRS)

Hickman, H.; Dekker, A. J.; Chen, T. M.

1991-01-01

The most energetically favorable vortex in YBa2Cu3O7 forms perpendicular to an anisotropic plane. This vortex is elliptical in shape and is distinguished by an effective interchange of London penetration depths from one axis of the ellipse to another. By generalizing qualitatively from the isotropic to the anisotropic case, we suggest that the flux flow resistivity for the vortex that forms perpendicular to an anistropic plane should have a preferred direction. Similar reasoning indicates that the Kosterlitz-Thouless transition temperature for a vortex mediated transition should be lower if the vortex is elliptical in shape.

Universal Power Law of the Gravity Wave Manifestation in the AIM CIPS Polar Mesospheric Cloud Images

NASA Astrophysics Data System (ADS)

Rong, P. P.; Yue, J.; Russell, J. M., III; Siskind, D. E.; Randall, C. E.

2017-12-01

A large ensemble of gravity waves (GWs) resides in the PMCs and we aim to extract the universal law that governs the wave display throughout the GW population. More specifically, we examined how wave display morphology and clarity level varies throughout the wave population manifested through the PMC albedo data. Higher clarity refers to more distinct exhibition of the features which often correspond to larger variances and better organized nature. A gravity wave tracking algorithm is designed and applied to the PMC albedo data taken by the AIM Cloud Imaging and Particle Size (CIPS) instrument to obtain the gravity wave detections throughout the two northern summers in 2007 and 2010. The horizontal wavelengths in the range of 20-60km are the focus of the study because they are the most commonly observed and readily captured in the CIPS orbital strips. A 1-dimensional continuous wavelet transform (CWT) is applied to PMC albedo along all radial directions within an elliptical region that has a radius of 400 km and an axial ratio of 0.65. The center of the elliptical region moves around the CIPS orbital strips so that waves at different locations and orientations can be captured. It shows that the CWT albedo power statistically increases as the background gets brighter. We resample the wave detections to conform to a normal distribution via removing the dependence of the albedo power on the background cloud brightness because we tend to examine the wave morphology beyond the cloud brightness impact. Sample cases are selected at the two tails and the peak of the normal distribution, and at three brightness levels, to represent the high, medium, and low albedo power categories. For these cases the albedo CWT power spectra follow exponential decay toward smaller scales. The high albedo power has the most rapid decay (i.e., exponent=-3.2) and corresponds to the most distinct wave display. Overall higher albedo power and more rapid decay both contributed to the more distinct display. The wave display becomes increasingly more blurry for the medium and low power categories that hold the exponents of -2.9 and -2.5, respectively. The majority of waves are straight waves whose clarity levels can be collapsed irrespective of the brightness levels but in the brighter background the wave signatures seem to exhibit mildly turbulent-like behavior.

Mars Atmosphere and Volatile Evolution (MAVEN) Mission Design

NASA Technical Reports Server (NTRS)

Folta, David C.

2010-01-01

The Mars Atmosphere and Volatile EvolutioN (MAVEN) mission was selected as the second in the low-cost Mars Scout mission series. MAVEN will determine the role that loss of volatiles to space has played through time from a highly inclined elliptical orbit. The launch period opens November 18. 2013 with arrival September 16, 2014. After achieving a 35-hour capture orbit, maneuvers will reduce the period to 4.5-hours with periapsis near 150 kilometers and maintain the periapsis within a specified density corridor. MAVEN will also execute "Deep Dip" campaigns, with periapsis at an altitude near 125 kilometers. This paper presents the unique mission design challenges of the MAVEN mission.

Solving the BM Camelopardalis puzzle

NASA Technical Reports Server (NTRS)

Teke, Mathias; Busby, Michael R.; Hall, Douglas S.

1989-01-01

BM Camelopardalis (=12 Cam) is a chromospherically active binary star with a relatively large orbital eccentricity. Systems with large eccentricities usually rotate pseudosynchronously. However, BM Cam has been a puzzle since its observed rotation rate is virtually equal to its orbital period indicating synchronization. All available photometry data for BM Cam have been collected and analyzed. Two models of modulated ellipticity effect are proposed, one based on equilibrium tidal deformation of the primary star and the other on a dynamical tidal effect. When the starspot variability is removed from the data, the dynamical tidal model was the better approximation to the real physical situation. The analysis indicates that BM Cam is not rotating pseudosynchronously but rotating in virtual synchronism after all.

DROMO formulation for planar motions: solution to the Tsien problem

NASA Astrophysics Data System (ADS)

Urrutxua, Hodei; Morante, David; Sanjurjo-Rivo, Manuel; Peláez, Jesús

2015-06-01

The two-body problem subject to a constant radial thrust is analyzed as a planar motion. The description of the problem is performed in terms of three perturbation methods: DROMO and two others due to Deprit. All of them rely on Hansen's ideal frame concept. An explicit, analytic, closed-form solution is obtained for this problem when the initial orbit is circular (Tsien problem), based on the DROMO special perturbation method, and expressed in terms of elliptic integral functions. The analytical solution to the Tsien problem is later used as a reference to test the numerical performance of various orbit propagation methods, including DROMO and Deprit methods, as well as Cowell and Kustaanheimo-Stiefel methods.

THE ROLE OF PICKUP IONS ON THE STRUCTURE OF THE VENUSIAN BOW SHOCK AND ITS IMPLICATIONS FOR THE TERMINATION SHOCK

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

Lu Quanming; Shan Lican; Zhang Tielong

2013-08-20

The recent crossing of the termination shock by Voyager 2 has demonstrated the important role of pickup ions (PUIs) in the physics of collisionless shocks. The Venus Express (VEX) spacecraft orbits Venus in a 24 hr elliptical orbit that crosses the bow shock twice a day. VEX provides a unique opportunity to investigate the role of PUIs on the structure of collisionless shocks more generally. Using VEX observations, we find that the strength of the Venusian bow shock is weaker when solar activity is strong. We demonstrate that this surprising anti-correlation is due to PUIs mediating the Venusian bow shock.

The Lunar IceCube Mission Design: Construction of Feasible Transfer Trajectories with a Constrained Departure

NASA Technical Reports Server (NTRS)

Folta, David C.; Bosanac, Natasha; Cox, Andrew; Howell, Kathleen C.

2016-01-01

Lunar IceCube, a 6U CubeSat, will prospect for water and other volatiles from a low-periapsis, highly inclined elliptical lunar orbit. Injected from Exploration Mission-1, a lunar gravity assisted multi-body transfer trajectory will capture into a lunar science orbit. The constrained departure asymptote and value of trans-lunar energy limit transfer trajectory types that re-encounter the Moon with the necessary energy and flight duration. Purdue University and Goddard Space Flight Center's Adaptive Trajectory Design tool and dynamical system research is applied to uncover cislunar spatial regions permitting viable transfer arcs. Numerically integrated transfer designs applying low-thrust and a design framework are described.

Health Monitoring of a Satellite System

NASA Technical Reports Server (NTRS)

Chen, Robert H.; Ng, Hok K.; Speyer, Jason L.; Guntur, Lokeshkumar S.; Carpenter, Russell

2004-01-01

A health monitoring system based on analytical redundancy is developed for satellites on elliptical orbits. First, the dynamics of the satellite including orbital mechanics and attitude dynamics is modelled as a periodic system. Then, periodic fault detection filters are designed to detect and identify the satellite's actuator and sensor faults. In addition, parity equations are constructed using the algebraic redundant relationship among the actuators and sensors. Furthermore, a residual processor is designed to generate the probability of each of the actuator and sensor faults by using a sequential probability test. Finally, the health monitoring system, consisting of periodic fault detection lters, parity equations and residual processor, is evaluated in the simulation in the presence of disturbances and uncertainty.

Experiment definition phase shuttle laboratory LDRL-10.6 experiment. [applying optical communication

NASA Technical Reports Server (NTRS)

1975-01-01

The 10.6 microns laser data relay link (LDRL 10.6) program was directed to applying optical communications to NASA's wideband data transmission requirements through the 1980's. The LDRL consists of a transmitter on one or more low earth orbit satellites with an elliptical orbit satellite receivers. Topics discussed include: update of the LDRL design control table to detail the transmitter optical chain losses and to incorporate the change to a reflective beam pre-expander; continued examination of the link establishment sequence, including its dependence upon spacecraft stability; design of the transmitter pointing and tracking control system; and finalization of the transmitter brassboard optical and mechanical design.

Coverage and control of constellations of elliptical inclined frozen lunar orbits

NASA Technical Reports Server (NTRS)

Ely, Todd A.

2005-01-01

A great deal of scientific interest exists regarding the permanently shadowed craters near the poles of the Moon where there may be frozen volatiles. These regions, particularly the Moon's South Pole, have been proposed for extensive robotic and human exploration. Unfortunately, they are typically not in view of Earth, and would require some form of communication relay to facilitate exploration via robotic and/or human missions. One solution for such a relay is a long-lived constellation of lunar telecommunication orbiters providing focused coverage at the pole of interest. Robust support requires this coverage to be continuous, redundant, and, in order to minimize costs, this constellation should consist of 3 satellites or fewer.

Preliminary Investigation of the Satellite Gravitational Red Shift Experiment

NASA Technical Reports Server (NTRS)

Zacharias, J. R.; Searle, C. L.; Graham, J. W.; Badessa, R. S.; Bates, V. J.; Kent, R. L.

1961-01-01

The work performed under this contract involved study, design, and construction of experimental equipment to perform a short-term measurement of the gravitational red shift. In the system designed, phase comparison techniques are employed so that the time interval required to obtain a single measurement for one altitude is of the order of one minute. An elliptical orbit was chosen to permit measurement of frequency shift as a function of altitude. One particularly attractive orbit is that having a 12-hour orbiting period (perigee, 270 miles, apogee 24,800 miles). This orbit, shown in Fig. 1, allows continuous measurements to be made over an 11-hour interval during which time the altitude is varying greatly. Measurements can not be made for the succeeding 14 hours. Since the variation of frequency difference with altitude is of greatest interest, a fixed offset or a slow drift between the oscillator on the ground and. the oscillator in the satellite will not invalidate the measurements.

Space dust and debris; Proceedings of the Topical Meeting of the Interdisciplinary Scientific Commission B (Meetings B2, B3, and B5) of the COSPAR 28th Plenary Meeting, The Hague, Netherlands, June 25-July 6, 1990

NASA Technical Reports Server (NTRS)

Kessler, D. J. (Editor); Zarnecki, J. C. (Editor); Matson, D. L. (Editor)

1991-01-01

The present conference on space dust and debris encompasses orbital debris, in situ measurements and laboratory analysis of space-dust particles, comparative studies of comets, asteroids, and dust, the protection and maneuvering of spacecraft in space-debris environments, and the out-of-elliptic distribution of interplanetary dust derived from near-earth flux. Specific issues addressed include asteroid taxonomy, the optical properties of dust from cometary and interplanetary grains, light scattering by rough surfaces on asteroidal/lunar regoliths, and the first results of particulate impacts and foil perforations on the Long Duration Exposure Facility. Also addressed are collision probability and spacecraft disposition in the geostationary orbit, a flash on the moon caused by orbital debris, the limits of population growth in low earth orbit due to collisional cascading, and the simulation of cosmic man-made dust effects on space-vehicle elements in rocket and laboratory experiments.

On the Milankovitch orbital elements for perturbed Keplerian motion

NASA Astrophysics Data System (ADS)

Rosengren, Aaron J.; Scheeres, Daniel J.

2014-03-01

We consider sets of natural vectorial orbital elements of the Milankovitch type for perturbed Keplerian motion. These elements are closely related to the two vectorial first integrals of the unperturbed two-body problem; namely, the angular momentum vector and the Laplace-Runge-Lenz vector. After a detailed historical discussion of the origin and development of such elements, nonsingular equations for the time variations of these sets of elements under perturbations are established, both in Lagrangian and Gaussian form. After averaging, a compact, elegant, and symmetrical form of secular Milankovitch-like equations is obtained, which reminds of the structure of canonical systems of equations in Hamiltonian mechanics. As an application of this vectorial formulation, we analyze the motion of an object orbiting about a planet (idealized as a point mass moving in a heliocentric elliptical orbit) and subject to solar radiation pressure acceleration (obeying an inverse-square law). We show that the corresponding secular problem is integrable and we give an explicit closed-form solution.

An Overview of the Topography of Mars from the Mars Orbiter Laser Altimeter (MOLA)

NASA Technical Reports Server (NTRS)

Smith, David E.; Zuber, Maria T.

2000-01-01

The Mars Global Surveyor (MGS) spacecraft has now completed more than half of its one-Mars-year mission to globally map Mars. During the MGS elliptical and circular orbit mapping phases, the Mars Orbiter Laser Altimeter (MOLA), an instrument on the MGS payload, has collected over 300 million precise elevation measurements. MOLA measures the range from the MGS spacecraft to the Martian surface and to atmospheric reflections. Range is converted to topography through knowledge of the MGS spacecraft orbit. Ranges from MOLA have resulted in a precise global topographic map of Mars. The instrument has also provided measurements of the width of the backscattered optical pulse and of the 1064 nm reflectivity of the Martian surface and atmosphere. The range resolution of the MOLA instrument is 37.5 cm and the along-track resolution of MOLA ground shots is approx. 300 m; the across-track spacing depends on latitude and time in the mapping orbit. The best current topographic grid has a spatial resolution of approx. 1/16 deg and vertical accuracy of approx. one meter. Additional information is contained in the original extended abstract.

Deliberate Satellite Fragmentations and their Effects on the Long-Term Space Environment

NASA Technical Reports Server (NTRS)

Johnson, N. L.

2010-01-01

Since 1964 at least 56 spacecraft and two launch vehicle upper stages have been deliberately fragmented while in Earth orbit. Many of these events have had no long-lasting effects on the near-Earth space environment, but one represents the most devastating satellite breakup in history that will pose hazards to operational spacecraft in low Earth orbit for decades to come. International space debris mitigation guidelines now call for avoiding the creation of long-lived debris from intentional satellite fragmentations. This paper summarizes the reasons for and environmental consequences of deliberate satellite fragmentations. Contrary to popular belief, only one in five deliberate fragmentations have been related to the testing of anti-satellite weapon systems, for which only one such test has occurred during the past 25 years. Other reasons for deliberate satellite fragmentations range from engineering tests to protecting national security information. Whereas the majority of deliberate satellite fragmentations have occurred in low Earth orbits, some have involved spacecraft in highly elliptical orbits. The former Soviet Union and the current Russian Federation have been responsible for 90% of all identified deliberate on-orbit satellite fragmentations.

Symmetric functions and wavefunctions of XXZ-type six-vertex models and elliptic Felderhof models by Izergin-Korepin analysis

NASA Astrophysics Data System (ADS)

Motegi, Kohei

2018-05-01

We present a method to analyze the wavefunctions of six-vertex models by extending the Izergin-Korepin analysis originally developed for domain wall boundary partition functions. First, we apply the method to the case of the basic wavefunctions of the XXZ-type six-vertex model. By giving the Izergin-Korepin characterization of the wavefunctions, we show that these wavefunctions can be expressed as multiparameter deformations of the quantum group deformed Grothendieck polynomials. As a second example, we show that the Izergin-Korepin analysis is effective for analysis of the wavefunctions for a triangular boundary and present the explicit forms of the symmetric functions representing these wavefunctions. As a third example, we apply the method to the elliptic Felderhof model which is a face-type version and an elliptic extension of the trigonometric Felderhof model. We show that the wavefunctions can be expressed as one-parameter deformations of an elliptic analog of the Vandermonde determinant and elliptic symmetric functions.

Generation of Elliptically Polarized Terahertz Waves from Antiferromagnetic Sandwiched Structure.

PubMed

Zhou, Sheng; Zhang, Qiang; Fu, Shu-Fang; Wang, Xuan-Zhang; Song, Yu-Ling; Wang, Xiang-Guang; Qu, Xiu-Rong

2018-04-01

The generation of elliptically polarized electromagnetic wave of an antiferromagnetic (AF)/dielectric sandwiched structure in the terahertz range is studied. The frequency and external magnetic field can change the AF optical response, resulting in the generation of elliptical polarization. An especially useful geometry with high levels of the generation of elliptical polarization is found in the case where an incident electromagnetic wave perpendicularly illuminates the sandwiched structure, the AF anisotropy axis is vertical to the wave-vector and the external magnetic field is pointed along the wave-vector. In numerical calculations, the AF layer is FeF2 and the dielectric layers are ZnF2. Although the effect originates from the AF layer, it can be also influenced by the sandwiched structure. We found that the ZnF2/FeF2/ZnF2 structure possesses optimal rotation of the principal axis and ellipticity, which can reach up to about thrice that of a single FeF2 layer.

Unified approach to probing Coulomb effects in tunnel ionization for any ellipticity of laser light.

PubMed

Landsman, A S; Hofmann, C; Pfeiffer, A N; Cirelli, C; Keller, U

2013-12-27

We present experimental data that show significant deviations from theoretical predictions for the location of the center of the electron momenta distribution at low values of ellipticity ε of laser light. We show that these deviations are caused by significant Coulomb focusing along the minor axis of polarization, something that is normally neglected in the analysis of electron dynamics, even in cases where the Coulomb correction is otherwise taken into account. By investigating ellipticity-resolved electron momenta distributions in the plane of polarization, we show that Coulomb focusing predominates at lower values of ellipticity of laser light, while Coulomb asymmetry becomes important at higher values, showing that these two complementary phenomena can be used to probe long-range Coulomb interaction at all polarizations of laser light. Our results suggest that both the breakdown of Coulomb focusing and the onset of Coulomb asymmetry are linked to the disappearance of Rydberg states with increasing ellipticity.

Elliptical varied line-space (EVLS) gratings

NASA Astrophysics Data System (ADS)

Thomas, Roger J.

2004-10-01

Imaging spectroscopy at wavelengths below 2000 Å offers an especially powerful method for studying many extended high-temperature astronomical objects, like the Sun and its outer layers. But the technology to make such measurements is also especially challenging, because of the poor reflectance of all standard materials at these wavelengths, and because the observation must be made from above the absorbing effects of the Earth's atmosphere. To solve these problems, single-reflection stigmatic spectrographs for XUV wavelengths have bee flown on several space missions based on designs with toroidal uniform line-space (TULS) or spherical varied line-space (SVLS) gratings that operate at near normal-incidence. More recently, three solar EUV/UV instruments have been selected that use toroidal varied line-space (TVLS) gratings; these are SUMI and RAISE, both sounding rocket payloads, and NEXUS, a SMEX satellite-mission. The next logical extension to such designs is the use of elliptical surfaces for varied line-space (EVLS) rulings. In fact, EVLS designs are found to provide superior imaging even at very large spectrograph magnifications and beam-speeds, permitting extremely high-quality performance in remarkably compact instrument packages. In some cases, such designs may be optimized even further by using a hyperbolic surface for the feeding telescope. The optical characteristics of two solar EUV spectrometers based on these concepts are described: EUS and EUI, both being developed as possible instruments for ESA's Solar Orbiter mission by consortia led by RAL and by MSSL, respectively.

Trajectory Design Analysis over the Lunar Nodal Cycle for the Multi-Purpose Crew Vehicle (MPCV) Exploration Mission 2 (EM-2)

NASA Technical Reports Server (NTRS)

Gutkowski, Jeffrey P.; Dawn, Timothy F.; Jedrey, Richard M.

2014-01-01

The first crewed mission, Exploration Mission 2 (EM-2), for the MPCV Orion spacecraft is scheduled for August 2021, and its current mission is to orbit the Moon in a highly elliptical lunar orbit for 3 days. A 21-year scan was performed to identify feasible missions that satisfy the propulsive capabilities of the Interim Cryogenic Propulsion Stage (ICPS) and MPCV Service Module (SM). The mission is divided into 4 phases: (1) a lunar free return trajectory, (2) a hybrid maneuver, during the translunar coast, to lower the approach perilune altitude to 100 km, (3) lunar orbit insertion into a 100 x 10,000 km orbit, and (4) lunar orbit loiter and Earth return to a splashdown off the coast of Southern California. Trajectory data was collected for all feasible missions and converted to information that influence different subsystems including propulsion, power, thermal, communications, and mission operations. The complete 21-year scan data shows seasonal effects that are due to the Earth-Moon geometry and the initial Earth parking orbit. The data and information is also useful to identify mission opportunities around the current planned launch date for EM-2.

Further Evidence of a Brown Dwarf Orbiting the Post-Common Envelope Eclipsing Binary V470 Cam (HS 0705+6700)

NASA Astrophysics Data System (ADS)

Bogensberger, David; Clarke, Fraser; Lynas-Gray, Anthony Eugene

2017-12-01

Several post-common envelope binaries have slightly increasing, decreasing or oscillating orbital periods. One of several possible explanations is light travel-time changes, caused by the binary centre-of-mass being perturbed by the gravitational pull of a third body. Further studies are necessary because it is not clear how a third body could have survived subdwarf progenitor mass-loss at the tip of the Red Giant Branch, or formed subsequently. Thirty-nine primary eclipse times for V470 Cam were secured with the Philip Wetton Telescope during the period 2016 November 25th to 2017 January 27th. Available eclipse timings suggest a brown dwarf tertiary having a mass of at least 0.0236(40) M⊙, an elliptical orbit with an eccentricity of 0.376(98) and an orbital period of 11.77(67) years about the binary centreof- mass. The mass and orbit suggest a hybrid formation, in which some ejected material from the subdwarf progenitor was accreted on to a precursor tertiary component, although additional observations would be needed to confirm this interpretation and investigate other possible origins for the binary orbital period change.

Optimizing Mars Sphere of Influence Maneuvers for NASA's Evolvable Mars Campaign

NASA Technical Reports Server (NTRS)

Merrill, Raymond G.; Komar, D. R.; Chai, Patrick; Qu, Min

2016-01-01

NASA's Human Spaceflight Architecture Team is refining human exploration architectures that will extend human presence to the Martian surface. For both Mars orbital and surface missions, NASA's Evolvable Mars Campaign assumes that cargo and crew can be delivered repeatedly to the same destination. Up to this point, interplanetary trajectories have been optimized to minimize the total propulsive requirements of the in-space transportation systems, while the pre-deployed assets and surface systems are optimized to minimize their respective propulsive requirements separate from the in-space transportation system. There is a need to investigate the coupled problem of optimizing the interplanetary trajectory and optimizing the maneuvers within Mars's sphere of influence. This paper provides a description of the ongoing method development, analysis and initial results of the effort to resolve the discontinuity between the interplanetary trajectory and the Mars sphere of influence trajectories. Assessment of Phobos and Deimos orbital missions shows the in-space transportation and crew taxi allocations are adequate for missions in the 2030s. Because the surface site has yet to be selected, the transportation elements must be sized to provide enough capability to provide surface access to all landing sites under consideration. Analysis shows access to sites from elliptical parking orbits with a lander that is designed for sub-periapsis landing location is either infeasible or requires expensive orbital maneuvers for many latitude ranges. In this case the locus of potential arrival perigee vectors identifies the potential maximum north or south latitudes accessible. Higher arrival velocities can decrease reorientation costs and increase landing site availability. Utilizing hyperbolic arrival and departure vectors in the optimization scheme will increase transportation site accessibility and provide more optimal solutions.

Role of an elliptical structure in photosynthetic energy transfer: Collaboration between quantum entanglement and thermal fluctuation

PubMed Central

Oka, Hisaki

2016-01-01

Recent experiments have revealed that the light-harvesting complex 1 (LH1) in purple photosynthetic bacteria has an elliptical structure. Generally, symmetry lowering in a structure leads to a decrease in quantum effects (quantum coherence and entanglement), which have recently been considered to play a role in photosynthetic energy transfer, and hence, elliptical structure seems to work against efficient photosynthetic energy transfer. Here we analyse the effect of an elliptical structure on energy transfer in a purple photosynthetic bacterium and reveal that the elliptical distortion rather enhances energy transfer from peripheral LH2 to LH1 at room temperature. Numerical results show that quantum entanglement between LH1 and LH2 is formed over a wider range of high energy levels than would have been the case with circular LH1. Light energy absorbed by LH2 is thermally pumped via thermal fluctuation and is effectively transferred to LH1 through the entangled states at room temperature rather than at low temperature. This result indicates the possibility that photosynthetic systems adopt an elliptical structure to effectively utilise both quantum entanglement and thermal fluctuation at physiological temperature. PMID:27173144

Role of an elliptical structure in photosynthetic energy transfer: Collaboration between quantum entanglement and thermal fluctuation

NASA Astrophysics Data System (ADS)

Oka, Hisaki

2016-05-01

Recent experiments have revealed that the light-harvesting complex 1 (LH1) in purple photosynthetic bacteria has an elliptical structure. Generally, symmetry lowering in a structure leads to a decrease in quantum effects (quantum coherence and entanglement), which have recently been considered to play a role in photosynthetic energy transfer, and hence, elliptical structure seems to work against efficient photosynthetic energy transfer. Here we analyse the effect of an elliptical structure on energy transfer in a purple photosynthetic bacterium and reveal that the elliptical distortion rather enhances energy transfer from peripheral LH2 to LH1 at room temperature. Numerical results show that quantum entanglement between LH1 and LH2 is formed over a wider range of high energy levels than would have been the case with circular LH1. Light energy absorbed by LH2 is thermally pumped via thermal fluctuation and is effectively transferred to LH1 through the entangled states at room temperature rather than at low temperature. This result indicates the possibility that photosynthetic systems adopt an elliptical structure to effectively utilise both quantum entanglement and thermal fluctuation at physiological temperature.

Role of an elliptical structure in photosynthetic energy transfer: Collaboration between quantum entanglement and thermal fluctuation.

PubMed

Oka, Hisaki

2016-05-13

Recent experiments have revealed that the light-harvesting complex 1 (LH1) in purple photosynthetic bacteria has an elliptical structure. Generally, symmetry lowering in a structure leads to a decrease in quantum effects (quantum coherence and entanglement), which have recently been considered to play a role in photosynthetic energy transfer, and hence, elliptical structure seems to work against efficient photosynthetic energy transfer. Here we analyse the effect of an elliptical structure on energy transfer in a purple photosynthetic bacterium and reveal that the elliptical distortion rather enhances energy transfer from peripheral LH2 to LH1 at room temperature. Numerical results show that quantum entanglement between LH1 and LH2 is formed over a wider range of high energy levels than would have been the case with circular LH1. Light energy absorbed by LH2 is thermally pumped via thermal fluctuation and is effectively transferred to LH1 through the entangled states at room temperature rather than at low temperature. This result indicates the possibility that photosynthetic systems adopt an elliptical structure to effectively utilise both quantum entanglement and thermal fluctuation at physiological temperature.

Feasibility of Reusable Continuous Thrust Spacecraft for Cargo Resupply Missions to Mars

NASA Astrophysics Data System (ADS)

Rabotin, C. B.

Continuous thrust propulsion systems benefit from a much greater efficiency in vacuum than chemical rockets, at the expense of lower instantaneous thrust and high power requirements. The satellite telecommunications industry, known for greatly emphasizing heritage over innovation, now uses electric propulsion for station keeping on a number of spacecraft, and for orbit raising for some smaller satellites, such as the Boeing 702SP platform. Only a few interplanetary missions have relied on continuous thrust for most of their mission, such as ESA's 367 kg SMART-1 and NASA's 1217 kg Dawn mission. The high specific impulse of these continuous thrust engines should make them suitable for transportation of heavy payloads to inner solar system destinations in such a way to limit the dependency on heavy rocket launches. Additionally, such spacecraft should be able to perform orbital insertions at destination in order to deliver the cargo directly in a desired orbit. An example application is designing round-trip missions to Mars to support exploration and eventually colonization. This research investigates the feasibility of return journeys to Mars based on the performance of existing or in-development continuous thrust propulsion systems. In order to determine the business viability of such missions, an emphasis is made on the time of flight during different parts of the mission, the relative velocity with respect to the destination planet, and the fuel requirements. The study looks at the applicability for interplanetary mission design of simple control laws for efficient correction of orbital elements, and of thrusting purely in velocity or anti-velocity direction. The simulations explore different configurations of continuous thrusting technologies using a patched-conics approach. In addition, all simulation scenarios facilitate escape from planetary gravity wells as the initial spacecraft orbit is highly elliptical, both around the Earth and around Mars. This work does not include any optimal trajectory design. For this research, a highly configurable orbit propagation software with SPICE ephemerides was developed from scratch in Go, a modern compiled computer language. The outcome of this research is that simple orbital element control laws do not lead to more efficient or faster interplanetary transfers. In addition, spiraling out of Earth's gravity wells requires a substantial amount of time despite starting from a highly elliptical orbit, and even with clustered high thrust engines like the VASIMR VX-200. Further investigation should look into hybrid solutions with a chemical engine for departing Earth; outbound spirals from Mars take a more reasonable amount of time.

On some theoretical and practical aspects of multigrid methods. [to solve finite element systems from elliptic equations

NASA Technical Reports Server (NTRS)

Nicolaides, R. A.

1979-01-01

A description and explanation of a simple multigrid algorithm for solving finite element systems is given. Numerical results for an implementation are reported for a number of elliptic equations, including cases with singular coefficients and indefinite equations. The method shows the high efficiency, essentially independent of the grid spacing, predicted by the theory.

High-performance mirror for space applications using anodic bonding technology

NASA Astrophysics Data System (ADS)

Otto, W.; Fischer, E.; Kemper, J.; Koch, S.; Kolberg, J.; Kramer, C.; Kunde, J.; Läger, M.

2017-11-01

Berliner Glas developed and manufactured the plane elliptical shaped mirrors for the Synopta Coarse Pointing Assembly (CPA) being one of the key elements of the TESAT Spacecom Laser Communication Terminals (LCT's). The first TESAT LCT containing a Synopta CPA was embarked on Sentinel 1A and is in orbit since April 2014. TESAT Spacecom LCT's have been successfully tested in space since 2007 and are now operationally used in commercial satellite communication systems.

Constellations of elliptical inclined lunar orbits providing polar and global coverage

NASA Technical Reports Server (NTRS)

Ely, Todd A.; Lieb, Erica

2005-01-01

Prior results have developed a methodology for selecting a long-lived constellation of 3 satellites that provide persistent, stable coverage to either the North or South Pole with no requirement for stationkeeping under the influence of only gravitational perturbations. In the present study, the sensitivity of this coverage in the presence of non-gravitational forces is determined, and a design strategy is formulated that minimizes any potential sensitivity to these accelerations.

Heliotropic dust rings for Earth climate engineering

NASA Astrophysics Data System (ADS)

Bewick, R.; Lücking, C.; Colombo, C.; Sanchez, J. P.; McInnes, C. R.

2013-04-01

This paper examines the concept of a Sun-pointing elliptical Earth ring comprised of dust grains to offset global warming. A new family of non-Keplerian periodic orbits, under the effects of solar radiation pressure and the Earth's J2 oblateness perturbation, is used to increase the lifetime of the passive cloud of particles and, thus, increase the efficiency of this geoengineering strategy. An analytical model is used to predict the orbit evolution of the dust ring due to solar-radiation pressure and the J2 effect. The attenuation of the solar radiation can then be calculated from the ring model. In comparison to circular orbits, eccentric orbits yield a more stable environment for small grain sizes and therefore achieve higher efficiencies when the orbit decay of the material is considered. Moreover, the novel orbital dynamics experienced by high area-to-mass ratio objects, influenced by solar radiation pressure and the J2 effect, ensure the ring will maintain a permanent heliotropic shape, with dust spending the largest portion of time on the Sun facing side of the orbit. It is envisaged that small dust grains can be released from a circular generator orbit with an initial impulse to enter an eccentric orbit with Sun-facing apogee. Finally, a lowest estimate of 1 × 1012 kg of material is computed as the total mass required to offset the effects of global warming.

Elliptic flow from Coulomb interaction and low density elastic scattering

NASA Astrophysics Data System (ADS)

Sun, Yuliang; Li, Qingfeng; Wang, Fuqiang

2018-04-01

In high energy heavy ion collisions and interacting cold atom systems, large elliptic flow anisotropies have been observed. For the large opacity (ρ σ L ˜103 ) of the latter hydrodynamics is a natural consequence, but for the small opacity (ρ σ L ˜1 ) of the former the hydrodynamic description is questionable. To shed light onto the situation, we simulate the expansion of a low density argon ion (or atom) system, initially trapped in an elliptical region, under the Coulomb interaction (or elastic scattering). Significant elliptic anisotropy is found in both cases, and the anisotropy depends on the initial spatial eccentricity and the density of the system. The results may provide insights into the physics of anisotropic flow in high energy heavy ion collisions and its role in the study of quantum chromodynamics.

The Wall Interference of a Wind Tunnel of Elliptic Cross Section

NASA Technical Reports Server (NTRS)

Tani, Itiro; Sanuki, Matao

1944-01-01

The wall interference is obtained for a wind tunnel of elliptic section for the two cases of closed and open working sections. The approximate and exact methods used gave results in practically good agreement. Corresponding to the result given by Glauert for the case of the closed rectangular section, the interference is found to be a minimum for a ratio of minor to major axis of 1:square root of 6 This, however, is true only for the case where the span of the airfoil is small in comparison with the width of the tunnel. For a longer airfoil the favorable ellipse is flatter. In the case of the open working section the circular shape gives the minimum interference.

Four Classical Methods for Determining Planetary Elliptic Elements: A Comparison

NASA Astrophysics Data System (ADS)

Celletti, Alessandra; Pinzari, Gabriella

2005-09-01

The discovery of the asteroid Ceres by Piazzi in 1801 motivated the development of a mathematical technique proposed by Gauss, (Theory of the Motion of the Heavenly Bodies Moving about the Sun in Conic Sections, 1963) which allows to recover the orbit of a celestial body starting from a minimum of three observations. Here we compare the method proposed by Gauss (Theory of the Motion of the Heavenly Bodies Moving about the Sun in Conic Sections, New York, 1963) with the techniques (based on three observations) developed by Laplace (Collected Works 10, 93 146, 1780) and by Mossotti (Memoria Postuma, 1866). We also consider another method developed by Mossotti (Nuova analisi del problema di determinare le orbite dei corpi celesti, 1816 1818), based on four observations. We provide a theoretical and numerical comparison among the different procedures. As an application, we consider the computation of the orbit of the asteroid Juno.

Spin manipulation and relaxation in spin-orbit qubits

NASA Astrophysics Data System (ADS)

Borhani, Massoud; Hu, Xuedong

2012-03-01

We derive a generalized form of the electric dipole spin resonance (EDSR) Hamiltonian in the presence of the spin-orbit interaction for single spins in an elliptic quantum dot (QD) subject to an arbitrary (in both direction and magnitude) applied magnetic field. We predict a nonlinear behavior of the Rabi frequency as a function of the magnetic field for sufficiently large Zeeman energies, and present a microscopic expression for the anisotropic electron g tensor. Similarly, an EDSR Hamiltonian is devised for two spins confined in a double quantum dot (DQD), where coherent Rabi oscillations between the singlet and triplet states are induced by jittering the inter-dot distance at the resonance frequency. Finally, we calculate two-electron-spin relaxation rates due to phonon emission, for both in-plane and perpendicular magnetic fields. Our results have immediate applications to current EDSR experiments on nanowire QDs, g-factor optimization of confined carriers, and spin decay measurements in DQD spin-orbit qubits.

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

NASA Technical Reports Server (NTRS)

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

2005-01-01

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

Spacecraft exploration of Phobos and Deimos

NASA Astrophysics Data System (ADS)

Duxbury, Thomas C.; Zakharov, Alexander V.; Hoffmann, Harald; Guinness, Edward A.

2014-11-01

We review the previous exploration of Phobos and Deimos by spacecraft. The first close-up images of Phobos and Deimos were obtained by the Mariner 9 spacecraft in 1971, followed by much image data from the two Viking orbiters at the end of the 70s, which formed the basis for early Phobos and Deimos shape and dynamic models. The Soviet Phobos 2 spacecraft came within 100 km of landing on Phobos in 1988. Mars Global Surveyor (1996-2006) and Mars Reconnaissance Orbiter (since 2005) made close-up observations of Phobos on several occasions. Mars Express (since 2003) in its highly elliptical orbit is currently the only spacecraft to make regular Phobos encounters and has returned large volumes of science data for this satellite. Landers and rovers on the ground (Viking Landers, Mars Pathfinder, MER rovers, MSL rover) frequently made observations of Phobos, Deimos and their transits across the solar disk.

Radial-orbit instability in modified Newtonian dynamics

NASA Astrophysics Data System (ADS)

Nipoti, Carlo; Ciotti, Luca; Londrillo, Pasquale

2011-07-01

The stability of radially anisotropic spherical stellar systems in modified Newtonian dynamics (MOND) is explored by means of numerical simulations performed with the N-body code N-MODY. We find that Osipkov-Merritt MOND models require for stability larger minimum anisotropy radii than equivalent Newtonian systems (ENSs) with the dark matter, and also than purely baryonic Newtonian models with the same density profile. The maximum value for stability of the Fridman-Polyachenko-Shukhman parameter in MOND models is lower than in ENSs, but higher than in Newtonian models with no dark matter. We conclude that MOND systems are substantially more prone to radial-orbit instability than ENSs with dark matter, while they are able to support a larger amount of kinetic energy stored in radial orbits than purely baryonic Newtonian systems. An explanation of these results is attempted and their relevance to the MOND interpretation of the observed kinematics of globular clusters, dwarf spheroidal and elliptical galaxies is briefly discussed.

An Overview of the Juno Mission to Jupiter

NASA Technical Reports Server (NTRS)

Grammier, Richard S.

2006-01-01

Arriving in orbit around the planet Jupiter in 2016 after a five-year journey, the Juno spacecraft will begin a one-year investigation of the gas giant in order to understand its origin and evolution by determining its water abundance and constraining its core mass. In addition, Juno will map the planet's magnetic and gravitational fields, map its atmosphere, and explore the three-dimensional structure of Jupiter's polar magnetosphere and auroras. Juno will discriminate among different models for giant planet formation. These investigations will be conducted over the course of thirty-two 11-day elliptical polar orbits of the planet. The orbits are designed to avoid Jupiter's highest radiation regions. The spacecraft is a spinning, solar-powered system carrying a complement of eight science instruments for conducting the investigations. The spacecraft systems and instruments take advantage of significant design and operational heritage from previous space missions.

Radial velocity measurements of the chromospherically-active stars (2): HD 28591 = V492 Per

NASA Technical Reports Server (NTRS)

Dadonas, V.; Sperauskas, J.; Fekel, F. C.; Morton, M. D.

1994-01-01

From two sets of the spectroscopic observations covering a ten year period we have obtained 59 radial velocities of the chromospherically-active star HD 28591 = V492 Per. It is a G9III single-lined spectroscopic binary with a period of 21.2910 days and a circular orbit. The upsilon sin i of 24.6 km/sec, results in a minimum radius 10.3 solar radii. We estimate a distance of 165 +/- 40 pc and an orbital inclination of 65 +/- 25 degrees. The secondary is probably a mid to late-type K dwarf. The star is brighter than the limiting magnitude of the Bright Star Catalogue. The mean photometric and the orbital periods are identical within their uncertainties. Since the star fills a significant fraction of its Roche lobe, about 62%, the photometric light curve may be the result of starspots and a modest ellipticity effect.

Indirect (source-free) integration method. I. Wave-forms from geodesic generic orbits of EMRIs

NASA Astrophysics Data System (ADS)

Ritter, Patxi; Aoudia, Sofiane; Spallicci, Alessandro D. A. M.; Cordier, Stéphane

2016-12-01

The Regge-Wheeler-Zerilli (RWZ) wave-equation describes Schwarzschild-Droste black hole perturbations. The source term contains a Dirac distribution and its derivative. We have previously designed a method of integration in time domain. It consists of a finite difference scheme where analytic expressions, dealing with the wave-function discontinuity through the jump conditions, replace the direct integration of the source and the potential. Herein, we successfully apply the same method to the geodesic generic orbits of EMRI (Extreme Mass Ratio Inspiral) sources, at second order. An EMRI is a Compact Star (CS) captured by a Super-Massive Black Hole (SMBH). These are considered the best probes for testing gravitation in strong regime. The gravitational wave-forms, the radiated energy and angular momentum at infinity are computed and extensively compared with other methods, for different orbits (circular, elliptic, parabolic, including zoom-whirl).

Navigation of space VLBI missions: Radioastron and VSOP

NASA Technical Reports Server (NTRS)

Ellis, Jordan

1993-01-01

In the mid-1990s, Russian and Japanese space agencies will each place into highly elliptic earth orbit a radio telescope consisting of a large antenna and radio astronomy receivers. Very long baseline interferometry (VLBI) techniques will be used to obtain high resolution images of radio sources observed by the space and ground based antennas. Stringent navigation accuracy requirements are imposed on the space VLBI missions by the need to transfer an ultra-stable ground reference frequency standard to the spacecraft and by the demands of the VLBI correlation process. Orbit determination for the mission will be the joint responsibility of navigation centers in the U.S., Russia, and Japan with orbit estimates based on combining tracking data from NASA, Russian, and Japanese sites. This paper describes the operational plans, the inter-agency coordination, and data exchange between the navigation centers required for space VLBI navigation.

Galileo disposal strategy: stability, chaos and predictability

NASA Astrophysics Data System (ADS)

Rosengren, Aaron J.; Daquin, Jérôme; Tsiganis, Kleomenis; Alessi, Elisa Maria; Deleflie, Florent; Rossi, Alessandro; Valsecchi, Giovanni B.

2017-02-01

Recent studies have shown that the medium-Earth orbit (MEO) region of the global navigation satellite systems is permeated by a devious network of lunisolar secular resonances, which can interact to produce chaotic and diffusive motions. The precarious state of the four navigation constellations, perched on the threshold of instability, makes it understandable why all past efforts to define stable graveyard orbits, especially in the case of Galileo, were bound to fail; the region is far too complex to allow for an adoption of the simple geosynchronous disposal strategy. We retrace one such recent attempt, funded by ESA's General Studies Programme in the frame of the GreenOPS initiative, that uses a systematic parametric approach and the straightforward maximum-eccentricity method to identify long-term-stable regions, suitable for graveyards, as well as large-scale excursions in eccentricity, which can be used for post-mission deorbiting of constellation satellites. We then apply our new results on the stunningly rich dynamical structure of the MEO region towards the analysis of these disposal strategies for Galileo, and discuss the practical implications of resonances and chaos in this regime. We outline how the identification of the hyperbolic and elliptic fixed points of the resonances near Galileo can lead to explicit criteria for defining optimal disposal strategies.

The initial value problem as it relates to numerical relativity.

PubMed

Tichy, Wolfgang

2017-02-01

Spacetime is foliated by spatial hypersurfaces in the 3+1 split of general relativity. The initial value problem then consists of specifying initial data for all fields on one such a spatial hypersurface, such that the subsequent evolution forward in time is fully determined. On each hypersurface the 3-metric and extrinsic curvature describe the geometry. Together with matter fields such as fluid velocity, energy density and rest mass density, the 3-metric and extrinsic curvature then constitute the initial data. There is a lot of freedom in choosing such initial data. This freedom corresponds to the physical state of the system at the initial time. At the same time the initial data have to satisfy the Hamiltonian and momentum constraint equations of general relativity and can thus not be chosen completely freely. We discuss the conformal transverse traceless and conformal thin sandwich decompositions that are commonly used in the construction of constraint satisfying initial data. These decompositions allow us to specify certain free data that describe the physical nature of the system. The remaining metric fields are then determined by solving elliptic equations derived from the constraint equations. We describe initial data for single black holes and single neutron stars, and how we can use conformal decompositions to construct initial data for binaries made up of black holes or neutron stars. Orbiting binaries will emit gravitational radiation and thus lose energy. Since the emitted radiation tends to circularize the orbits over time, one can thus expect that the objects in a typical binary move on almost circular orbits with slowly shrinking radii. This leads us to the concept of quasi-equilibrium, which essentially assumes that time derivatives are negligible in corotating coordinates for binaries on almost circular orbits. We review how quasi-equilibrium assumptions can be used to make physically well motivated approximations that simplify the elliptic equations we have to solve.

The initial value problem as it relates to numerical relativity

NASA Astrophysics Data System (ADS)

Tichy, Wolfgang

2017-02-01

Spacetime is foliated by spatial hypersurfaces in the 3+1 split of general relativity. The initial value problem then consists of specifying initial data for all fields on one such a spatial hypersurface, such that the subsequent evolution forward in time is fully determined. On each hypersurface the 3-metric and extrinsic curvature describe the geometry. Together with matter fields such as fluid velocity, energy density and rest mass density, the 3-metric and extrinsic curvature then constitute the initial data. There is a lot of freedom in choosing such initial data. This freedom corresponds to the physical state of the system at the initial time. At the same time the initial data have to satisfy the Hamiltonian and momentum constraint equations of general relativity and can thus not be chosen completely freely. We discuss the conformal transverse traceless and conformal thin sandwich decompositions that are commonly used in the construction of constraint satisfying initial data. These decompositions allow us to specify certain free data that describe the physical nature of the system. The remaining metric fields are then determined by solving elliptic equations derived from the constraint equations. We describe initial data for single black holes and single neutron stars, and how we can use conformal decompositions to construct initial data for binaries made up of black holes or neutron stars. Orbiting binaries will emit gravitational radiation and thus lose energy. Since the emitted radiation tends to circularize the orbits over time, one can thus expect that the objects in a typical binary move on almost circular orbits with slowly shrinking radii. This leads us to the concept of quasi-equilibrium, which essentially assumes that time derivatives are negligible in corotating coordinates for binaries on almost circular orbits. We review how quasi-equilibrium assumptions can be used to make physically well motivated approximations that simplify the elliptic equations we have to solve.

REVIEWS OF TOPICAL PROBLEMS Gravitational radiation of systems and the role of their force field

NASA Astrophysics Data System (ADS)

Nikishov, Anatolii I.; Ritus, Vladimir I.

2011-02-01

Gravitational radiation (GR) from compact relativistic systems with a known energy-momentum tensor (EMT) and GR from two masses elliptically orbiting their common center of inertia are considered. In the ultrarelativistic limit, the GR spectrum of a charge rotating in a uniform magnetic field, a Coulomb field, a magnetic moment field, and a combination of the last two fields differs by a factor 4πGm2Γ2/e2 (Γ being of the order of the charge Lorentz factor) from its electromagnetic radiation (EMR) spectrum. This factor is independent of the radiation frequency but does depend on the wave vector direction and the way the field behaves outside of the orbit. For a plane wave external field, the proportionality between the gravitational and electromagnetic radiation spectra is exact, whatever the velocity of the charge. Qualitative estimates of Γ are given for a charge moving ultrarelativistically in an arbitrary field, showing that it is of the order of the ratio of the nonlocal and local source contributions to the GR. The localization of external forces near the orbit violates the proportionality of the spectra and reduces GR by about the Lorentz factor squared. The GR spectrum of a rotating relativistic string with masses at the ends is given, and it is shown that the contributions by the masses and string are of the same order of magnitude. In the nonrelativistic limit, the harmonics of GR spectra behave universally for all the rotating systems considered. A trajectory method is developed for calculating the GR spectrum. In this method, the spatial (and hence polarization) components of the conserved EMT are calculated in the long wavelength approximation from the time component of the EMTs of the constituent masses of the system. Using this method, the GR spectrum of two masses moving in elliptic orbits about their common center of inertia is calculated, as are the relativistic corrections to it.

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

NASA Astrophysics Data System (ADS)

Hiday, Lisa Ann

1992-09-01

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

Flower elliptical constellation of millimeter-wave radiometers for precipitating cloud monitoring at geostationary scale

NASA Astrophysics Data System (ADS)

Marzano, F. S.; Cimini, D.; Montopoli, M.; Rossi, T.; Mortari, D.; di Michele, S.; Bauer, P.

2009-04-01

Millimeter-wave observation of the atmospheric parameters is becoming an appealing goal within satellite radiometry applications. The major technological advantage of millimeter-wave (MMW) radiometers is the reduced size of the overall system, for given performances, with respect to microwave sensor. On the other hand, millimeter-wave sounding can exploit window frequencies and various gaseous absorption bands at 50/60 GHz, 118 GHz and 183 GHz. These bands can be used to estimate tropospheric temperature profiles, integrated water vapor and cloud liquid content and, using a differentia spectral mode, light rainfall and snowfall. Millimeter-wave radiometers, for given observation conditions, can also exhibit relatively small field-of-views (FOVs), of the order of some kilometers for low-Earth-orbit (LEO) satellites. However, the temporal resolution of LEO millimeter-wave system observations remains a major drawback with respect to the geostationary-Earth-orbit (GEO) satellites. An overpass every about 12 hours for a single LEO platform (conditioned to a sufficiently large swath of the scanning MMW radiometer) is usually too much when compared with the typical temporal scale variation of atmospheric fields. This feature cannot be improved by resorting to GEO platforms due to their high orbit altitude and consequent degradation of the MMW-sensor FOVs. A way to tackle this impasse is to draw our attention at the regional scale and to focus non-circular orbits over the area of interest, exploiting the concept of micro-satellite flower constellations. The Flower Constellations (FCs) is a general class of elliptical orbits which can be optimized, through genetic algorithms, in order to maximize the revisiting time and the orbital height, ensuring also a repeating ground-track. The constellation concept nicely matches the choice of mini-satellites as a baseline choice, due to their small size, weight (less than 500 kilograms) and relatively low cost (essential when deploying several identical speceborne platforms). Moreover, the micro-satellite solution clearly addresses the choice of small passive sensors with small size, low weight and power consumption, features which cannot be usually satisfied by active sensors. In this respect, MMW technology is the most compatible with the specifications and constraints of micro-satellites. In this work, we will discuss the numerical results of a feasibility study aimed at designing a Flower elliptical constellation of 3 micro-satellite millimeter-wave radiometers for pseudo-geostationary atmospheric observations over the Mediterranean region. The Flower constellation will be optimized in such a way to simulate a pseudo-geostationary observation of the Mediterranean area with an observation repetition time less than 2 hours. The mission requirements request the retrieval of thermodinamical and hydrological properties of the troposphere, specifically temperature profiles, integrated water vapor and cloud liquid content, rainfall and snowfall. Several configurations of the MMW radiometer multi-band channels will be discussed, pointing out the trade-off between performances and complexity. Integrated estimation algorithms, based on a Bayesian approache, will be illustrated to retrieve the requested atmospheric parameters, discussing its sensitivity to sensor radiometric precision and accuracy within each frequency-set configuration. After this numerical study, a review of the mission requirements and specifications will be also proposed.

An alternative theoretical model for an anomalous hollow beam.

PubMed

Cai, Yangjian; Wang, Zhaoying; Lin, Qiang

2008-09-15

An alternative and convenient theoretical model is proposed to describe a flexible anomalous hollow beam of elliptical symmetry with an elliptical solid core, which was observed in experiment recently (Phys. Rev. Lett, 94 (2005) 134802). In this model, the electric field of anomalous hollow beam is expressed as a finite sum of elliptical Gaussian modes. Flattopped beams, dark hollow beams and Gaussian beams are special cases of our model. Analytical propagation formulae for coherent and partially coherent anomalous hollow beams passing through astigmatic ABCD optical systems are derived. Some numerical examples are calculated to show the propagation and focusing properties of coherent and partially coherent anomalous hollow beams.

On the unity of activity in galaxies

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

Rowan-Robinson, M.

1977-05-01

A scheme is presented which unites quasars, radio galaxies, N galaxies, and Seyfert galaxies into a single picture of activity in galaxies. Probability functions are given for optical and radio cores, and extended radio sources (in the case of ellipticals), for both spirals and ellipticals. Activity occurs in galaxies of all luminosities, but the strength of it is made proportional to galaxy luminosity. It is assumed that there is dust surrounding the optical cores, to explain the strong infrared emission in Seyferts.Quasars may, in this picture, occur in both spirals and ellipticals, and in fact most optically selected QSOs aremore » predicted to be in spirals.« less

1+1 Gaudin Model

NASA Astrophysics Data System (ADS)

Zotov, Andrei V.

2011-07-01

We study 1+1 field-generalizations of the rational and elliptic Gaudin models. For sl(N) case we introduce equations of motion and L-A pair with spectral parameter on the Riemann sphere and elliptic curve. In sl(2) case we study the equations in detail and find the corresponding Hamiltonian densities. The n-site model describes n interacting Landau-Lifshitz models of magnets. The interaction depends on position of the sites (marked points on the curve). We also analyze the 2-site case in its own right and describe its relation to the principal chiral model. We emphasize that 1+1 version impose a restriction on a choice of flows on the level of the corresponding 0+1 classical mechanics.

Strengthening the Mars Telecommunications Network

NASA Image and Video Library

2016-11-29

On Nov. 22, 2016, a NASA radio aboard the European Space Agency's (ESA's) Trace Gas Orbiter, which arrived at Mars the previous month, succeeded in its first test of receiving data transmitted from NASA Mars rovers, both Opportunity and Curiosity. This graphic depicts the geometry of Opportunity transmitting data to the orbiter, using the ultra-high frequency (UHF) band of radio wavelengths. The orbiter received that data using one of its twin Electra UHF-band radios. Data that the orbiter's Electra received from the two rovers was subsequently transmitted from the orbiter to Earth, using the orbiter's main X-band radio. The Trace Gas Orbiter is part of ESA's ExoMars program. During the initial months after its Oct. 19, 2016, arrival, it is flying in a highly elliptical orbit. Each loop takes 4.2 days to complete, with distances between the orbiter and the planet's surface ranging from about 60,000 miles (about 100,000 kilometers) to less than 200 miles (less than 310 kilometers). Later, the mission will reshape the orbit to a near-circular path about 250 miles (400 kilometers) above the surface of Mars. Three NASA orbiters and one other ESA orbiter currently at Mars also have relayed data from Mars rovers to Earth. This strategy enables receiving much more data from the surface missions than would be possible with a direct-to-Earth radio link from rovers or stationary landers. Successful demonstration of the capability added by the Trace Gas Orbiter strengthens and extends the telecommunications network at Mars for supporting future missions to the surface of the Red Planet. http://photojournal.jpl.nasa.gov/catalog/PIA21139

Angular ellipticity correlations in a composite alignment model for elliptical and spiral galaxies and inference from weak lensing

NASA Astrophysics Data System (ADS)

Tugendhat, Tim M.; Schäfer, Björn Malte

2018-05-01

We investigate a physical, composite alignment model for both spiral and elliptical galaxies and its impact on cosmological parameter estimation from weak lensing for a tomographic survey. Ellipticity correlation functions and angular ellipticity spectra for spiral and elliptical galaxies are derived on the basis of tidal interactions with the cosmic large-scale structure and compared to the tomographic weak-lensing signal. We find that elliptical galaxies cause a contribution to the weak-lensing dominated ellipticity correlation on intermediate angular scales between ℓ ≃ 40 and ℓ ≃ 400 before that of spiral galaxies dominates on higher multipoles. The predominant term on intermediate scales is the negative cross-correlation between intrinsic alignments and weak gravitational lensing (GI-alignment). We simulate parameter inference from weak gravitational lensing with intrinsic alignments unaccounted; the bias induced by ignoring intrinsic alignments in a survey like Euclid is shown to be several times larger than the statistical error and can lead to faulty conclusions when comparing to other observations. The biases generally point into different directions in parameter space, such that in some cases one can observe a partial cancellation effect. Furthermore, it is shown that the biases increase with the number of tomographic bins used for the parameter estimation process. We quantify this parameter estimation bias in units of the statistical error and compute the loss of Bayesian evidence for a model due to the presence of systematic errors as well as the Kullback-Leibler divergence to quantify the distance between the true model and the wrongly inferred one.

The curious history of Tethys as evidenced by irregular craters and variable tectonism

NASA Astrophysics Data System (ADS)

Ferguson, S. N.; Rhoden, A.; Nayak, M.; Asphaug, E. I.

2017-12-01

At first glance, the surface of Saturn's moon Tethys appears dominated by craters and its large canyon system, Ithaca Chasma. However, high-resolution Cassini imagery reveals a surface rife with curious geologic features, perhaps indicative of non-heliocentric impact populations and, potentially, a history of tectonic activity. We mapped three regions on Tethys to survey the diversity of features present on the surface, determine crater counts for each region, map and analyze fracture patterns, and identify constraints on the impactor populations. One study region is just south and west of the Odysseus impact basin (R1), and the other two regions sit slightly west of Ithaca Chasma (R2 and R3). The regions were imaged at average resolutions of 200m/pix, which is adequate to identify craters down to D=1km. Of 1200 total craters counted, we have identified 195 elliptical craters and 28 polygonal craters. Elliptical craters likely form from slow, oblique impacts, whereas polygonal craters are indicative of underlying tectonic structure. We identified 605 small craters, D=1-2km, across the three regions; we find that R1 has many more 1-10 km craters than R2 and R3. We also mapped 367 linear features. The median and range of orientations of the linear features vary across the regions. Despite their proximity, the orientations of lineations in R2 and R3 are not consistent with the orientation of Ithaca Chasma. This could be suggestive of different epochs of tectonic activity on Tethys. When compared with R2 and R3, R1 has more small craters, more lineations, and a preferred orientation of lineations that is distinct from the other two regions. Possible causes for a larger population of small craters in R1 include secondary craters from Odysseus and oblique impacts from debris ejected from Tethys' co-orbital moons, which should create many more 1km craters in R1 than the other regions. Due to the oblique impact angles predicted for incoming co-orbital debris, these impacts may have also produced some of the lineations observed in R1. Oblique impacts can also form elliptical craters, but that would imply much larger debris than expected from the craters presently observed on the co-orbitals. We discuss additional analysis and implications of Tethys' curious geologic features on its bombardment and tectonic history.

Human Mars Mission: SEP Architecture Crew Taxi Propulsion Stage Study and Design and Technology for Reaction and Control System. Part 1

NASA Technical Reports Server (NTRS)

Young, Archie

1999-01-01

The Mars exploration is a candidate pathway to expand human presence and useful activities in the solar system. There are several propulsion system options being considered to place the Mars payload on its inter-planetary transfer trajectory. One propulsion option is the use of Solar Electric Propulsion (SEP) to spiral out with the Mars payload from an initial Low Earth Orbit (LEO) to an elliptical High Earth Orbit (HEO). This report, presented in annotated facing page format, describes the work completed on the design of a crew taxi propulsion stage used in conjunction with the SEP. Transportation system/mission analysis topics covered in this report include sub-system analysis, trajectory profile description, mass performance and crew taxi stage sizing, stage configuration, stage cost, and Trans-Mars Injection (TMI) launch window. The high efficiency of SEP is used to provide the major part of the TMI propulsion maneuver. Orbital energy is continuously added over a period of approximately twelve months. The SEP and Mars payload follow a spiral trajectory from an initial LEO to a final elliptical HEO. A small chemical stage is then used to provide the final part of the TMI. The now unloaded SEP returns to LEO to repeat another spiral trajectory with payload to HEO. The spiral phase of the SEP's trajectory takes several months to reach HEO, thus significantly increasing the exposure time of the crew to zero-gravity. In order to minimize the long zero-gravity effects, a high thrust chemical stage delivers the crew to the SEP's HEO. The crew rendezvous with the Mars payload in HEO. After a checkout period the Mars payload with the crew is injected onto a Trans-Mars Trajectory by a small chemical stage.

Human Mars Mission: SEP Architecture, Crew Taxi Propulsion Stage Study and Design and Technology for Reaction and Control System. Pt. 1

NASA Technical Reports Server (NTRS)

Young, Archie

1999-01-01

The Mars exploration is a candidate pathway to expand human presence and useful activities in the solar system. There are several propulsion system options being considered to place the Mars payload on its interplanetary transfer trajectory. One propulsion option is the use of Solar Electric Propulsion (SEP) to spiral out with the Mars payload from an initial Low Earth Orbit (LEO) to an elliptical High Earth Orbit (HEO). This report, presented in annotated facing page format, describes the work completed on the design of a crew taxi propulsion stage used in conjunction with the SEP. Transportation system/mission analysis topics covered in this report include sub-system analysis, trajectory profile description, mass performance and crew taxi stage sizing, stage configuration, stage cost, and Trans-Mars Injection (TMI) launch window. The high efficiency of SEP is used to provide the major part of the TMI propulsion maneuver. Orbital energy is continuously added over a period of approximately twelve months. The SEP and Mars payload follow a spiral trajectory from an initial LEO to a final elliptical HEO. A small chemical stage is then used to provide the final part of the TMI. The now unloaded SEP returns to LEO to repeat another spiral trajectory with payload to HEO. The spiral phase of the SEP's trajectory takes several months to reach HEO, thus significantly increasing the exposure time of the crew to zero-gravity. In order to minimize the long zero-gravity effects, a high thrust chemical stage delivers the crew to the SEP's HEO. The crew rendezvous with the Mars payload in HEO. After a checkout period the Mars payload with the crew is injected onto a Trans-Mars Trajectory by a small chemical stage.

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

NASA Astrophysics Data System (ADS)

Guzman

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

Birefringent corrugated waveguide

DOEpatents

Moeller, Charles P.

1990-01-01

A corrugated waveguide having a circular bore and noncircularly symmetric corrugations, and preferably elliptical corrugations, provides birefringence for rotation of polarization in the HE.sub.11 mode. The corrugated waveguide may be fabricated by cutting circular grooves on a lathe in a cylindrical tube or rod of aluminum of a diameter suitable for the bore of the waveguide, and then cutting an approximation to ellipses for the corrugations using a cutting radius R.sub.0 from the bore axis that is greater than the bore radius, and then making two circular cuts using a radius R.sub.1 less than R.sub.0 at centers +b and -b from the axis of the waveguide bore. Alternatively, stock for the mandrel may be formed with an elliptical transverse cross section, and then only the circular grooves need be cut on a lathe, leaving elliptical corrugations between the grooves. In either case, the mandrel is first electroplated and then dissolved leaving a corrugated waveguide with noncircularly symmetric corrugations. A transition waveguide is used that gradually varies from circular to elliptical corrugations to couple a circularly corrugated waveguide to an elliptically corrugated waveguide.

Instability of elliptic liquid jets: Temporal linear stability theory and experimental analysis

NASA Astrophysics Data System (ADS)

Amini, Ghobad; Lv, Yu; Dolatabadi, Ali; Ihme, Matthias

2014-11-01

The instability dynamics of inviscid liquid jets issuing from elliptical orifices is studied, and effects of the surrounding gas and the liquid surface tension on the stability behavior are investigated. A dispersion relation for the zeroth azimuthal (axisymmetric) instability mode is derived. Consistency of the analysis is confirmed by demonstrating that these equations reduce to the well-known dispersion equations for the limiting cases of round and planar jets. It is shown that the effect of the ellipticity is to increase the growth rate over a large range of wavenumbers in comparison to those of a circular jet. For higher Weber numbers, at which capillary forces have a stabilizing effect, the growth rate decreases with increasing ellipticity. Similar to circular and planar jets, increasing the density ratio between gas and liquid increases the growth of disturbances significantly. These theoretical investigations are complemented by experiments to validate the local linear stability results. Comparisons of predicted growth rates with measurements over a range of jet ellipticities confirm that the theoretical model provides a quantitatively accurate description of the instability dynamics in the Rayleigh and first wind-induced regimes.

Instability of low viscosity elliptic jets with varying aspect ratio

NASA Astrophysics Data System (ADS)

Kulkarni, Varun

2011-11-01

In this work an analytical description of capillary instability of liquid elliptic jets with varying aspect ratio is presented. Linear stability analysis in the long wave approximation with negligible gravitational effects is employed. Elliptic cylindrical coordinate system is used and perturbation velocity potential substituted in the Laplace equation to yield Mathieu and Modified Mathieu differential equations. The dispersion relation for elliptical orifices of any aspect ratio is derived and validated for axisymmetric disturbances with m = 0, in the limit of aspect ratio, μ = 1 , i.e. the case of a circular jet. As Mathieu functions and Modified Mathieu function solutions converge to Bessel's functions in this limit the Rayleigh-Plateau instability criterion is met. Also, stability of solutions corresponding to asymmetric disturbances for the kink mode, m = 1 and flute modes corresponding to m >= 2 is discussed. Experimental data from earlier works is used to compare observations made for elliptical orifices with μ ≠ 1 . This novel approach aims at generalizing the results pertaining to cylindrical jets with circular cross section leading to better understanding of breakup in liquid jets of various geometries.

A survey of aerobraking orbital transfer vehicle design concepts

NASA Technical Reports Server (NTRS)

Park, Chul

1987-01-01

The five existing design concepts of the aerobraking orbital transfer vehicle (namely, the raked sphere-cone designs, conical lifting-brake, raked elliptic-cone, lifting-body, and ballute) are reviewed and critiqued. Historical backgrounds, and the geometrical, aerothermal, and operational features of these designs are reviewed first. Then, the technological requirements for the vehicle (namely, navigation, aerodynamic stability and control, afterbody flow impingement, nonequilibrium radiation, convective heat-transfer rates, mission abort and multiple atmospheric passes, transportation and construction, and the payload-to-vehicle weight requirements) are delineated by summarizing the recent advancements made on these issues. Each of the five designs are critiqued and rated on these issues. The highest and the lowest ratings are given to the raked sphere-cone and the ballute design, respectively.

Kalman Filter for Mass Property and Thrust Identification (MMS)

NASA Technical Reports Server (NTRS)

Queen, Steven

2015-01-01

The Magnetospheric Multiscale (MMS) mission consists of four identically instrumented, spin-stabilized observatories, elliptically orbiting the Earth in a tetrahedron formation. For the operational success of the mission, on-board systems must be able to deliver high-precision orbital adjustment maneuvers. On MMS, this is accomplished using feedback from on-board star sensors in tandem with accelerometers whose measurements are dynamically corrected for errors associated with a spinning platform. In order to determine the required corrections to the measured acceleration, precise estimates of attitude, rate, and mass-properties is necessary. To this end, both an on-board and ground-based Multiplicative Extended Kalman Filter (MEKF) were formulated and implemented in order to estimate the dynamic and quasi-static properties of the spacecraft.

HD 143 418 - An Interacting Binary with a Subsynchronously Rotating Primary

NASA Astrophysics Data System (ADS)

Mikulášek, Z.; Zverko, J.; Žižňovský, J.; Krtička, J.; Iliev, I. Kh.; Kudryavtsev, D. O.; Gráf, T.; Zejda, M.

2010-12-01

HD 143418 is a non-eclipsing double-lined close binary with orbital period Porb=2.282520 d. The photometrically and spectroscopically dominant primary component is a normal A5V star in the middle of its stay on the main sequence with extremely slow, subsynchronous rotation (Prot being about 14 days!). Its photometric monitoring since 1982 revealed orbitally modulated variations with changing form and amplitude. The advanced principal component analysis (APCA) disentangling extract-ed a steady part of light curves obviously caused by the ellipticity of the primary. Seasonal components of the light curves may be related to an expected incidence of circumstellar matter ejected from the tidally spinning up primary component. A possible scenario of the synchronisation process is also briefly discussed.

An asymptotically consistent approximant for the equatorial bending angle of light due to Kerr black holes

NASA Astrophysics Data System (ADS)

Barlow, Nathaniel S.; Weinstein, Steven J.; Faber, Joshua A.

2017-07-01

An accurate closed-form expression is provided to predict the bending angle of light as a function of impact parameter for equatorial orbits around Kerr black holes of arbitrary spin. This expression is constructed by assuring that the weak- and strong-deflection limits are explicitly satisfied while maintaining accuracy at intermediate values of impact parameter via the method of asymptotic approximants (Barlow et al 2017 Q. J. Mech. Appl. Math. 70 21-48). To this end, the strong deflection limit for a prograde orbit around an extremal black hole is examined, and the full non-vanishing asymptotic behavior is determined. The derived approximant may be an attractive alternative to computationally expensive elliptical integrals used in black hole simulations.

Dynamical instabilities in axisymmetric stellar systems. I - Oblate E6 models

NASA Technical Reports Server (NTRS)

Levison, Harold F.; Duncan, Martin J.; Smith, Bruce F.

1990-01-01

The stability of a set of models based on isothermal oblate E6 elliptical galaxies is studied using N-body techniques. The only stable models are those that are near the isotropic model and have nearly equal number of stars in retrograde and prograde orbits. Fast rotators are unstable to modes that appear to be analogous to the classical streaming instability seen in many disk systems. Systems with a large velocity dispersion in the direction of the cylindrical radius are unstable to modes that appear to be similar to the radial orbit instability observed in some spherical systems. However, evidence is presented that these two instabilities may be related, and an instability criterion that applies to both is constructed.

HEOS-A2: Press kit

NASA Technical Reports Server (NTRS)

Allaway, H. G.; Kukowski, J.

1972-01-01

The characteristics of the HEOS-A2 satellite and its assigned mission are discussed. The spacecraft carries seven experiments to investigate the strength and direction of the magnetic fields encountered, the energy distribution of protons and electrons, the nature of the solar winds, detection of micrometeorites, and low frequency solar observations. The highly elliptical polar orbit required for this mission will have an apogee of 38 earth radii. The lifetime of the satellite is expected to be one year minimum.

Heaviest Satcom: Inmarsat's Business Propelled to New Heights by Extra Aerojet Solid Motors on Atlas V

NASA Technical Reports Server (NTRS)

Covault, Craig

2005-01-01

The first EADS/Astrium Inmarsat 4, the largest commercial communications satellite ever launched, has completed four maneuvers to reach geosynchronous orbit where it has deployed its 30 X 40-ft. elliptical reflector and solar arrays spanning 148 ft. The 13,183-1b. spacecraft was launched Mar. 11 from Cape Canavera1 on the most powerful version to date of the Lockheed Martin International Launch Services (ILS) Atlas V.

Resonant torus-assisted tunneling.

PubMed

Yi, Chang-Hwan; Yu, Hyeon-Hye; Kim, Chil-Min

2016-01-01

We report a new type of dynamical tunneling, which is mediated by a resonant torus, i.e., a nonisolated periodic orbit. To elucidate the phenomenon, we take an open elliptic cavity and show that a pair of resonances localized on two classically disconnected tori tunnel through a resonant torus when they interact with each other. This so-called resonant torus-assisted tunneling is verified by using Husimi functions, corresponding actions, Husimi function distributions, and the standard deviations of the actions.

A Scientific Analysis of Galaxy Tangential Speed of Revolution Curves III

NASA Astrophysics Data System (ADS)

Taff, Laurence

2015-04-01

I last reported on my preliminary analysis of 350 + spiral, lenticular, irregular, polar ring, ring, and dwarf elliptical galaxies' tangential speed of revolution curves [TSRCs; and not rotation (sic) curves]. I now know that the consensus opinion in the literature--for which I can find no geometrical, numerical, statistical, nor scientific testing in 2,500 + publications--that the TSRC, vB(r), in the central bulges of these galaxies, is a linear function of the radial distance from the minor axis of symmetry r--is false. For the majority (>98%) vB(r) is rarely well represented by vB(r) = ωB r (for which the unique material model is an homogeneous, oblate, spheroid). Discovered via a scientific analysis of the gravitational potential energy computed directly from the observational data, vB(r) is almost exactly given by vB2(r) = (ωB r)2(1 + η r2) with | η | < 10-2 and frequently orders of magnitude less. The corresponding mass model is the simplest generalization: a two component homoeoid. The set of possible periodic orbits, based on circular trigonometric functions, becomes a set of periodic orbits based on the Jacobian elliptic functions. Once again it is possible to prove that the mass-to-light ratio can neither be a constant nor follow the de Vaucouleurs R1/4 rule.

Weak-lensing shear estimates with general adaptive moments, and studies of bias by pixellation, PSF distortions, and noise

NASA Astrophysics Data System (ADS)

Simon, Patrick; Schneider, Peter

2017-08-01

In weak gravitational lensing, weighted quadrupole moments of the brightness profile in galaxy images are a common way to estimate gravitational shear. We have employed general adaptive moments (GLAM ) to study causes of shear bias on a fundamental level and for a practical definition of an image ellipticity. The GLAM ellipticity has useful properties for any chosen weight profile: the weighted ellipticity is identical to that of isophotes of elliptical images, and in absence of noise and pixellation it is always an unbiased estimator of reduced shear. We show that moment-based techniques, adaptive or unweighted, are similar to a model-based approach in the sense that they can be seen as imperfect fit of an elliptical profile to the image. Due to residuals in the fit, moment-based estimates of ellipticities are prone to underfitting bias when inferred from observed images. The estimation is fundamentally limited mainly by pixellation which destroys information on the original, pre-seeing image. We give an optimised estimator for the pre-seeing GLAM ellipticity and quantify its bias for noise-free images. To deal with images where pixel noise is prominent, we consider a Bayesian approach to infer GLAM ellipticity where, similar to the noise-free case, the ellipticity posterior can be inconsistent with the true ellipticity if we do not properly account for our ignorance about fit residuals. This underfitting bias, quantified in the paper, does not vary with the overall noise level but changes with the pre-seeing brightness profile and the correlation or heterogeneity of pixel noise over the image. Furthermore, when inferring a constant ellipticity or, more relevantly, constant shear from a source sample with a distribution of intrinsic properties (sizes, centroid positions, intrinsic shapes), an additional, now noise-dependent bias arises towards low signal-to-noise if incorrect prior densities for the intrinsic properties are used. We discuss the origin of this prior bias. With regard to a fully-Bayesian lensing analysis, we point out that passing tests with source samples subject to constant shear may not be sufficient for an analysis of sources with varying shear.

Chasing the peak: optimal statistics for weak shear analyses

NASA Astrophysics Data System (ADS)

Smit, Merijn; Kuijken, Konrad

2018-01-01

Context. Weak gravitational lensing analyses are fundamentally limited by the intrinsic distribution of galaxy shapes. It is well known that this distribution of galaxy ellipticity is non-Gaussian, and the traditional estimation methods, explicitly or implicitly assuming Gaussianity, are not necessarily optimal. Aims: We aim to explore alternative statistics for samples of ellipticity measurements. An optimal estimator needs to be asymptotically unbiased, efficient, and robust in retaining these properties for various possible sample distributions. We take the non-linear mapping of gravitational shear and the effect of noise into account. We then discuss how the distribution of individual galaxy shapes in the observed field of view can be modeled by fitting Fourier modes to the shear pattern directly. This allows scientific analyses using statistical information of the whole field of view, instead of locally sparse and poorly constrained estimates. Methods: We simulated samples of galaxy ellipticities, using both theoretical distributions and data for ellipticities and noise. We determined the possible bias Δe, the efficiency η and the robustness of the least absolute deviations, the biweight, and the convex hull peeling (CHP) estimators, compared to the canonical weighted mean. Using these statistics for regression, we have shown the applicability of direct Fourier mode fitting. Results: We find an improved performance of all estimators, when iteratively reducing the residuals after de-shearing the ellipticity samples by the estimated shear, which removes the asymmetry in the ellipticity distributions. We show that these estimators are then unbiased in the absence of noise, and decrease noise bias by more than 30%. Our results show that the CHP estimator distribution is skewed, but still centered around the underlying shear, and its bias least affected by noise. We find the least absolute deviations estimator to be the most efficient estimator in almost all cases, except in the Gaussian case, where it's still competitive (0.83 < η < 5.1) and therefore robust. These results hold when fitting Fourier modes, where amplitudes of variation in ellipticity are determined to the order of 10-3. Conclusions: The peak of the ellipticity distribution is a direct tracer of the underlying shear and unaffected by noise, and we have shown that estimators that are sensitive to a central cusp perform more efficiently, potentially reducing uncertainties by more 0% and significantly decreasing noise bias. These results become increasingly important, as survey sizes increase and systematic issues in shape measurements decrease.

Topological strings on singular elliptic Calabi-Yau 3-folds and minimal 6d SCFTs

NASA Astrophysics Data System (ADS)

Del Zotto, Michele; Gu, Jie; Huang, Min-xin; Kashani-Poor, Amir-Kian; Klemm, Albrecht; Lockhart, Guglielmo

2018-03-01

We apply the modular approach to computing the topological string partition function on non-compact elliptically fibered Calabi-Yau 3-folds with higher Kodaira singularities in the fiber. The approach consists in making an ansatz for the partition function at given base degree, exact in all fiber classes to arbitrary order and to all genus, in terms of a rational function of weak Jacobi forms. Our results yield, at given base degree, the elliptic genus of the corresponding non-critical 6d string, and thus the associated BPS invariants of the 6d theory. The required elliptic indices are determined from the chiral anomaly 4-form of the 2d worldsheet theories, or the 8-form of the corresponding 6d theories, and completely fix the holomorphic anomaly equation constraining the partition function. We introduce subrings of the known rings of Weyl invariant Jacobi forms which are adapted to the additional symmetries of the partition function, making its computation feasible to low base wrapping number. In contradistinction to the case of simpler singularities, generic vanishing conditions on BPS numbers are no longer sufficient to fix the modular ansatz at arbitrary base wrapping degree. We show that to low degree, imposing exact vanishing conditions does suffice, and conjecture this to be the case generally.

Aeroheating Thermal Model Correlation for Mars Global Surveyor (MGS) Solar Array

NASA Technical Reports Server (NTRS)

Amundsen, Ruth M.; Dec, John A.; George, Benjamin E.

2003-01-01

The Mars Global Surveyor (MGS) Spacecraft made use of aerobraking to gradually reduce its orbit period from a highly elliptical insertion orbit to its final science orbit. Aerobraking produces a high heat load on the solar arrays, which have a large surface area exposed to the airflow and relatively low mass. To accurately model the complex behavior during aerobraking, the thermal analysis needed to be tightly coupled to the spatially varying, time dependent aerodynamic heating. Also, the thermal model itself needed to accurately capture the behavior of the solar array and its response to changing heat load conditions. The correlation of the thermal model to flight data allowed a validation of the modeling process, as well as information on what processes dominate the thermal behavior. Correlation in this case primarily involved detailing the thermal sensor nodes, using as-built mass to modify material property estimates, refining solar cell assembly properties, and adding detail to radiation and heat flux boundary conditions. This paper describes the methods used to develop finite element thermal models of the MGS solar array and the correlation of the thermal model to flight data from the spacecraft drag passes. Correlation was made to data from four flight thermal sensors over three of the early drag passes. Good correlation of the model was achieved, with a maximum difference between the predicted model maximum and the observed flight maximum temperature of less than 5%. Lessons learned in the correlation of this model assisted in validating a similar model and method used for the Mars Odyssey solar array aeroheating analysis, which were used during onorbit operations.

Canonical forms of multidimensional steady inviscid flows

NASA Technical Reports Server (NTRS)

Taasan, Shlomo

1993-01-01

Canonical forms and canonical variables for inviscid flow problems are derived. In these forms the components of the system governed by different types of operators (elliptic and hyperbolic) are separated. Both the incompressible and compressible cases are analyzed, and their similarities and differences are discussed. The canonical forms obtained are block upper triangular operator form in which the elliptic and non-elliptic parts reside in different blocks. The full nonlinear equations are treated without using any linearization process. This form enables a better analysis of the equations as well as better numerical treatment. These forms are the analog of the decomposition of the one dimensional Euler equations into characteristic directions and Riemann invariants.

Classification of Stellar Orbits in Axisymmetric Galaxies

NASA Astrophysics Data System (ADS)

Li, Baile; Holley-Bockelmann, Kelly; Khan, Fazeel Mahmood

2015-09-01

It is known that two supermassive black holes (SMBHs) cannot merge in a spherical galaxy within a Hubble time; an emerging picture is that galaxy geometry, rotation, and large potential perturbations may usher the SMBH binary through the critical three-body scattering phase and ultimately drive the SMBH to coalesce. We explore the orbital content within an N-body model of a mildly flattened, non-rotating, SMBH-embedded elliptical galaxy. When used as the foundation for a study on the SMBH binary coalescence, the black holes bypassed the binary stalling often seen within spherical galaxies and merged on gigayear timescales. Using both frequency-mapping and angular momentum criteria, we identify a wealth of resonant orbits in the axisymmetric model, including saucers, that are absent from an otherwise identical spherical system and that can potentially interact with the binary. We quantified the set of orbits that could be scattered by the SMBH binary, and found that the axisymmetric model contained nearly six times the number of these potential loss cone orbits compared to our equivalent spherical model. In this flattened model, the mass of these orbits is more than three times that of the SMBH, which is consistent with what the SMBH binary needs to scatter to transition into the gravitational wave regime.

CLASSIFICATION OF STELLAR ORBITS IN AXISYMMETRIC GALAXIES

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

Li, Baile; Holley-Bockelmann, Kelly; Khan, Fazeel Mahmood, E-mail: baile.li@vanderbilt.edu, E-mail: k.holley@vanderbilt.edu, E-mail: khanfazeel.ist@gmail.com

2015-09-20

It is known that two supermassive black holes (SMBHs) cannot merge in a spherical galaxy within a Hubble time; an emerging picture is that galaxy geometry, rotation, and large potential perturbations may usher the SMBH binary through the critical three-body scattering phase and ultimately drive the SMBH to coalesce. We explore the orbital content within an N-body model of a mildly flattened, non-rotating, SMBH-embedded elliptical galaxy. When used as the foundation for a study on the SMBH binary coalescence, the black holes bypassed the binary stalling often seen within spherical galaxies and merged on gigayear timescales. Using both frequency-mapping andmore » angular momentum criteria, we identify a wealth of resonant orbits in the axisymmetric model, including saucers, that are absent from an otherwise identical spherical system and that can potentially interact with the binary. We quantified the set of orbits that could be scattered by the SMBH binary, and found that the axisymmetric model contained nearly six times the number of these potential loss cone orbits compared to our equivalent spherical model. In this flattened model, the mass of these orbits is more than three times that of the SMBH, which is consistent with what the SMBH binary needs to scatter to transition into the gravitational wave regime.« less

Navigation Guidelines for Orbital Formation Flying Missions

NASA Technical Reports Server (NTRS)

Carpenter, J. Russell

2003-01-01

Some simple guidelines based on the accuracy in determining a satellite formation's semi-major axis differences are useful in making preliminary assessments of the navigation accuracy needed to support such missions. These guidelines are valid for any elliptical orbit, regardless of eccentricity. Although maneuvers required for formation establishment, reconfiguration, and station-keeping require accurate prediction of the state estimate to the maneuver time, and hence are directly affected by errors in all the orbital elements, experience has shown that determination of orbit plane orientation and orbit shape to acceptable levels is less challenging than the determination of orbital period or semi-major axis. Furthermore, any differences among the member's semi-major axis are undesirable for a satellite formation, since it will lead to differential along-track drift due to period differences. Since inevitable navigation errors prevent these differences from ever being zero, one may use the guidelines this paper presents to determine how much drift will result from a given relative navigation accuracy, or vice versa. Since the guidelines do not account for non-two-body perturbations, they may be viewed as useful preliminary design tools, rather than as the basis for mission navigation requirements, which should be based on detailed analysis of the mission configuration, including all relevant sources of uncertainty.

Space Technology 5: Changing the Mission Design without Changing the Hardware

NASA Technical Reports Server (NTRS)

Carlisle, Candace C.; Webb, Evan H.; Slavin, James A.

2005-01-01

The Space Technology 5 (ST-5) Project is part of NASA's New Millennium Program. The validation objectives are to demonstrate the research-quality science capability of the ST-5 spacecraft; to operate the three spacecraft as a constellation; and to design, develop, test and flight-validate three capable micro-satellites with new technologies. A three-month flight demonstration phase is planned, beginning in March 2006. This year, the mission was re-planned for a Pegasus XL dedicated launch into an elliptical polar orbit (instead of the Originally-planned Geosynchronous Transfer Orbit.) The re-plan allows the mission to achieve the same high-level technology validation objectives with a different launch vehicle. The new mission design involves a revised science validation strategy, a new orbit and different communication strategy, while minimizing changes to the ST-5 spacecraft itself. The constellation operations concepts have also been refined. While the system engineers, orbit analysts, and operations teams were re-planning the mission, the implementation team continued to make progress on the flight hardware. Most components have been delivered, and the first spacecraft is well into integration and test.

Multi-Objective Online Initialization of Spacecraft Formations

NASA Technical Reports Server (NTRS)

Jeffrey, Matthew; Breger, Louis; How, Jonathan P.

2007-01-01

This paper extends a previously developed method for finding spacecraft initial conditions (ICs) that minimize the drift resulting from J2 disturbances while also minimizing the fuel required to attain those ICs. It generalizes the single spacecraft optimization to a formation-wide optimization valid for an arbitrary number of vehicles. Additionally, the desired locations of the spacecraft, separate from the starting location, can be specified, either with respect to a reference orbit, or relative to the other spacecraft in the formation. The three objectives (minimize drift, minimize fuel, and maintain a geometric template) are expressed as competing costs in a linear optimization, and are traded against one another through the use of scalar weights. By carefully selecting these weights and re-initializing the formation at regular intervals, a closed-loop, formation-wide control system is created. This control system can be used to reconfigure the formations on the fly, and creates fuel-efficient plans by placing the spacecraft in semi-invariant orbits. The overall approach is demonstrated through nonlinear simulations for two formations a GEO orbit, and an elliptical orbit.

Aeroheating Thermal Analysis Methods for Aerobraking Mars Missions

NASA Technical Reports Server (NTRS)

Amundsen, Ruth M.; Dec, John A.; George, Benjamin E.

2002-01-01

Mars missions often employ aerobraking upon arrival at Mars as a low-mass method to gradually reduce the orbit period from a high-altitude, highly elliptical insertion orbit to the final science orbit. Two recent missions that made use of aerobraking were Mars Global Surveyor (MGS) and Mars Odyssey. Both spacecraft had solar arrays as the main aerobraking surface area. Aerobraking produces a high heat load on the solar arrays, which have a large surface area exposed to the airflow and relatively low mass. To accurately model the complex behavior during aerobraking, the thermal analysis must be tightly coupled to the flight mechanics, aerodynamics, and atmospheric modeling efforts being performed during operations. To properly represent the temperatures prior to and during the drag pass, the model must include the orbital solar and planetary heat fluxes. The correlation of the thermal model to flight data allows a validation of the modeling process, as well as information on what processes dominate the thermal behavior. This paper describes the thermal modeling method that was developed for this purpose, as well as correlation for two flight missions, and a discussion of improvements to the methodology.

The anisosphere as a new tool for interpreting Foucault pendulum experiments. Part I: harmonic oscillators

NASA Astrophysics Data System (ADS)

Verreault, René

2017-08-01

In an attempt to explain the tendency of Foucault pendula to develop elliptical orbits, Kamerlingh Onnes derived equations of motion that suggest the use of great circles on a spherical surface as a graphical illustration for an anisotropic bi-dimensional harmonic oscillator, although he did not himself exploit the idea any further. The concept of anisosphere is introduced in this work as a new means of interpreting pendulum motion. It can be generalized to the case of any two-dimensional (2-D) oscillating system, linear or nonlinear, including the case where coupling between the 2 degrees of freedom is present. Earlier pendulum experiments in the literature are revisited and reanalyzed as a test for the anisosphere approach. While that graphical method can be applied to strongly nonlinear cases with great simplicity, this part I is illustrated through a revisit of Kamerlingh Onnes' dissertation, where a high performance pendulum skillfully emulates a 2-D harmonic oscillator. Anisotropy due to damping is also described. A novel experiment strategy based on the anisosphere approach is proposed. Finally, recent original results with a long pendulum using an electronic recording alidade are presented. A gain in precision over traditional methods by 2-3 orders of magnitude is achieved.

Orbit period modulation for relative motion using continuous low thrust in the two-body and restricted three-body problems

NASA Astrophysics Data System (ADS)

Arnot, C. S.; McInnes, C. R.; McKay, R. J.; Macdonald, M.; Biggs, J.

2018-02-01

This paper presents rich new families of relative orbits for spacecraft formation flight generated through the application of continuous thrust with only minimal intervention into the dynamics of the problem. Such simplicity facilitates implementation for small, low-cost spacecraft with only position state feedback, and yet permits interesting and novel relative orbits in both two- and three-body systems with potential future applications in space-based interferometry, hyperspectral sensing, and on-orbit inspection. Position feedback is used to modify the natural frequencies of the linearised relative dynamics through direct manipulation of the system eigenvalues, producing new families of stable relative orbits. Specifically, in the Hill-Clohessy-Wiltshire frame, simple adaptations of the linearised dynamics are used to produce a circular relative orbit, frequency-modulated out-of-plane motion, and a novel doubly periodic cylindrical relative trajectory for the purposes of on-orbit inspection. Within the circular restricted three-body problem, a similar minimal approach with position feedback is used to generate new families of stable, frequency-modulated relative orbits in the vicinity of a Lagrange point, culminating in the derivation of the gain requirements for synchronisation of the in-plane and out-of-plane frequencies to yield a singly periodic tilted elliptical relative orbit with potential use as a Lunar far-side communications relay. The Δ v requirements for the cylindrical relative orbit and singly periodic Lagrange point orbit are analysed, and it is shown that these requirements are modest and feasible for existing low-thrust propulsion technology.

Imaging of supersonic flow over a double elliptic surface

NASA Astrophysics Data System (ADS)

Zhang, Qing-Hu; Yi, Shi-He; He, Lin; Zhu, Yang-Zhu; Chen, Zhi

2013-11-01

The coherent structures of flow over a double elliptic surface are experimentally investigated in a supersonic low-noise wind tunnel at Mach number 3 using nano-tracer planar laser scattering (NPLS) and particle image velocimetry (PIV) techniques. High spatiotemporal resolution images and velocity fields of both laminar and turbulent inflows over the test model are captured. Based on the time-correlation images, the spatial and temporal evolutionary characteristics of the coherent structures are investigated. The flow structures in the NPLS images are in good agreement with the velocity fluctuation fields by PIV. From statistically significant ensembles, spatial correlation analysis of both cases is performed to quantify the mean size and the orientation of coherent structures. The results indicate that the mean structure is elliptical in shape and the structural angles in the separated region of laminar inflow are slightly smaller than that of turbulent inflow. Moreover, the structural angles of both cases increase with their distance away from the wall.

Equivalence of expressions for the radiation force on cylinders and application to elliptical cylinders

NASA Astrophysics Data System (ADS)

Wei, Wei; Marston, Philip L.

2005-09-01

Using an appropriate grouping of terms, a radiation force expression for cylinders in a standing wave based on far-field scattering [W. Wei, D. B. Thiessen, and P. L. Marston, J. Acoust. Soc. Am. 116, 202-208 (2004)] is transformed to an expression given elsewhere [F. G. Mitri, Eur. Phys. J. B 44, 71-78 (2005)]. Mitri's result is from a near-field derivation for the specific case of a circular cylinder. In the usual case, in an ideal lossless media the far-field derivation is not an approximation. The far-field derivation also applies to noncircular objects having mirror symmetry about the incident wave vector. Some general and historical aspects of far-field derivations of optical and acoustical radiation force (going back to 1909) will be noted. Our formulation yields a simple low-frequency approximation for the radiation force on elliptical cylinders by introducing approximations for the partial-wave scattering coefficients of elliptical cylinders first derived by Rayleigh. [Work supported by NASA.

Drift-free solar sail formations in elliptical Sun-synchronous orbits

NASA Astrophysics Data System (ADS)

Parsay, Khashayar; Schaub, Hanspeter

2017-10-01

To study the spatial and temporal variations of plasma in the highly dynamic environment of the magnetosphere, multiple spacecraft must fly in a formation. The objective for this study is to investigate the feasibility of solar sail formation flying in the Earth-centered, Sun-synchronous orbit regime. The focus of this effort is to enable formation flying for a group of solar sails that maintain a nominally fixed Sun-pointing attitude during formation flight, solely for the purpose of precessing their orbit apse lines Sun-synchronously. A fixed-attitude solar sail formation is motivated by the difficulties in the simultaneous control of orbit and attitude in flying solar sails. First, the secular rates of the orbital elements resulting from the effects of solar radiation pressure (SRP) are determined using averaging theory for a Sun-pointing attitude sail. These averaged rates are used to analytically derive the first-order necessary conditions for a drift-free solar sail formation in Sun-synchronous orbits, assuming a fixed Sun-pointing orientation for each sail in formation. The validity of the first-order necessary conditions are illustrated by designing quasi-periodic relative motions. Next, nonlinear programming is applied to design truly drift-free two-craft solar sail formations. Lastly, analytic expressions are derived to determine the long-term dynamics and sensitivity of the formation with respect to constant attitude errors, uncertainty in orbital elements, and uncertainty in a sail's characteristic acceleration.

Satellite and lunar laser ranging in infrared

NASA Astrophysics Data System (ADS)

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

2017-05-01

We report on the implementation of a new infrared detection at the Grasse lunar laser ranging station and describe how infrared telemetry improves the situation. We present our first results on the lunar reflectors and show that infrared detection permits us to densify the observations and allows measurements during the new and the full moon periods. We also present the benefit obtained on the ranging of Global Navigation Satellite System (GNSS) satellites and on RadioAstron which have a very elliptic orbit.

Experimental investigation of supersonic flow over elliptic surface

NASA Astrophysics Data System (ADS)

Zhang, Qinghu; Yi, Shihe; He, Lin; Zhu, Yangzhu; Chen, Zhi

2013-11-01

The coherent structures of flow over a compression elliptic surface are experimentally investigated in a supersonic low-noise wind tunnel at Mach Number 3 using nano-tracer planar laser scattering (NPLS) and particle image velocimetry (PIV) techniques. High spacial resolution images and the average velocity profiles of both laminar inflow and turbulent inflow over the testing model were captured. From statistically significant ensembles, spatial correlation analysis of both cases is performed to quantify the mean size and orientation of large structures. The results indicate that the mean structure is elliptical in shape and structure angles in separated region of laminar inflow are slightly smaller than that of turbulent inflow. Moreover, the structure angle of both cases increases with its distance away from from the wall. POD analysis of velocity and vorticity fields is performed for both cases. The energy portion of the first mode for the velocity data is much larger than that for the vorticity field. For vorticity decompositions, the contribution from the first mode for the laminar inflow is slightly larger than that for the turbulent inflow and the cumulative contributions for laminar inflow converges slightly faster than that for turbulent inflow

Adler-Kostant-Symes scheme for face and Calogero-Moser-Sutherland-type models

NASA Astrophysics Data System (ADS)

Jurčo, Branislav; Schupp, Peter

1998-07-01

We give the construction of quantum Lax equations for IRF models and the difference version of the Calogero-Moser-Sutherland model introduced by Ruijsenaars. We solve the equations using factorization properties of the underlying face Hopf algebras/elliptic quantum groups. This construction is in the spirit of the Adler-Kostant-Symes method and generalizes our previous work to the case of face Hopf algebras/elliptic quantum groups with dynamical R matrices.

Similarity considerations and conservation laws for magneto-static atmospheres

NASA Technical Reports Server (NTRS)

Webb, G. M.

1986-01-01

The equations of magnetohydrostatic equilibria for a plasma in a gravitational field are investigated analytically. For equilibria with one ignorable spatial coordinate, the equations reduce to a single nonlinear elliptic equation for the magnetic potential. Similarity solutions of the elliptic equation are obtained for the case of an isothermal atmosphere in a uniform gravitational field. The solutions are obtained from a consideration of the invariance group of the elliptic equation. The importance of symmetries of the elliptic equation also appears in the determination of conservation laws. It turns out that the elliptic equation can be written as a variational principle, and the symmetries of the variational functional lead (via Noether's theorem) to conservation laws for the equation. As an example of the application of the similarity solutions, a model magnetostatic atmosphere is constructed in which the current density J is proportional to the cube of the magnetic potential, and falls off exponentially with distance vertical to the base, with an 'e-folding' distance equal to the gravitational scale height. The solutions show the interplay between the gravitational force, the J x B force (B, magnetic field induction) and the gas pressure gradient.

Capillary instability of elliptic liquid jets

NASA Astrophysics Data System (ADS)

Amini, Ghobad; Dolatabadi, Ali

2011-08-01

Instability of a liquid jet issuing from an elliptic nozzle in Rayleigh mode is investigated and its behavior is compared with a circular jet. Mathematical solution of viscous free-surface flow for asymmetric geometry is complicated if 3-D analytical solutions are to be obtained. Hence, one-dimensional Cosserat (directed curve) equations are used which can be assumed as a low order form of Navier-Stokes equations for slender jets. Linear solution is performed using perturbation method. Temporal dispersion equation is derived to find the most unstable wavelength responsible for the jet breakup. The obtained results for a circular jet (i.e., an ellipse with an aspect ratio of one) are compared with the classical results of Rayleigh and Weber for inviscid and viscous cases, respectively. It is shown that in the Rayleigh regime, which is the subject of this research, symmetric perturbations are unstable while asymmetric perturbations are stable. Consequently, spatial analysis is performed and the variation of growth rate under the effect of perturbation frequencies for various jet velocities is demonstrated. Results reveal that in comparison with a circular jet, the elliptic jet is more unstable. Furthermore, among liquid jets with elliptical cross sections, those with larger ellipticities have a larger instability growth rate.

Elastohydrodynamics of elliptical contacts for materials of low elastic modulus

NASA Technical Reports Server (NTRS)

Hamrock, B. J.; Dowson, D.

1983-01-01

The influence of the ellipticity parameter k and the dimensionless speed U, load W, and materials G parameters on minimum film thickness for materials of low elastic modulus was investigated. The ellipticity parameter was varied from 1 (a ball-on-plane configuration) to 12 (a configuration approaching a line contact); U and W were each varied by one order of magnitude. Seventeen cases were used to generate the minimum- and central-film-thickness relations. The influence of lubricant starvation on minimum film thickness in starved elliptical, elastohydrodynamic configurations was also investigated for materials of low elastic modulus. Lubricant starvation was studied simply by moving the inlet boundary closer to the center of the conjunction in the numerical solutions. Contour plots of pressure and film thickness in and around the contact were presented for both fully flooded and starved lubrication conditions. It is evident from these figures that the inlet pressure contours become less circular and closer to the edge of the Hertzian contact zone and that the film thickness decreases substantially as the serverity of starvation increases. The results presented reveal the essential features of both fully flooded and starved, elliptical, elastohydrodynamic conjunctions for materials of low elastic modulus.

Entire radial solutions of elliptic systems and inequalities of the mean curvature type

NASA Astrophysics Data System (ADS)

Filippucci, Roberta

2007-10-01

In this paper we study first nonexistence of radial entire solutions of elliptic systems of the mean curvature type with a singular or degenerate diffusion depending on the solution u. In particular we extend a previous result given in [R. Filippucci, Nonexistence of radial entire solutions of elliptic systems, J. Differential Equations 188 (2003) 353-389]. Moreover, in the scalar case we obtain nonexistence of all entire solutions, radial or not, of differential inequalities involving again operators of the mean curvature type and a diffusion term. We prove that in the scalar case, nonexistence of entire solutions is due to the explosion of the derivative of every nonglobal radial solution in the right extremum of the maximal interval of existence, while in that point the solution is bounded. This behavior is qualitatively different with respect to what happens for the m-Laplacian operator, studied in [R. Filippucci, Nonexistence of radial entire solutions of elliptic systems, J. Differential Equations 188 (2003) 353-389], where nonexistence of entire solutions is due, even in the vectorial case, to the explosion in norm of the solution at a finite point. Our nonexistence theorems for inequalities extend previous results given by Naito and Usami in [YE Naito, H. Usami, Entire solutions of the inequality div(A(=u)=u)[greater-or-equal, slanted]f(u), Math. Z. 225 (1997) 167-175] and Ghergu and Radulescu in [M. Ghergu, V. Radulescu, Existence and nonexistence of entire solutions to the logistic differential equation, Abstr. Appl. Anal. 17 (2003) 995-1003].

Preliminary analysis of LDEF instrument A0187-1: Chemistry of Micrometeoroids Experiment

NASA Technical Reports Server (NTRS)

Hoerz, Friedrich; Bernhard, Ronald P.; Warren, Jack; See, Thomas H.; Brownlee, Donald E.; Laurance, Mark R.; Messenger, Scott; Peterson, Robert B.

1992-01-01

The Chemistry of Micrometeoroids Experiment (CME) exposed approximately 0.8 sq. m of gold on the Long Duration Exposure Facility's (LDEF's) trailing edge (location A03) and approximately 1.1 sq. m of aluminum in the forward-facing A11 location. The most significant results to date relate to the discovery of unmelted pyroxene and olivine fragments associated with natural cosmic dust impacts. The latter are sufficiently large for detailed phase studies, and they serve to demonstrate that recovery of unmelted dust fragments is a realistic prospect for further dust experiments that will employ more advanced collector media. We also discovered that man-made debris impacts occur on the LDEF's trailing edge with substantially higher frequency than expected, suggesting that orbital debris in highly elliptical orbits may have been somewhat underestimated.

A Kalman Filter for Mass Property and Thrust Identification of the Spin-Stabilized Magnetospheric Multiscale Formation

NASA Technical Reports Server (NTRS)

Queen, Steven Z.

2015-01-01

The Magnetospheric Multiscale (MMS) mission consists of four identically instrumented, spin-stabilized observatories, elliptically orbiting the Earth in a tetrahedron formation. For the operational success of the mission, on-board systems must be able to deliver high-precision orbital adjustment maneuvers. On MMS, this is accomplished using feedback from on-board star sensors in tandem with accelerometers whose measurements are dynamically corrected for errors associated with a spinning platform. In order to determine the required corrections to the measured acceleration, precise estimates of attitude, rate, and mass-properties are necessary. To this end, both an on-board and ground-based Multiplicative Extended Kalman Filter (MEKF) were formulated and implemented in order to estimate the dynamic and quasi-static properties of the spacecraft.

Analytic expressions for perturbations and partial derivatives of range and range rate of a spacecraft with respect to the coefficient of the second harmonic

NASA Technical Reports Server (NTRS)

Georgevic, R. M.

1973-01-01

Closed-form analytic expressions for the time variations of instantaneous orbital parameters and of the topocentric range and range rate of a spacecraft moving in the gravitational field of an oblate large body are derived using a first-order variation of parameters technique. In addition, the closed-form analytic expressions for the partial derivatives of the topocentric range and range rate are obtained, with respect to the coefficient of the second harmonic of the potential of the central body (J sub 2). The results are applied to the motion of a point-mass spacecraft moving in the orbit around the equatorially elliptic, oblate sun, with J sub 2 approximately equal to .000027.

Magnetospheric Multiscale Mission Attitude Dynamics: Observations from Flight Data

NASA Technical Reports Server (NTRS)

Williams, Trevor; Shulman, Seth; Sedlak, Joseph E.; Ottenstein, Neil; Lounsbury, Brian

2016-01-01

The NASA Magnetospheric Multiscale mission, launched on Mar. 12, 2015, is flying four spinning spacecraft in highly elliptical orbits to study the magnetosphere of the Earth. Extensive attitude data is being collected, including spin rate, spin axis orientation, and nutation rate. The paper will discuss the various environmental disturbance torques that act on the spacecraft, and will describe the observed results of these torques. In addition, a slow decay in spin rate has been observed for all four spacecraft in the extended periods between maneuvers. It is shown that this despin is consistent with the effects of an additional disturbance mechanism, namely that produced by the Active Spacecraft Potential Control devices. Finally, attitude dynamics data is used to analyze a micrometeoroid/orbital debris impact event with MMS4 that occurred on Feb. 2, 2016.

Arbitrary spin-to-orbital angular momentum conversion of light

NASA Astrophysics Data System (ADS)

Devlin, Robert C.; Ambrosio, Antonio; Rubin, Noah A.; Mueller, J. P. Balthasar; Capasso, Federico

2017-11-01

Optical elements that convert the spin angular momentum (SAM) of light into vortex beams have found applications in classical and quantum optics. These elements—SAM-to-orbital angular momentum (OAM) converters—are based on the geometric phase and only permit the conversion of left- and right-circular polarizations (spin states) into states with opposite OAM. We present a method for converting arbitrary SAM states into total angular momentum states characterized by a superposition of independent OAM. We designed a metasurface that converts left- and right-circular polarizations into states with independent values of OAM and designed another device that performs this operation for elliptically polarized states. These results illustrate a general material-mediated connection between SAM and OAM of light and may find applications in producing complex structured light and in optical communication.

Dynamical properties of a family of collisionless models of elliptical galaxies

NASA Astrophysics Data System (ADS)

Bertin, G.; Trenti, M.

2004-04-01

N-body simulations of collisionless collapse have offered important clues to the construction of realistic stellar dynamical models of elliptical galaxies. Such simulations confirm and quantify the qualitative expectation that rapid collapse of a self-gravitating collisionless system, initially cool and significantly far from equilibrium, leads to incomplete relaxation, that is to a quasi-equilibrium configuration characterized by isotropic, quasi-Maxwellian distribution of stellar orbits in the inner regions and by radially biased anisotropic pressure in the outer parts. In earlier studies, as illustrated in a number of papers several years ago, the attention was largely focused on the successful comparison between the models (constructed under the qualitative clues offered by the N-body simulations mentioned above) and the observations. In this paper we revisit the problem of incomplete violent relaxation, by making a direct comparison between the detailed properties of a family of distribution functions and those of the products of collisionless collapse found in N-body simulations.

Perturbed Equations of Motion for Formation Flight Near the Sun-Earth L2 Point

NASA Technical Reports Server (NTRS)

Segerman, Alan M.; Zedd, Michael F.

2005-01-01

This Memorandum Report consists of a compilation of three individual reports, of increasing complexity, describing investigations of formation flight of spacecraft in the vicinity of the L2 Sun-Earth 1ibration point. The individual reports form the following parts of this compilation: - Introduction to the relative motion of spacecraft about the Sun-Earth L2 Point - Linear and quadratic modelling and solution of the relative motion - Modelling the Perturbations - Elliptical Earth Orbit, Lunar Gravity, Solar Radiation Pressure, Thrusters. The three parts are self-contained, with somewhat, varying notation and terminology. After fair1y significant literature searches: this new work (of Parts 2 and 3) is deemed to be unique because it describes the primary perturbations to the description of relative motion between nearby spacecraft. The effect of the elliptical motion of the Earth about the Sun was verified to be the dominant perturbation to the circular restricted three body problem. Contributions due to lunar gravity and solar radiation pressure are seen to have much smaller effect.

Forward Modeling of a Coronal Cavity

NASA Technical Reports Server (NTRS)

Kucera, T. A.; Gibson, S. E.; Schmit, D. J.

2011-01-01

We apply a forward model of emission from a coronal cavity in an effort to determine the temperature and density distribution in the cavity. Coronal cavities are long, low-density structures located over filament neutral lines and are often seen as dark elliptical features at the solar limb in white light, EUV and X-rays. When these structures erupt they form the cavity portions of CMEs The model consists of a coronal streamer model with a tunnel-like cavity with elliptical cross-section and a Gaussian variation of height along the tunnel length. Temperature and density can be varied as a function of altitude both in the cavity and streamer. We apply this model to a cavity observed in Aug. 2007 by a wide array of instruments including Hinode/EIS, STEREO/EUVI and SOHO/EIT. Studies such as these will ultimately help us understand the the original structures which erupt to become CMEs and ICMES, one of the prime Solar Orbiter objectives.

The role of service areas in the optimization of FSS orbital and frequency assignments

NASA Technical Reports Server (NTRS)

Levis, C. A.; Wang, C.-W.; Yamamura, Y.; Reilly, C. H.; Gonsalvez, D. J.

1986-01-01

An implicit relationship is derived which relates the topocentric separation of two satellites required for a given level of single-entry protection to the separation and orientation of their service areas. The results are presented explicitly for circular beams and topocentric angles. A computational approach is given for elliptical beams and for use with longitude and latitude variables. It is found that the geocentric separation depends primarily on the service area separation, secondarily on a parameter which characterizes the electrical design, and only slightly on the mean orbital position of the satellites. Both linear programming and mixed integer programming algorithms are implemented. Possible objective function choices are discussed, and explicit formulations are presented for the choice of the sum of the absolute deviations of the orbital locations from some prescribed 'ideal' location set. A test problem involving six service areas is examined with results that are encouraging with respect to applying the linear programming procedure to larger scenarios.

State dependent model predictive control for orbital rendezvous using pulse-width pulse-frequency modulated thrusters

NASA Astrophysics Data System (ADS)

Li, Peng; Zhu, Zheng H.; Meguid, S. A.

2016-07-01

This paper studies the pulse-width pulse-frequency modulation based trajectory planning for orbital rendezvous and proximity maneuvering near a non-cooperative spacecraft in an elliptical orbit. The problem is formulated by converting the continuous control input, output from the state dependent model predictive control, into a sequence of pulses of constant magnitude by controlling firing frequency and duration of constant-magnitude thrusters. The state dependent model predictive control is derived by minimizing the control error of states and control roughness of control input for a safe, smooth and fuel efficient approaching trajectory. The resulting nonlinear programming problem is converted into a series of quadratic programming problem and solved by numerical iteration using the receding horizon strategy. The numerical results show that the proposed state dependent model predictive control with the pulse-width pulse-frequency modulation is able to effectively generate optimized trajectories using equivalent control pulses for the proximity maneuvering with less energy consumption.

Quasimodular instanton partition function and the elliptic solution of Korteweg-de Vries equations

NASA Astrophysics Data System (ADS)

He, Wei

2015-02-01

The Gauge/Bethe correspondence relates Omega-deformed N = 2 supersymmetric gauge theories to some quantum integrable models, in simple cases the integrable models can be treated as solvable quantum mechanics models. For SU(2) gauge theory with an adjoint matter, or with 4 fundamental matters, the potential of corresponding quantum model is the elliptic function. If the mass of matter takes special value then the potential is an elliptic solution of KdV hierarchy. We show that the deformed prepotential of gauge theory can be obtained from the average densities of conserved charges of the classical KdV solution, the UV gauge coupling dependence is assembled into the Eisenstein series. The gauge theory with adjoint mass is taken as the example.

Fiber-dependent deautonomization of integrable 2D mappings and discrete Painlevé equations

NASA Astrophysics Data System (ADS)

Carstea, Adrian Stefan; Dzhamay, Anton; Takenawa, Tomoyuki

2017-10-01

It is well known that two-dimensional mappings preserving a rational elliptic fibration, like the Quispel-Roberts-Thompson mappings, can be deautonomized to discrete Painlevé equations. However, the dependence of this procedure on the choice of a particular elliptic fiber has not been sufficiently investigated. In this paper we establish a way of performing the deautonomization for a pair of an autonomous mapping and a fiber. Starting from a single autonomous mapping but varying the type of a chosen fiber, we obtain different types of discrete Painlevé equations using this deautonomization procedure. We also introduce a technique for reconstructing a mapping from the knowledge of its induced action on the Picard group and some additional geometric data. This technique allows us to obtain factorized expressions of discrete Painlevé equations, including the elliptic case. Further, by imposing certain restrictions on such non-autonomous mappings we obtain new and simple elliptic difference Painlevé equations, including examples whose symmetry groups do not appear explicitly in Sakai’s classification.

A Model for Displacements Between Parallel Plates That Shows Change of Type from Hyperbolic to Elliptic

NASA Astrophysics Data System (ADS)

Shariati, Maryam; Yortsos, Yannis; Talon, Laurent; Martin, Jerome; Rakotomalala, Nicole; Salin, Dominique

2003-11-01

We consider miscible displacement between parallel plates, where the viscosity is a function of the concentration. By selecting a piece-wise representation, the problem can be considered as ``three-phase'' flow. Assuming a lubrication-type approximation, the mathematical description is in terms of two quasi-linear hyperbolic equations. When the mobility of the middle phase is smaller than its neighbors, the system is genuinely hyperbolic and can be solved analytically. However, when it is larger, an elliptic region develops. This change-of-type behavior is for the first time proved here based on sound physical principles. Numerical solutions with a small diffusion are presented. Good agreement is obtained outside the elliptic region, but not inside, where the numerical results show unstable behavior. We conjecture that for the solution of the real problem in the mixed-type case, the full higher-dimensionality problem must be considered inside the elliptic region, in which the lubrication (parallel-flow) approximation is no longer appropriate. This is discussed in a companion presentation.

Eta Carinae: Orientation of The Orbital Plane

NASA Technical Reports Server (NTRS)

Gull, T. R.; Nielsen, K. E.; Ivarsson, S.; Corcoran, M. F.; Verner, E.; Hillier, J. D.

2006-01-01

Evidence continues to build that Eta Carinae is a massive binary system with a hidden hot companion in a highly elliptical orbit. We present imaging and spectroscopic evidence that provide clues to the orientation of the orbital plane. The circumstellar ejecta, known as the Homunculus and Little Homunculus, are hourglass-shaped structures, one encapsulated within the other, tilted at about 45 degrees from the sky plane. A disk region lies between the bipolar lobes. Based upon their velocities and proper motions, Weigelt blobs B, C and D, very bright emission clumps 0.1 to 0.3" Northwest from Eta Carinae, lie in the disk. UV flux from the hot companion, Eta Car B, photoexcites the Weigelt blobs. Other clumps form a complete chain around the star, but are not significantly photoexcited. The strontium filament, a 'neutral' emission structure, lies in the same general direction as the Weigelt blobs and exhibits peculiar properties indicative that much mid-UV, but no hydrogen-ionizing radiation impinges on this structure. It is shielded by singly-ionized iron. P Cygni absorptions in Fe I I lines, seen directly in line of sight from Eta Carinae, are absent in the stellar light scattered by the Weigelt blobs. Rather than a strong absorption extending to -600 km/s, a low velocity absorption feature extends from -40 to -150 km/s. No absorbing Fe II exists between Eta Carinae and Weigelt D, but the outer reaches of the wind are intercepted in line of sight from Weigelt D to the observer. This indicates that the UV radiation is constrained by the dominating wind of Eta Car A to a small cavity carved out by the weaker wind of Eta Car B. Since the high excitation nebular lines are seen in the Weigelt blobs at most phases, the cavity, and hence the major axis of the highly elliptical orbit, must lie in the general direction of the Weigelt blobs. The evidence is compelling that the orbital major axis of Eta Carinae is projected at -45 degrees position angle on the sky. Moreover the milliarcsecond-scale extended structure of Eta Carinae, recently detected by VLTI, may be evidence of the binary companion in the disk plane, not necessarily of a single star as a prolate spheroid extending along the ejecta polar axis.

Dynamical evolution of space debris on high-elliptical orbits near high-order resonance zones

NASA Astrophysics Data System (ADS)

Kuznetsov, Eduard; Zakharova, Polina

Orbital evolution of objects on Molniya-type orbits is considered near high-order resonance zones. Initial conditions correspond to high-elliptical orbits with the critical inclination 63.4 degrees. High-order resonances are analyzed. Resonance orders are more than 5 and less than 50. Frequencies of perturbations caused by the effect of sectorial and tesseral harmonics of the Earth's gravitational potential are linear combinations of the mean motion of a satellite, angular velocities of motion of the pericenter and node of its orbit, and the angular velocity of the Earth. Frequencies of perturbations were calculated by taking into account secular perturbations from the Earth oblateness, the Moon, the Sun, and a solar radiation pressure. Resonance splitting effect leads to three sub-resonances. The study of dynamical evolution on long time intervals was performed on the basis of the results of numerical simulation. We used "A Numerical Model of the Motion of Artificial Earth's Satellites", developed by the Research Institute of Applied Mathematics and Mechanics of the Tomsk State University. The model of disturbing forces taken into account the main perturbing factors: the gravitational field of the Earth, the attraction of the Moon and the Sun, the tides in the Earth’s body, the solar radiation pressure, taking into account the shadow of the Earth, the Poynting-Robertson effect, and the atmospheric drag. Area-to-mass ratio varied from small values corresponding to satellites to big ones corresponding to space debris. The locations and sizes of resonance zones were refined from numerical simulation. The Poynting-Robertson effect results in a secular decrease in the semi-major axis of a spherically symmetrical satellite. In resonance regions the effect weakens slightly. Reliable estimates of secular perturbations of the semi-major axis were obtained from the numerical simulation. Under the Poynting-Robertson effect objects pass through the regions of high-order resonances. The Poynting-Robertson effect and secular perturbations of the semi-major axis lead to formation weak stochastic trajectories. The integral autocorrelation function was used to analysis stochastic properties trajectories. This work was supported by the Ministry of Education and Science of the Russian Federation and the Russian Foundation for Basic Researches (grant 13-02-00026a).

Displacement-length relationship of normal faults in Acheron Fossae, Mars: new observations with HRSC.

NASA Astrophysics Data System (ADS)

Charalambakis, E.; Hauber, E.; Knapmeyer, M.; Grott, M.; Gwinner, K.

2007-08-01

For Earth, data sets and models have shown that for a fault loaded by a constant remote stress, the maximum displacement on the fault is linearly related to its length by d = gamma · l [1]. The scaling and structure is self-similar through time [1]. The displacement-length relationship can provide useful information about the tectonic regime.We intend to use it to estimate the seismic moment released during the formation of Martian fault systems and to improve the seismicity model [2]. Only few data sets have been measured for extraterrestrial faults. One reason is the limited number of reliable topographic data sets. We used high-resolution Digital Elevation Models (DEM) [3] derived from HRSC image data taken from Mars Express orbit 1437. This orbit covers an area in the Acheron Fossae region, a rift-like graben system north of Olympus Mons with a "banana"-shaped topography [4]. It has a fault trend which runs approximately WNW-ESE. With an interactive IDL-based software tool [5] we measured the fault length and the vertical offset for 34 faults. We evaluated the height profile by plotting the fault lengths l vs. their observed maximum displacement (dmax-model). Additionally, we computed the maximum displacement of an elliptical fault scarp where the plane has the same area as in the observed case (elliptical model). The integration over the entire fault length necessary for the computation of the area supresses the "noise" introduced by local topographic effects like erosion or cratering. We should also mention that fault planes dipping 60 degree are usually assumed for Mars [e.g., 6] and even shallower dips have been found for normal fault planes [7]. This dip angle is used to compute displacement from vertical offset via d = h/(h*sinα), where h is the observed topographic step height, and ? is the fault dip angle. If fault dip angles of 30 degree are considered, the displacement differs by 40% from the one of dip angles of 60 degree. Depending on the data quality, especially the lighting conditions in the region, different errors can be made by determining the various values. Based on our experiences, we estimate that the error measuring the length of the fault is smaller than 10% and that the measurement error of the offset is smaller than 5%. Furthermore the horizontal resolution of the HRSC images is 12.5 m/pixel or 25 m/pixel and of the DEM derived from HRSC images 50 m/pixel because of re-sampling. That means that image resolution does not introduce a significant error at fault lengths in kilometer range. For the case of Mars it is known that in the growth of fault populations linkage is an essential process [8]. We obtained the d/l-values from selected examples of faults that were connected via a relay ramp. The error of ignoring an existing fault linkage is 20% to 50% if the elliptical fault model is used and 30% to 50% if only the dmax value is used to determine d l . This shows an advantage of the elliptic model. The error increases if more faults are linked, because the underestimation of the relevant length gets worse the longer the linked system is. We obtained a value of gamma=d/l of about 2 · 10-2 for the elliptic model and a value of approximately 2.7 · 10-2 for the dmax-model. The data show a relatively large scatter, but they can be compared to data from terrestrial faults ( d/l= ~1 · 10-2...5 · 10-2; [9] and references therein). In a first inspection of the Acheron Fossae 2 region in the orbit 1437 we could confirm our first observations [10]. If we consider fault linkage the d/l values shift towards lower d/l-ratios, since linkage means that d remains essentially constant, but l increases significantly. We will continue to measure other faults and obtain values for linked faults and relay ramps. References: [1] Cowie, P. A. and Scholz, C. H. (1992) JSG, 14, 1133-1148. [2] Knapmeyer, M. et al. (2006) JGR, 111, E11006. [3] Neukum, G. et al. (2004) ESA SP-1240, 17-35. [4] Kronberg, P. et al. (2007) J. Geophys. Res., 112, E04005, doi:10.1029/2006JE002780. [5] Hauber, E. et al. (2007) LPSC, XXXVIII, abstract 1338. [6] Wilkins, S. J. et al. (2002) GRL, 29, 1884, doi: 10.1029/2002GL015391. [7] Fueten, F. et al. (2007) LPSC, XXXVIII, abstract 1388. [8] Schultz, R. A. (2000) Tectonophysics, 316, 169-193. [9] Schultz, R. A. et al. (2006) JSG, 28, 2182-2193. [10] Hauber, E. et al. (2007) 7th Mars Conference, submitted.

Metrics in Keplerian orbits quotient spaces

NASA Astrophysics Data System (ADS)

Milanov, Danila V.

2018-03-01

Quotient spaces of Keplerian orbits are important instruments for the modelling of orbit samples of celestial bodies on a large time span. We suppose that variations of the orbital eccentricities, inclinations and semi-major axes remain sufficiently small, while arbitrary perturbations are allowed for the arguments of pericentres or longitudes of the nodes, or both. The distance between orbits or their images in quotient spaces serves as a numerical criterion for such problems of Celestial Mechanics as search for common origin of meteoroid streams, comets, and asteroids, asteroid families identification, and others. In this paper, we consider quotient sets of the non-rectilinear Keplerian orbits space H. Their elements are identified irrespective of the values of pericentre arguments or node longitudes. We prove that distance functions on the quotient sets, introduced in Kholshevnikov et al. (Mon Not R Astron Soc 462:2275-2283, 2016), satisfy metric space axioms and discuss theoretical and practical importance of this result. Isometric embeddings of the quotient spaces into R^n, and a space of compact subsets of H with Hausdorff metric are constructed. The Euclidean representations of the orbits spaces find its applications in a problem of orbit averaging and computational algorithms specific to Euclidean space. We also explore completions of H and its quotient spaces with respect to corresponding metrics and establish a relation between elements of the extended spaces and rectilinear trajectories. Distance between an orbit and subsets of elliptic and hyperbolic orbits is calculated. This quantity provides an upper bound for the metric value in a problem of close orbits identification. Finally the invariance of the equivalence relations in H under coordinates change is discussed.

Transmission of isotropic light across a dielectric surface in two and three dimensions.

NASA Technical Reports Server (NTRS)

Allen, W. A.

1973-01-01

Average transmittance of polarized diffuse light across a dielectric surface is calculated in both two and three dimensions. The incident light in both cases is confined to an angular range measured from the surface normal. Limiting values in three dimensions correspond to known results for two cases, (1) normal incidence, and (2) diffuse light incident from a 180 deg cone. The two-dimensional formulation is solvable in terms of elliptic functions and incomplete elliptic integrals of the first, second, and third kinds. Results are displayed graphically for values of transmittances in excess of 0.9 associated with relative indices of refraction in the range m = 1.0 to m = 2.6.

Exact Delaunay normalization of the perturbed Keplerian Hamiltonian with tesseral harmonics

NASA Astrophysics Data System (ADS)

Mahajan, Bharat; Vadali, Srinivas R.; Alfriend, Kyle T.

2018-03-01

A novel approach for the exact Delaunay normalization of the perturbed Keplerian Hamiltonian with tesseral and sectorial spherical harmonics is presented in this work. It is shown that the exact solution for the Delaunay normalization can be reduced to quadratures by the application of Deprit's Lie-transform-based perturbation method. Two different series representations of the quadratures, one in powers of the eccentricity and the other in powers of the ratio of the Earth's angular velocity to the satellite's mean motion, are derived. The latter series representation produces expressions for the short-period variations that are similar to those obtained from the conventional method of relegation. Alternatively, the quadratures can be evaluated numerically, resulting in more compact expressions for the short-period variations that are valid for an elliptic orbit with an arbitrary value of the eccentricity. Using the proposed methodology for the Delaunay normalization, generalized expressions for the short-period variations of the equinoctial orbital elements, valid for an arbitrary tesseral or sectorial harmonic, are derived. The result is a compact unified artificial satellite theory for the sub-synchronous and super-synchronous orbit regimes, which is nonsingular for the resonant orbits, and is closed-form in the eccentricity as well. The accuracy of the proposed theory is validated by comparison with numerical orbit propagations.

A meteor stream study of 1966

NASA Astrophysics Data System (ADS)

Terentjeva, Alexandra

2017-03-01

3600 individual photographic orbits of meteor bodies and about 2000 visual meteor radiants with corresponding velocities were compiled and carefully studied in detail. 154 minor meteor streams were detected in the Solar System, their basic orbital and other data are given. Firstly some remarkable shower and stream properties are established: examples of the large elliptic radiation areas with semi-major axes perpendicular to the Ecliptic; the existence of the Northern (N) , Southern (S) and Ecliptical (Q) branches of some streams; stream-antipodes and radiant-antipodes (symmetrically arranged relatively to the Ecliptic) with angular distances from the Ecliptic to 40-80°; a number of short-perihelion streams (q 0.05-0.07 A.U.); some meteor streams perpendicular to the Ecliptic's plane. There are also some unique meteor bodies with their orbits enclosed within the limits of the Earth's one, or having the clockwise and anticlockwise direction in two similar orbits. Hyperbolic photographic velocities vh = 57-88 km /sec are treated as real ones according to the best radar and visual observations. A "bunch" of ecliptical streams, discovered in the USSR in 1950, is a complex of orbits of the mostly massive meteor particles of the Zodiacal Cloud. The stream evolution rate is comparatively high. The total complex of sporadic meteor bodies is not totally chaotic and accidental.

Formation of most of our coal brought Earth close to global glaciation.

PubMed

Feulner, Georg

2017-10-24

The bulk of Earth's coal deposits used as fossil fuel today was formed from plant debris during the late Carboniferous and early Permian periods. The high burial rate of organic carbon correlates with a significant drawdown of atmospheric carbon dioxide (CO 2 ) at that time. A recent analysis of a high-resolution record reveals large orbitally driven variations in atmospheric CO 2 concentration between [Formula: see text]150 and 700 ppm for the latest Carboniferous and very low values of 100 [Formula: see text] 80 ppm for the earliest Permian. Here, I explore the sensitivity of the climate around the Carboniferous/Permian boundary to changes in Earth's orbital parameters and in atmospheric CO 2 using a coupled climate model. The coldest orbital configurations are characterized by large axial tilt and small eccentricities of Earth's elliptical orbit, whereas the warmest configuration occurs at minimum tilt, maximum eccentricity, and a perihelion passage during Northern hemisphere spring. Global glaciation occurs at CO 2 concentrations <40 ppm, suggesting a rather narrow escape from a fully glaciated Snowball Earth state given the low levels and large fluctuations of atmospheric CO 2 These findings highlight the importance of orbital cycles for the climate and carbon cycle during the late Paleozoic ice age and the climatic significance of the fossil carbon stored in Earth's coal deposits.

A star in a 15.2-year orbit around the supermassive black hole at the centre of the Milky Way.

PubMed

Schödel, R; Ott, T; Genzel, R; Hofmann, R; Lehnert, M; Eckart, A; Mouawad, N; Alexander, T; Reid, M J; Lenzen, R; Hartung, M; Lacombe, F; Rouan, D; Gendron, E; Rousset, G; Lagrange, A-M; Brandner, W; Ageorges, N; Lidman, C; Moorwood, A F M; Spyromilio, J; Hubin, N; Menten, K M

2002-10-17

Many galaxies are thought to have supermassive black holes at their centres-more than a million times the mass of the Sun. Measurements of stellar velocities and the discovery of variable X-ray emission have provided strong evidence in favour of such a black hole at the centre of the Milky Way, but have hitherto been unable to rule out conclusively the presence of alternative concentrations of mass. Here we report ten years of high-resolution astrometric imaging that allows us to trace two-thirds of the orbit of the star currently closest to the compact radio source (and massive black-hole candidate) Sagittarius A*. The observations, which include both pericentre and apocentre passages, show that the star is on a bound, highly elliptical keplerian orbit around Sgr A*, with an orbital period of 15.2 years and a pericentre distance of only 17 light hours. The orbit with the best fit to the observations requires a central point mass of (3.7 +/- 1.5) x 10(6) solar masses (M(*)). The data no longer allow for a central mass composed of a dense cluster of dark stellar objects or a ball of massive, degenerate fermions.

Navigation Accuracy Guidelines for Orbital Formation Flying

NASA Technical Reports Server (NTRS)

Carpenter, J. Russell; Alfriend, Kyle T.

2004-01-01

Some simple guidelines based on the accuracy in determining a satellite formation s semi-major axis differences are useful in making preliminary assessments of the navigation accuracy needed to support such missions. These guidelines are valid for any elliptical orbit, regardless of eccentricity. Although maneuvers required for formation establishment, reconfiguration, and station-keeping require accurate prediction of the state estimate to the maneuver time, and hence are directly affected by errors in all the orbital elements, experience has shown that determination of orbit plane orientation and orbit shape to acceptable levels is less challenging than the determination of orbital period or semi-major axis. Furthermore, any differences among the member s semi-major axes are undesirable for a satellite formation, since it will lead to differential along-track drift due to period differences. Since inevitable navigation errors prevent these differences from ever being zero, one may use the guidelines this paper presents to determine how much drift will result from a given relative navigation accuracy, or conversely what navigation accuracy is required to limit drift to a given rate. Since the guidelines do not account for non-two-body perturbations, they may be viewed as useful preliminary design tools, rather than as the basis for mission navigation requirements, which should be based on detailed analysis of the mission configuration, including all relevant sources of uncertainty.

Navigation Accuracy Guidelines for Orbital Formation Flying Missions

NASA Technical Reports Server (NTRS)

Carpenter, J. Russell; Alfriend, Kyle T.

2003-01-01

Some simple guidelines based on the accuracy in determining a satellite formation's semi-major axis differences are useful in making preliminary assessments of the navigation accuracy needed to support such missions. These guidelines are valid for any elliptical orbit, regardless of eccentricity. Although maneuvers required for formation establishment, reconfiguration, and station-keeping require accurate prediction of the state estimate to the maneuver we, and hence are directly affected by errors in all the orbital elements, experience has shown that determination of orbit plane orientation and orbit shape to acceptable levels is less challenging than the determination of orbital period or semi-major axis. Furthermore, any differences among the member s semi-major axes are undesirable for a satellite formation, since it will lead to differential along-track drift due to period differences. Since inevitable navigation errors prevent these differences from ever being zero, one may use the guidelines this paper presents to determine how much drift will result from a given relative navigation accuracy, or conversely what navigation accuracy is required to limit drift to a given rate. Since the guidelines do not account for non-two-body perturbations, they may be viewed as useful preliminary design tools, rather than as the basis for mission navigation requirements, which should be based on detailed analysis of the mission configuration, including all relevant sources of uncertainty.

The engineering of a nuclear thermal landing and ascent vehicle utilizing indigenous Martian propellant

NASA Technical Reports Server (NTRS)

Zubrin, Robert M.

1991-01-01

The following paper reports on a design study of a novel space transportation concept known as a 'NIMF' (Nuclear rocket using Indigenous Martian Fuel). The NIMF is a ballistic vehicle which obtains its propellant out of the Martian air by compression and liquefaction of atmospheric CO2. This propellant is subsequently used to generate rocket thrust at a specific impulse of 264 s by being heated to high temperature (2800 K) gas in the NIMFs' nuclear thermal rocket engines. The vehicle is designed to provide surface to orbit and surface to surface transportation, as well as housing, for a crew of three astronauts. It is capable of refueling itself for a flight to its maximum orbit in less than 50 days. The ballistic NIMF has a mass of 44.7 tonnes and, with the assumed 2800 K propellant temperature, is capable of attaining highly energetic (250 km by 34,000 km elliptical) orbits. This allows it to rendezvous with interplanetary transfer vehicles which are only very loosely bound into orbit around Mars. If a propellant temperature of 2000 K is assumed, then low Mars orbit can be attained; while if 3100 K is assumed, then the ballistic NIMF is capable of injecting itself onto a minimum energy transfer orbit to Earth in a direct ascent from the Martian surface.

The origin and evolution of fast and slow rotators in the Illustris simulation

NASA Astrophysics Data System (ADS)

Penoyre, Zephyr; Moster, Benjamin P.; Sijacki, Debora; Genel, Shy

2017-07-01

Using the Illustris simulation, we follow thousands of elliptical galaxies back in time to identify how the dichotomy between fast- and slow-rotating ellipticals (FRs and SRs) develops. Comparing to the ATLAS3D survey, we show that Illustris reproduces similar elliptical galaxy rotation properties, quantified by the degree of ordered rotation, λR. There is a clear segregation between low-mass (M* < 1011 M⊙) ellipticals, which form a smooth distribution of FRs, and high-mass galaxies (M* > 1011.5 M⊙), which are mostly SRs, in agreement with observations. We find that SRs are very gas poor, metal rich and red in colour, while FRs are generally more gas rich and still star forming. We suggest that ellipticals begin naturally as FRs and, as they grow in mass, lose their spin and become SRs. While at z = 1, the progenitors of SRs and FRs are nearly indistinguishable, their merger and star formation histories differ thereafter. We find that major mergers tend to disrupt galaxy spin, though in rare cases can lead to a spin-up. No major difference is found between the effects of gas-rich and gas-poor mergers, and the number of minor mergers seems to have little correlation with galaxy spin. In between major mergers, lower mass ellipticals, which are mostly gas rich, tend to recover their spin by accreting gas and stars. For galaxies with M* above ˜1011 M⊙, this trend reverses; galaxies only retain or steadily lose their spin. More frequent mergers, accompanied by an inability to regain spin, lead massive ellipticals to lose most of ordered rotation and transition from FRs to SRs.

The method of A-harmonic approximation and optimal interior partial regularity for nonlinear elliptic systems under the controllable growth condition

NASA Astrophysics Data System (ADS)

Chen, Shuhong; Tan, Zhong

2007-11-01

In this paper, we consider the nonlinear elliptic systems under controllable growth condition. We use a new method introduced by Duzaar and Grotowski, for proving partial regularity for weak solutions, based on a generalization of the technique of harmonic approximation. We extend previous partial regularity results under the natural growth condition to the case of the controllable growth condition, and directly establishing the optimal Hölder exponent for the derivative of a weak solution.

Constraining the Properties of the Eta Carinae System via 3-D SPH Models of Space-Based Observations: The Absolute Orientation of the Binary Orbit

NASA Technical Reports Server (NTRS)

Madura, Thomas I.; Gull, Theodore R.; Owocki, Stanley P.; Okazaki, Atsuo T.; Russell, Christopher M. P.

2010-01-01

The extremely massive (> 90 Solar Mass) and luminous (= 5 x 10(exp 6) Solar Luminosity) star Eta Carinae, with its spectacular bipolar "Homunculus" nebula, comprises one of the most remarkable and intensely observed stellar systems in the galaxy. However, many of its underlying physical parameters remain a mystery. Multiwavelength variations observed to occur every 5.54 years are interpreted as being due to the collision of a massive wind from the primary star with the fast, less dense wind of a hot companion star in a highly elliptical (e approx. 0.9) orbit. Using three-dimensional (3-D) Smoothed Particle Hydrodynamics (SPH) simulations of the binary wind-wind collision in Eta Car, together with radiative transfer codes, we compute synthetic spectral images of [Fe III] emission line structures and compare them to existing Hubble Space Telescope/Space Telescope Imaging Spectrograph (HST/STIS) observations. We are thus able, for the first time, to constrain the absolute orientation of the binary orbit on the sky. An orbit with an inclination of i approx. 40deg, an argument of periapsis omega approx. 255deg, and a projected orbital axis with a position angle of approx. 312deg east of north provides the best fit to the observations, implying that the orbital axis is closely aligned in 3-1) space with the Homunculus symmetry axis, and that the companion star orbits clockwise on the sky relative to the primary.

Constraining the Properties of the Eta Carinae System via 3-D SPH Models of Space-Based Observations: The Absolute Orientation of the Binary Orbit

NASA Technical Reports Server (NTRS)

Madura, Thomas I.; Gull, Theodore R.; Owocki, Stanley P.; Okazaki, Atsuo T.; Russell, Christopher M. P.

2011-01-01

The extremely massive (> 90 Stellar Mass) and luminous (= 5 x 10(exp 6) Stellar Luminosity) star Eta Carinae, with its spectacular bipolar "Homunculus" nebula, comprises one of the most remarkable and intensely observed stellar systems in the Galaxy. However, many of its underlying physical parameters remain unknown. Multiwavelength variations observed to occur every 5.54 years are interpreted as being due to the collision of a massive wind from the primary star with the fast, less dense wind of a hot companion star in a highly elliptical (e approx. 0.9) orbit. Using three-dimensional (3-D) Smoothed Particle Hydrodynamics (SPH) simulations of the binary wind-wind collision, together with radiative transfer codes, we compute synthetic spectral images of [Fe III] emission line structures and compare them to existing Hubble Space Telescope/Space Telescope Imaging Spectrograph (HST/STIS) observations. We are thus able, for the first time, to tightly constrain the absolute orientation of the binary orbit on the sky. An orbit with an inclination of approx. 40deg, an argument of periapsis omega approx. 255deg, and a projected orbital axis with a position angle of approx. 312deg east of north provides the best fit to the observations, implying that the orbital axis is closely aligned in 3-D space with the Homunculus symmetry axis, and that the companion star orbits clockwise on the sky relative to the primary.

Electromagnetically induced transparency in the case of elliptic polarization of interacting fields

NASA Astrophysics Data System (ADS)

Parshkov, Oleg M.

2018-04-01

The theoretical investigation results of disintegration effect of elliptic polarized shot probe pulses of electromagnetically induced transparency in the counterintuitive superposed elliptic polarized control field and in weak probe field approximation are presented. It is shown that this disintegration occurs because the probe field in the medium is the sum of two normal modes, which correspond to elliptic polarized pulses with different speeds of propagation. The polarization ellipses of normal modes have equal eccentricities and mutually perpendicular major axes. Major axis of polarization ellipse of one normal mode is parallel to polarization ellipse major axis of control field, and electric vector of this mode rotates in the opposite direction, than electric vector of the control field. The electric vector other normal mode rotates in the same direction that the control field electric vector. The normal mode speed of the first type aforementioned is less than that of the second type. The polarization characteristics of the normal mode depend uniquely on the polarization characteristics of elliptic polarized control field and remain changeless in the propagation process. The theoretical investigation is performed for Λ-scheme of degenerated quantum transitions between 3P0, 3P10 and 3P2 energy levels of 208Pb isotope.

Advancement of a 30K W Solar Electric Propulsion System Capability for NASA Human and Robotic Exploration Missions

NASA Technical Reports Server (NTRS)

Smith, Bryan K.; Nazario, Margaret L.; Manzella, David H.

2012-01-01

Solar Electric Propulsion has evolved into a demonstrated operational capability performing station keeping for geosynchronous satellites, enabling challenging deep-space science missions, and assisting in the transfer of satellites from an elliptical orbit Geostationary Transfer Orbit (GTO) to a Geostationary Earth Orbit (GEO). Advancing higher power SEP systems will enable numerous future applications for human, robotic, and commercial missions. These missions are enabled by either the increased performance of the SEP system or by the cost reductions when compared to conventional chemical propulsion systems. Higher power SEP systems that provide very high payload for robotic missions also trade favorably for the advancement of human exploration beyond low Earth orbit. Demonstrated reliable systems are required for human space flight and due to their successful present day widespread use and inherent high reliability, SEP systems have progressively become a viable entrant into these future human exploration architectures. NASA studies have identified a 30 kW-class SEP capability as the next appropriate evolutionary step, applicable to wide range of both human and robotic missions. This paper describes the planning options, mission applications, and technology investments for representative 30kW-class SEP mission concepts under consideration by NASA

Complementary satellite sound broadcasting systems: A NASA assessment for the Voice of America

NASA Technical Reports Server (NTRS)

Stevens, Grady H.; Spence, Rodney L.

1988-01-01

Satellite concepts are examined which offer potentially significant sound broadcast coverage of audio as a complement to VOA's existing and planned terrestrial sound broadcasting system. HF bands are emphasized but additional discussion is included for systems using higher frequencies. Low altitude satellites, shuttle altitude (275 km) and sun synchronous (about 1600 to 1800 km), would not be practical for international broadcasting since many satellites would be required for reliable and widespread coverage. Two concepts are discussed which would offer significant and practical broadcast coverage at HF. One, an 8-hr posigrade equatorial orbit, would offer about 1 hr of widespread, twice daily, coverage to three areas of the globe. The time of coverage is even greater when confined to densely populated areas only (2 to 3 hrs). Another orbit, the Apogee at Constant Time/Equatorial (ACE), provides the same coverage, but only once daily to each area. The latter orbit is highly elliptical, allowing insertion of a greater payload (more broadcast channels) with the existing launch capability. The ACE and 8-hr orbit concepts led to systems of about equal costs, with the ACE being slightly better.

Low energy stage study. Volume 1: Executive summary. [propulsion system configurations for orbital launching of space shuttle payloads

NASA Technical Reports Server (NTRS)

1978-01-01

Cost effective approaches for placing automated payloads into circular and elliptical orbits using energy requirements significantly lower than that provided by the smallest, currently planned shuttle upper stage, SSUS-D, were investigated. Launch costs were derived using both NASA existing/planned launch approaches as well as new propulsion concepts meeting low-energy regime requirements. Candidate new propulsion approaches considered were solid (tandem, cluster, and controlled), solid/liquid combinations and all-liquid stages. Results show that the most economical way to deliver the 129 low energy payloads is basically with a new modular, short liquid bipropellant stage system for the large majority of the payloads. For the remainder of the payloads, use the shuttle with integral OMS and the Scout form for a few specialized payloads until the Shuttle becomes operational.

Coupling of the Magnetosphere-Ionosphere/Thermosphere and Oxygen Outflow-- MIT Mission

NASA Astrophysics Data System (ADS)

Fu, S.

2017-12-01

The goal of the MIT mission is to understand the coupling of the magnetosphere and ionosphere from the prospective of particles. It will focus on the outflow of the ionosphere particles (mainly oxygen ions) from the Earth, including the acceleration mechanisms of oxygen ions and their relative importance in different regions, the importance of these ions while transferred into the magnetosphere and the roles they played in magnetosphere activities. A constellation of four satellites orbiting at three elliptical orbits will provide the unique opportunities to observed there ions at three different altitude with temporal changes of the flux of these particles and the magnetic field environments. The conceptual design of the spacecraft and a summary of the payload will be presented. The MIT mission was selected as one of the five candidates for the upcoming mission plan in China.

The revised solar array synthesis computer program

NASA Technical Reports Server (NTRS)

1970-01-01

The Revised Solar Array Synthesis Computer Program is described. It is a general-purpose program which computes solar array output characteristics while accounting for the effects of temperature, incidence angle, charged-particle irradiation, and other degradation effects on various solar array configurations in either circular or elliptical orbits. Array configurations may consist of up to 75 solar cell panels arranged in any series-parallel combination not exceeding three series-connected panels in a parallel string and no more than 25 parallel strings in an array. Up to 100 separate solar array current-voltage characteristics, corresponding to 100 equal-time increments during the sunlight illuminated portion of an orbit or any 100 user-specified combinations of incidence angle and temperature, can be computed and printed out during one complete computer execution. Individual panel incidence angles may be computed and printed out at the user's option.

On the possibility to use semiconductive hybrid pixel detectors for study of radiation belt of the Earth.

NASA Astrophysics Data System (ADS)

Guskov, A.; Shelkov, G.; Smolyanskiy, P.; Zhemchugov, A.

2016-02-01

The scientific apparatus GAMMA-400 designed for study of electromagnetic and hadron components of cosmic rays will be launched to an elliptic orbit with the apogee of about 300 000 km and the perigee of about 500 km. Such a configuration of the orbit allows it to cross periodically the radiation belt and the outer part of magnetosphere. We discuss the possibility to use hybrid pixel detecters based on the Timepix chip and semiconductive sensors on board the GAMMA-400 apparatus. Due to high granularity of the sensor (pixel size is 55 mum) and possibility to measure independently an energy deposition in each pixel, such compact and lightweight detector could be a unique instrument for study of spatial, energy and time structure of electron and proton components of the radiation belt.

Galactic Evolution

NASA Astrophysics Data System (ADS)

Brekke, Stewart

2013-04-01

All galaxies began as spiral galaxies. The early universe began with sets of two or more pre-galactic arms orbiting each other. As gravitational attraction between the arms took effect, the fore-sections of the arms tangentially collided forming spiral galaxies when they attached with the orbital motion of the arms being converted to the rotational motion of the newly formed spiral galaxies or (Iφ)arm1+ (Iφ)arm2+ ...+ (Iφ)armn= (Iφ)galaxy. If the centripetal force on the arms is more than the gravitational force on the arms, the spiral galaxy remains a spiral galaxy i.e. mv^2/r>=Gmarmmgalaxy/r^2. If the galaxy is slowly rotating, the spiral arms collapse into the body of the galaxy because the gravitational force is greater than the centripetal force on the arms and an elliptical galaxy is formed i.e. mv^2/r < Gmarmsmgalaxy/r^2.

Feasibility study on the ultra-small launch vehicle

NASA Astrophysics Data System (ADS)

Hayashi, T.; Matsuo, H.; Yamamoto, H.; Orii, T.; Kimura, A.

1986-10-01

An idea for a very small satellite launcher and a very small satellite is presented. The launcher is a three staged solid rocket based on a Japanese single stage sounding rocket S-520. Its payload capability is estimated to be 17 kg into 200 x 1000 km elliptical orbit. The spin-stabilized satellite with sun-pointing capability, though small, has almost all functions necessary for usual satellites. In its design, universality is stressed to meet various kinds of mission interface requirements; it can afford 5 kg to mission instruments.

Spectrum orbit utilization program technical manual SOUP5 Version 3.8

NASA Technical Reports Server (NTRS)

Davidson, J.; Ottey, H. R.; Sawitz, P.; Zusman, F. S.

1984-01-01

The underlying engineering and mathematical models as well as the computational methods used by the SOUP5 analysis programs, which are part of the R2BCSAT-83 Broadcast Satellite Computational System, are described. Included are the algorithms used to calculate the technical parameters and references to the relevant technical literature. The system provides the following capabilities: requirements file maintenance, data base maintenance, elliptical satellite beam fitting to service areas, plan synthesis from specified requirements, plan analysis, and report generation/query. Each of these functions are briefly described.

Four Years of Venus Express Magnetic Field Observations: Variable Bow Shock Location and Other Features

NASA Astrophysics Data System (ADS)

Zhang, Tielong; Baumjohann, Wolfgang; Russell, C. T.

Since the Venus Express insertion into a highly elliptical polar orbit with a period of 24 h around the planet Venus, the magnetometer has operated continuously for about 4 years and obtained a wealth of data in the solar minimum at rather low altitude, which was not reached by earlier missions. In this paper, we review the magnetic field observations by Venus Express emphasizing on the variable bow shock location and other space environment features such as the magnetic barrier and the magnetotail.

Planetary sample rapid recovery and handling

NASA Technical Reports Server (NTRS)

1985-01-01

Methods for recovering and cost effectively handling planetary samples following return to the vicinity of Earth were designed for planetary mission planners. Three topics are addressed: (1) a rough cost estimate was produced for each of a series of options for the handling of planetary samples following their return to the vicinity of Earth; (2) the difficulty of quickly retrieving planetary samples from low circular and high elliptical Earth orbit is assessed; and (3) a conceptual design for a biological isolation and thermal control system for the returned sample and spacecraft is developed.

A Doppler-Cancellation Technique for Determining the Altitude Dependence of Gravitational Red Shift in an Earth Satellite

NASA Technical Reports Server (NTRS)

Badessa, R. S.; Kent, R. L.; Nowell, J. C.; Searle, C. L.

1960-01-01

A cancellation technique permits measurement of the frequency of a source moving relative to an observer without the obscuring effect of first-order Doppler shifts. The application of this method to a gravitational red shift experiment involving the use of an earth satellite containing a highly stable oscillator is described. The rapidity with which a measurement can be made permits the taking of data at various altitudes in a given elliptical orbit. Tropospheric and ionospheric effects upon the accuracy of results are estimated.

Arnold diffusion in the planar elliptic restricted three-body problem: mechanism and numerical verification

NASA Astrophysics Data System (ADS)

Capiński, Maciej J.; Gidea, Marian; de la Llave, Rafael

2017-01-01

We present a diffusion mechanism for time-dependent perturbations of autonomous Hamiltonian systems introduced in Gidea (2014 arXiv:1405.0866). This mechanism is based on shadowing of pseudo-orbits generated by two dynamics: an ‘outer dynamics’, given by homoclinic trajectories to a normally hyperbolic invariant manifold, and an ‘inner dynamics’, given by the restriction to that manifold. On the inner dynamics the only assumption is that it preserves area. Unlike other approaches, Gidea (2014 arXiv:1405.0866) does not rely on the KAM theory and/or Aubry-Mather theory to establish the existence of diffusion. Moreover, it does not require to check twist conditions or non-degeneracy conditions near resonances. The conditions are explicit and can be checked by finite precision calculations in concrete systems (roughly, they amount to checking that Melnikov-type integrals do not vanish and that some manifolds are transversal). As an application, we study the planar elliptic restricted three-body problem. We present a rigorous theorem that shows that if some concrete calculations yield a non zero value, then for any sufficiently small, positive value of the eccentricity of the orbits of the main bodies, there are orbits of the infinitesimal body that exhibit a change of energy that is bigger than some fixed number, which is independent of the eccentricity. We verify numerically these calculations for values of the masses close to that of the Jupiter/Sun system. The numerical calculations are not completely rigorous, because we ignore issues of round-off error and do not estimate the truncations, but they are not delicate at all by the standard of numerical analysis. (Standard tests indicate that we get 7 or 8 figures of accuracy where 1 would be enough.) The code of these verifications is available. We hope that some full computer assisted proofs will be obtained in the near future since there are packages (CAPD) designed for problems of this type.

High-beta analytic equilibria in circular, elliptical, and D-shaped large aspect ratio axisymmetric configurations with poloidal and toroidal flows

NASA Astrophysics Data System (ADS)

López, O. E.; Guazzotto, L.

2017-03-01

The Grad-Shafranov-Bernoulli system of equations is a single fluid magnetohydrodynamical description of axisymmetric equilibria with mass flows. Using a variational perturbative approach [E. Hameiri, Phys. Plasmas 20, 024504 (2013)], analytic approximations for high-beta equilibria in circular, elliptical, and D-shaped cross sections in the high aspect ratio approximation are found, which include finite toroidal and poloidal flows. Assuming a polynomial dependence of the free functions on the poloidal flux, the equilibrium problem is reduced to an inhomogeneous Helmholtz partial differential equation (PDE) subject to homogeneous Dirichlet conditions. An application of the Green's function method leads to a closed form for the circular solution and to a series solution in terms of Mathieu functions for the elliptical case, which is valid for arbitrary elongations. To extend the elliptical solution to a D-shaped domain, a boundary perturbation in terms of the triangularity is used. A comparison with the code FLOW [L. Guazzotto et al., Phys. Plasmas 11(2), 604-614 (2004)] is presented for relevant scenarios.

Elliptically framed tip-tilt mirror optimized for stellar tracking

NASA Astrophysics Data System (ADS)

Clark, James H.; Penado, F. E.; Petak, Jeremy

2015-09-01

We compare a design innovation of an elliptically framed tip-tilt optical tracker with an existing circularly framed tracker for the Navy Precision Optical Interferometer. The tracker stabilizes a 12.5 cm stellar beam on a target hundreds of meters away and requires an increase in operational frequency. We reduced mass and size by integrating an elliptical mirror as one of the rotating components, which eliminated a rotating frame. We used the same materials as the existing tracker; however, light-weighted both the aluminum frame and Zerodur® mirror. We generated a computer-aided design model, converted it into a finite element model and performed modal analysis on two load cases. In load case 1, we tied down three points on the bottom surface of the tracker corresponding to the tie-down points of the comparison tracker. This reveals a first mode (lowest) frequency of 140 Hz, a factor of two over the baseline tracker's first mode frequency of 67 Hz. In load case 2, we constrained four additional points inboard of the corners of the tracker base, for a total of seven tie-downs, simulating a firmly bolted and secured mount. The first mode of vibration for this case is 211 Hz, an increase over load case 1 by a factor of 1.5 and more than three times the fundamental frequency of the existing tracker. We conclude that these geometrical changes with the additional tie-down bolts are a viable solution path forward to improve steering speed and recommend a continuation with this effort.

Infrared emission and mass loss from evolved stars in elliptical galaxies

NASA Technical Reports Server (NTRS)

Knapp, G. R.; Gunn, J. E.; Wynn-Williams, C. G.

1992-01-01

Small aperture 10.2-micron measurements of normal elliptical galaxies show that for almost all of these galaxies the 12-micron emission seen by IRAS is extended on the scale of the galaxy. NGC 1052 and NGC 3998 are exceptions to this; much of their 10-12-micron emission comes from the inner regions of the galaxies and may be associated with their active nuclei, as is the case for many radio galaxies. The distribution of the IR light and the IR colors of elliptical galaxies suggest that the most plausible source of the 12-micron emission is photospheric and circumstellear emission from cool evolved red giant stars. The 12-micron emission is well in excess of that expected from photospheric emission alone; about 40 percent of it probably comes from circumstellar dust.

A graphical approach to electric sail mission design with radial thrust

NASA Astrophysics Data System (ADS)

Mengali, Giovanni; Quarta, Alessandro A.; Aliasi, Generoso

2013-02-01

This paper describes a semi-analytical approach to electric sail mission analysis under the assumption that the spacecraft experiences a purely radial, outward, propulsive acceleration. The problem is tackled by means of the potential well concept, a very effective idea that was originally introduced by Prussing and Coverstone in 1998. Unlike a classical procedure that requires the numerical integration of the equations of motion, the proposed method provides an estimate of the main spacecraft trajectory parameters, as its maximum and minimum attainable distance from the Sun, with the simple use of analytical relationships and elementary graphs. A number of mission scenarios clearly show the effectiveness of the proposed approach. In particular, when the spacecraft parking orbit is either circular or elliptic it is possible to find the optimal performances required to reach an escape condition or a given distance from the Sun. Another example is given by the optimal strategy required to reach a heliocentric Keplerian orbit of prescribed orbital period. Finally the graphical approach is applied to the preliminary design of a nodal mission towards a Near Earth Asteroid.

GPS Navigation Above 76,000 km for the MMS Mission

NASA Technical Reports Server (NTRS)

Winternitz, Luke; Bamford, Bill; Price, Samuel; Long, Anne; Farahmand, Mitra; Carpenter, Russell

2016-01-01

NASA's MMS mission, launched in March of 2015,consists of a controlled formation of four spin-stabilized spacecraft in similar highly elliptic orbits reaching apogee at radial distances of 12and 25 Earth radii in the first and second phases of the mission. Navigation for MMS is achieved independently onboard each spacecraft by processing GPS observables using NASA GSFC's Navigator GPS receiver and the Goddard Enhanced Onboard Navigation System (GEONS) extended Kalman filter software. To our knowledge, MMS constitutes, by far, the highest-altitude operational use of GPS to date and represents the culmination of over a decade of high-altitude GPS navigation research and development at NASA GSFC. In this paper we will briefly describe past and ongoing high-altitude GPS research efforts at NASA GSFC and elsewhere, provide details on the design of the MMS GPS navigation system, and present on-orbit performance data. We extrapolate these results to predict performance in the Phase 2b mission orbit, and conclude with a discussion of the implications of the MMS results for future high-altitude GPS navigation, which we believe to be broad and far-reaching.

The Fate of Gas-rich Satellites in Clusters

NASA Astrophysics Data System (ADS)

Safarzadeh, Mohammadtaher; Scannapieco, Evan

2017-11-01

We investigate the stellar mass-loss of gas-rich galaxies falling into clusters due to the change in the gravitational potential caused by the ram-pressure-stripping of their gas. We model the satellites with exponential stellar and gas disk profiles, assume rapid ram-pressure-stripping, and follow the stellar orbits in the shocked potential. Due to the change of the potential, the stars move from circular orbits to elliptical orbits with apocenters that are often outside the tidal radius, causing those stars to be stripped. We explore the impact of the redshift of infall, gas fraction, satellite halo mass, and cluster mass on this process. The puffing of the satellites makes them appear as ultra-diffuse galaxies, and the stripped stars contribute to the intracluster light. Our results show that these effects are most significant for less massive satellites, which have larger gas fractions when they are accreted into clusters. The preferential destruction of low-mass systems causes the red fraction of cluster galaxies to be smaller at lower masses, an observation that is otherwise difficult to explain.

Targetting and guidance program documentation. [a user's manual

NASA Technical Reports Server (NTRS)

Harrold, E. F.; Neyhard, J. F.

1974-01-01

A FORTRAN computer program was developed which automatically targets two and three burn rendezvous missions and performs feedback guidance using the GUIDE algorithm. The program was designed to accept a large class of orbit specifications and to automatically choose a two or three burn mission depending upon the time alignment of the vehicle and target. The orbits may be specified as any combination of circular and elliptical orbits and may be coplanar or inclined, but must be aligned coaxially with their perigees in the same direction. The program accomplishes the required targeting by repeatedly converging successively more complex missions. It solves the coplanar impulsive version of the mission, then the finite burn coplanar mission, and finally, the full plane change mission. The GUIDE algorithm is exercised in a feedback guidance mode by taking the targeted solution and moving the vehicle state step by step ahead in time, adding acceleration and navigational errors, and reconverging from the perturbed states at fixed guidance update intervals. A program overview is presented, along with a user's guide which details input, output, and the various subroutines.

Elliptic Relaxation of a Tensor Representation for the Redistribution Terms in a Reynolds Stress Turbulence Model

NASA Technical Reports Server (NTRS)

Carlson, J. R.; Gatski, T. B.

2002-01-01

A formulation to include the effects of wall proximity in a second-moment closure model that utilizes a tensor representation for the redistribution terms in the Reynolds stress equations is presented. The wall-proximity effects are modeled through an elliptic relaxation process of the tensor expansion coefficients that properly accounts for both correlation length and time scales as the wall is approached. Direct numerical simulation data and Reynolds stress solutions using a full differential approach are compared for the case of fully developed channel flow.

Near Earth Network (NEN) CubeSat Communications

NASA Technical Reports Server (NTRS)

Schaire, Scott

2017-01-01

The NASA Near Earth Network (NEN) consists of globally distributed tracking stations, including NASA, commercial, and partner ground stations, that are strategically located to maximize the coverage provided to a variety of orbital and suborbital missions, including those in LEO (Low Earth Orbit), GEO (Geosynchronous Earth Orbit), HEO (Highly Elliptical Orbit), lunar and L1-L2 orbits. The NEN's future mission set includes and will continue to include CubeSat missions. The first NEN-supported CubeSat mission will be the Cubesat Proximity Operations Demonstration (CPOD) launching into LEO in 2017. The majority of the CubeSat missions destined to fly on EM-1, launching in late 2018, many in a lunar orbit, will communicate with ground-based stations via X-band and will utilize the NASA Jet Propulsion Laboratory (JPL)-developed IRIS (Satellite Communication for Air Traffic Management) radio. The NEN recognizes the important role CubeSats are beginning to play in carrying out NASAs mission and is therefore investigating the modifications needed to provide IRIS radio compatibility. With modification, the NEN could potentially expand support to the EM-1 (Exploration Mission-1) lunar CubeSats. The NEN could begin providing significant coverage to lunar CubeSat missions utilizing three to four of the NEN's mid-latitude sites. This coverage would supplement coverage provided by the JPL Deep Space Network (DSN). The NEN, with smaller apertures than DSN, provides the benefit of a larger beamwidth that could be beneficial in the event of uncertain ephemeris data. In order to realize these benefits the NEN would need to upgrade stations targeted based on coverage ability and current configuration ease of upgrade, to ensure compatibility with the IRIS radio. In addition, the NEN is working with CubeSat radio developers to ensure NEN compatibility with alternative CubeSat radios for Lunar and L1-L2 CubeSats. The NEN has provided NEN compatibility requirements to several radio developers who are developing radios that offer lower cost and, in some cases, more capabilities with fewer constraints. The NEN is ready to begin supporting CubeSat missions. The NEN is considering network upgrades to broaden the types of CubeSat missions that can be supported and is supporting both the CubeSat community and radio developers to ensure future CubeSat missions have multiple options when choosing a network for their communications support.

Efficient Development of High Fidelity Structured Volume Grids for Hypersonic Flow Simulations

NASA Technical Reports Server (NTRS)

Alter, Stephen J.

2003-01-01

A new technique for the control of grid line spacing and intersection angles of a structured volume grid, using elliptic partial differential equations (PDEs) is presented. Existing structured grid generation algorithms make use of source term hybridization to provide control of grid lines, imposing orthogonality implicitly at the boundary and explicitly on the interior of the domain. A bridging function between the two types of grid line control is typically used to blend the different orthogonality formulations. It is shown that utilizing such a bridging function with source term hybridization can result in the excessive use of computational resources and diminishes robustness. A new approach, Anisotropic Lagrange Based Trans-Finite Interpolation (ALBTFI), is offered as a replacement to source term hybridization. The ALBTFI technique captures the essence of the desired grid controls while improving the convergence rate of the elliptic PDEs when compared with source term hybridization. Grid generation on a blunt cone and a Shuttle Orbiter is used to demonstrate and assess the ALBTFI technique, which is shown to be as much as 50% faster, more robust, and produces higher quality grids than source term hybridization.

A Study into the Method of Precise Orbit Determination of a HEO Orbiter by GPS and Accelerometer

NASA Technical Reports Server (NTRS)

Ikenaga, Toshinori; Hashida, Yoshi; Unwin, Martin

2007-01-01

In the present day, orbit determination by Global Positioning System (GPS) is not unusual. Especially for low-cost small satellites, position determination by an on-board GPS receiver provides a cheap, reliable and precise method. However, the original purpose of GPS is for ground users, so the transmissions from all of the GPS satellites are directed toward the Earth s surface. Hence there are some restrictions for users above the GPS constellation to detect those signals. On the other hand, a desire for precise orbit determination for users in orbits higher than GPS constellation exists. For example, the next Japanese Very Long Baseline Interferometry (VLBI) mission "ASTRO-G" is trying to determine its orbit in an accuracy of a few centimeters at apogee. The use of GPS is essential for such ultra accurate orbit determination. This study aims to construct a method for precise orbit determination for such high orbit users, especially in High Elliptical Orbits (HEOs). There are several approaches for this objective. In this study, a hybrid method with GPS and an accelerometer is chosen. Basically, while the position cannot be determined by an on-board GPS receiver or other Range and Range Rate (RARR) method, all we can do to estimate the user satellite s position is to propagate the orbit along with the force model, which is not perfectly correct. However if it has an accelerometer (ACC), the coefficients of the air drag and the solar radiation pressure applied to the user satellite can be updated and then the propagation along with the "updated" force model can improve the fitting accuracy of the user satellite s orbit. In this study, it is assumed to use an accelerometer available in the present market. The effects by a bias error of an accelerometer will also be discussed in this paper.

Testing the uniqueness of mass models using gravitational lensing

NASA Astrophysics Data System (ADS)

Walls, Levi; Williams, Liliya L. R.

2018-06-01

The positions of images produced by the gravitational lensing of background-sources provide insight to lens-galaxy mass distributions. Simple elliptical mass density profiles do not agree well with observations of the population of known quads. It has been shown that the most promising way to reconcile this discrepancy is via perturbations away from purely elliptical mass profiles by assuming two super-imposed, somewhat misaligned mass distributions: one is dark matter (DM), the other is a stellar distribution. In this work, we investigate if mass modelling of individual lenses can reveal if the lenses have this type of complex structure, or simpler elliptical structure. In other words, we test mass model uniqueness, or how well an extended source lensed by a non-trivial mass distribution can be modeled by a simple elliptical mass profile. We used the publicly-available lensing software, Lensmodel, to generate and numerically model gravitational lenses and “observed” image positions. We then compared “observed” and modeled image positions via root mean square (RMS) of their difference. We report that, in most cases, the RMS is ≤0.05‧‧ when averaged over an extended source. Thus, we show it is possible to fit a smooth mass model to a system that contains a stellar-component with varying levels of misalignment with a DM-component, and hence mass modelling cannot differentiate between simple elliptical versus more complex lenses.

Equilibrium figures inside the dark-matter ring and the shapes of elliptical galaxies

NASA Astrophysics Data System (ADS)

Kondratyev, B. P.; Trubitsyna, N. G.; Kireeva, E. N.

We solve the general problem of the theory of equilibrium figures and analyze two classes of liquid rotating gravitating figures residing inside a gravitating ring or torus. These figures form families of sequences of generalized oblate spheroids and triaxial ellipsoids, which at the lower limit of the tidal parameter α = 0 have the form of the Maclaurin spheroids and the Jacobi ellipsoids. In intermediate cases 0 < α ≤ αmax each new sequence of axisymmetric equilibrium figures has two non-rotating boundary spheroids. At the upper limit αmax/(π Gρ ) = 0.1867 the sequence degenerates into a single non-rotating spheroid with the eccentricity {e cr} ≈ 0.96 corresponding to the flattening limit of elliptical galaxies (E7). We also perform a detailed study of the sequences of generalized triaxial ellipsoids and find bifurcation points of triaxial ellipsoids in the sequences of generalized spheroids. We use this method to explain the shapes of E-galaxies. According to observations, very slowly rotating oblate E-type galaxies are known that have the shapes, which, because of instability, cannot be supported by velocity dispersion anisotropy exclusively. The hypothesis of a massive dark-matter outer ring requires no extreme anisotropy of pressure; it not only explains the shape of these elliptical galaxies, but also sheds new light on the riddle of the ellipticity limit (E7) of elliptical galaxies.

Spectral asymptotics of Euclidean quantum gravity with diff-invariant boundary conditions

NASA Astrophysics Data System (ADS)

Esposito, Giampiero; Fucci, Guglielmo; Kamenshchik, Alexander Yu; Kirsten, Klaus

2005-03-01

A general method is known to exist for studying Abelian and non-Abelian gauge theories, as well as Euclidean quantum gravity, at 1-loop level on manifolds with boundary. In the latter case, boundary conditions on metric perturbations h can be chosen to be completely invariant under infinitesimal diffeomorphisms, to preserve the invariance group of the theory and BRST symmetry. In the de Donder gauge, however, the resulting boundary-value problem for the Laplace-type operator acting on h is known to be self-adjoint but not strongly elliptic. The latter is a technical condition ensuring that a unique smooth solution of the boundary-value problem exists, which implies, in turn, that the global heat-kernel asymptotics yielding 1-loop divergences and 1-loop effective action actually exists. The present paper shows that, on the Euclidean 4-ball, only the scalar part of perturbative modes for quantum gravity is affected by the lack of strong ellipticity. Further evidence for lack of strong ellipticity, from an analytic point of view, is therefore obtained. Interestingly, three sectors of the scalar-perturbation problem remain elliptic, while lack of strong ellipticity is 'confined' to the remaining fourth sector. The integral representation of the resulting ζ-function asymptotics on the Euclidean 4-ball is also obtained; this remains regular at the origin by virtue of a spectral identity here obtained for the first time.

Elliptical instability in stably stratified fluid interiors

NASA Astrophysics Data System (ADS)

Vidal, J.; Hollerbach, R.; Schaeffer, N.; Cebron, D.

2016-12-01

Self-sustained magnetic fields in celestial bodies (planets, moons, stars) are due to flows in internal electrically conducting fluids. These fluid motions are often attributed to convection, as it is the case for the Earth's liquid core and the Sun. However some past or present liquid cores may be stably stratified. Alternative mechanisms may thus be needed to understand the dynamo process in these celestial objects. Turbulent flows driven by mechanical forcings, such as tides or precession, seem very promising since they are dynamo capable. However the effect of density stratification is not clear, because it can stabilize or destabilize mechanically-driven flows.To mimic an elliptical distortion due to tidal forcing in spherical geometry (full sphere and shell), we consider a theoretical base flow with elliptical streamlines and an associated density profile. It allows to keep the numerical efficiency of spectral methods in this geometry. The flow satisfies the stress-free boundary condition. We perform the stability analysis of the base state using three-dimensional simulations to study both the linear and nonlinear regimes. Stable and unstable density profiles are considered. A complementary local stability analysis (WKB) is also performed. We show that elliptical instability can still grow upon a stable stratification. We also study the mixing of the stratification by the elliptical instability. Finally we look at the dynamo capability of these flows.

On the Post-Keplerian Corrections to the Orbital Periods of a Two-body System and Their Application to the Galactic Center

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

Iorio, Lorenzo; Zhang, Fupeng, E-mail: lorenzo.iorio@libero.it, E-mail: zhangfp7@mail.sysu.edu.cn

We perform detailed numerical analyses of the orbital motion of a test particle around a spinning primary, with the aim of investigating the possibility of using the post-Keplerian (pK) corrections to the orbiter’s periods (draconitic, anomalistic, and sidereal) as a further opportunity to perform new tests of post-Newtonian gravity. As a specific scenario, the S-stars orbiting the massive black hole (MBH) supposedly lurking in Sgr A* at the center of the Galaxy are adopted. We first study the effects of the pK Schwarzchild, Lense–Thirring, and quadrupole moment accelerations experienced by a target star for various possible initial orbital configurations. Itmore » turns out that the results of the numerical simulations are consistent with the analytical ones in the small eccentricity approximation for which almost all the latter ones were derived. For highly elliptical orbits, the sizes of the three pK corrections considered turn out to increase remarkably. The periods of the observed S2 and S0-102 stars as functions of the MBH’s spin axis orientation are considered as well. The pK accelerations lead to corrections of the orbital periods of the order of 1–100 days (Schwarzschild), 0.1–10 hr (Lense–Thirring), and 1–10{sup 3} s (quadrupole) for a target star with a = 300–800 au and e ≈ 0.8, which could be measurable with future facilities.« less

How well can charge transfer inefficiency be corrected? A parameter sensitivity study for iterative correction

NASA Astrophysics Data System (ADS)

Israel, Holger; Massey, Richard; Prod'homme, Thibaut; Cropper, Mark; Cordes, Oliver; Gow, Jason; Kohley, Ralf; Marggraf, Ole; Niemi, Sami; Rhodes, Jason; Short, Alex; Verhoeve, Peter

2015-10-01

Radiation damage to space-based charge-coupled device detectors creates defects which result in an increasing charge transfer inefficiency (CTI) that causes spurious image trailing. Most of the trailing can be corrected during post-processing, by modelling the charge trapping and moving electrons back to where they belong. However, such correction is not perfect - and damage is continuing to accumulate in orbit. To aid future development, we quantify the limitations of current approaches, and determine where imperfect knowledge of model parameters most degrades measurements of photometry and morphology. As a concrete application, we simulate 1.5 × 109 `worst-case' galaxy and 1.5 × 108 star images to test the performance of the Euclid visual instrument detectors. There are two separable challenges. If the model used to correct CTI is perfectly the same as that used to add CTI, 99.68 per cent of spurious ellipticity is corrected in our setup. This is because readout noise is not subject to CTI, but gets overcorrected during correction. Secondly, if we assume the first issue to be solved, knowledge of the charge trap density within Δρ/ρ = (0.0272 ± 0.0005) per cent and the characteristic release time of the dominant species to be known within Δτ/τ = (0.0400 ± 0.0004) per cent will be required. This work presents the next level of definition of in-orbit CTI calibration procedures for Euclid.

Two-component Jaffe models with a central black hole - I. The spherical case

NASA Astrophysics Data System (ADS)

Ciotti, Luca; Ziaee Lorzad, Azadeh

2018-02-01

Dynamical properties of spherically symmetric galaxy models where both the stellar and total mass density distributions are described by the Jaffe (1983) profile (with different scalelengths and masses) are presented. The orbital structure of the stellar component is described by Osipkov-Merritt anisotropy, and a black hole (BH) is added at the centre of the galaxy; the dark matter halo is isotropic. First, the conditions required to have a nowhere negative and monotonically decreasing dark matter halo density profile are derived. We then show that the phase-space distribution function can be recovered by using the Lambert-Euler W function, while in absence of the central BH only elementary functions appears in the integrand of the inversion formula. The minimum value of the anisotropy radius for consistency is derived in terms of the galaxy parameters. The Jeans equations for the stellar component are solved analytically, and the projected velocity dispersion at the centre and at large radii are also obtained analytically for generic values of the anisotropy radius. Finally, the relevant global quantities entering the Virial Theorem are computed analytically, and the fiducial anisotropy limit required to prevent the onset of Radial Orbit Instability is determined as a function of the galaxy parameters. The presented models, even though highly idealized, represent a substantial generalization of the models presented in Ciotti, and can be useful as starting point for more advanced modelling, the dynamics and the mass distribution of elliptical galaxies.

Heat transfer enhancement of PCM melting in 2D horizontal elliptical tube using metallic porous matrix

NASA Astrophysics Data System (ADS)

Jourabian, Mahmoud; Farhadi, Mousa; Rabienataj Darzi, Ahmad Ali

2016-12-01

In this study, the melting process of ice as a phase-change material (PCM) saturated with a nickel-steel porous matrix inside a horizontal elliptical tube is investigated. Due to the low thermal conductivity of the PCM, it is motivated to augment the heat transfer performance of the system simultaneously by finding an optimum value of the aspect ratio and impregnating a metallic porous matrix into the base PCM. The lattice Boltzmann method with a double distribution function formulated based on the enthalpy method, is applied at the representative elementary volume scale under the local thermal equilibrium assumption between the PCM and porous matrix in the composite. While reducing or increasing the aspect ratio of the circular tubes leads to the expedited melting, the 90° inclination of each elliptical tube in the case of the pure PCM melting does not affect the melting rate. With the reduction in the porosity, the effective thermal conductivity and melting rate in all tubes promoted. Although the natural convection is fully suppressed due to the significant flow blockage in the porous structure, the melting rates are generally increased in all cases.

Formation of most of our coal brought Earth close to global glaciation

PubMed Central

2017-01-01

The bulk of Earth’s coal deposits used as fossil fuel today was formed from plant debris during the late Carboniferous and early Permian periods. The high burial rate of organic carbon correlates with a significant drawdown of atmospheric carbon dioxide (CO2) at that time. A recent analysis of a high-resolution record reveals large orbitally driven variations in atmospheric CO2 concentration between ∼150 and 700 ppm for the latest Carboniferous and very low values of 100 ± 80 ppm for the earliest Permian. Here, I explore the sensitivity of the climate around the Carboniferous/Permian boundary to changes in Earth’s orbital parameters and in atmospheric CO2 using a coupled climate model. The coldest orbital configurations are characterized by large axial tilt and small eccentricities of Earth’s elliptical orbit, whereas the warmest configuration occurs at minimum tilt, maximum eccentricity, and a perihelion passage during Northern hemisphere spring. Global glaciation occurs at CO2 concentrations <40 ppm, suggesting a rather narrow escape from a fully glaciated Snowball Earth state given the low levels and large fluctuations of atmospheric CO2. These findings highlight the importance of orbital cycles for the climate and carbon cycle during the late Paleozoic ice age and the climatic significance of the fossil carbon stored in Earth’s coal deposits. PMID:29073052

Anisotropic particle in viscous shear flow: Navier slip, reciprocal symmetry, and Jeffery orbit.

PubMed

Zhang, Jiaolong; Xu, Xinpeng; Qian, Tiezheng

2015-03-01

The hydrodynamic reciprocal theorem for Stokes flows is generalized to incorporate the Navier slip boundary condition, which can be derived from Onsager's variational principle of least energy dissipation. The hydrodynamic reciprocal relations and the Jeffery orbit, both of which arise from the motion of a slippery anisotropic particle in a simple viscous shear flow, are investigated theoretically and numerically using the fluid particle dynamics method [Phys. Rev. Lett. 85, 1338 (2000)]. For a slippery elliptical particle in a linear shear flow, the hydrodynamic reciprocal relations between the rotational torque and the shear stress are studied and related to the Jeffery orbit, showing that the boundary slip can effectively enhance the anisotropy of the particle. Physically, by replacing the no-slip boundary condition with the Navier slip condition at the particle surface, the cross coupling between the rotational torque and the shear stress is enhanced, as manifested through a dimensionless parameter in both of the hydrodynamic reciprocal relations and the Jeffery orbit. In addition, simulations for a circular particle patterned with portions of no-slip and Navier slip are carried out, showing that the particle possesses an effective anisotropy and follows the Jeffery orbit as well. This effective anisotropy can be tuned by changing the ratio of no-slip portion to slip potion. The connection of the present work to nematic liquid crystals' constitutive relations is discussed.

Shuttle and Transfer Orbit Thermal Analysis and Testing of the Chandra X-Ray Observatory Charge-Couple Device Imaging Spectrometer Radiator Shades

NASA Technical Reports Server (NTRS)

Sharp, John R.

1999-01-01

Thermal analyses of the Shuttle and Transfer Orbit of the Advanced X-Ray Astrophysics Facility Charge-Coupled Device (CCD) Imaging Spectrometer (ACIS), one of two science instruments on the Chandra X-Ray Observatory, revealed a low-earth orbit (LEO) overheating problem on the goldized Kapton faces of two radiator shades. The shades were coated with the goldized Kapton to provide a low hemispherical emittance to minimize direct and backloaded heating from the sun and the observatory and high specularity to optimize the coupling to space on two passive radiators which cool the focal plane to -120 C +/- 1 C during on-orbit operations. Since the observatory has a highly elliptical final orbit of 10,000 kilometers by 140,000 kilometers and the ACIS radiators and shades are oriented anti-sun, the high solar absorptance to emittance ratio of the goldized Kapton was not an issue. However, during Shuttle bay-to-earth operations, the short duration solar heating occurring near the eclipse entry and exit resulted in shade temperatures in excess of the cure temperature of the adhesive used to bond the goldized Kapton and honeycomb face-sheets. The detailed thermal analysis demonstrating the LEO overheating as well as the redesign options and thermal testing of a redesigned development unit shade are presented.

Imaging interplanetary CMEs at radio frequency from solar polar orbit

NASA Astrophysics Data System (ADS)

Wu, Ji; Sun, Weiying; Zheng, Jianhua; Zhang, Cheng; Liu, Hao; Yan, Jingye; Wang, Chi; Wang, Chuanbing; Wang, Shui

2011-09-01

Coronal mass ejections (CMEs) represent a great concentration of mass and energy input into the lower corona. They have come to be recognized as the major driver of physical conditions change in the Sun-Earth system. Consequently, observations of CMEs are important for understanding and ultimately predicting space weather conditions. This paper discusses a proposed mission, the Solar Polar Orbit Radio Telescope (SPORT) mission, which will observe the propagation of interplanetary CMEs to distances of near 0.35 AU from the Sun. The orbit of SPORT is an elliptical solar polar orbit. The inclination angle between the orbit and ecliptic plane should be about 90°. The main payload on board SPORT will be an imaging radiometer working at the meter wavelength band (radio telescope), which can follow the propagation of interplanetary CMEs. The images that are obtained by the radio telescope embody the brightness temperature of the objectives. Due to the very large size required for the antenna aperture of the radio telescope, we adopt interferometric imaging technology to reduce it. Interferometric imaging technology is based on indirect spatial frequency domain measurements plus Fourier transformation. The SPORT spacecraft will also be equipped with a set of optical and in situ measurement instruments such as a EUV solar telescope, a solar wind ion instrument, an energetic particle detector, a magnetometer, a wave detector and a solar radio burst spectrometer.

About Tidal Evolution of Quasi-Periodic Orbits of Satellites

NASA Astrophysics Data System (ADS)

Ershkov, Sergey V.

2017-06-01

Tidal interactions between Planet and its satellites are known to be the main phenomena, which are determining the orbital evolution of the satellites. The modern ansatz in the theory of tidal dissipation in Saturn was developed previously by the international team of scientists from various countries in the field of celestial mechanics. Our applying to the theory of tidal dissipation concerns the investigating of the system of ODE-equations (ordinary differential equations) that govern the orbital evolution of the satellites; such an extremely non-linear system of 2 ordinary differential equations describes the mutual internal dynamics for the eccentricity of the orbit along with involving the semi-major axis of the proper satellite into such a monstrous equations. In our derivation, we have presented the elegant analytical solutions to the system above; so, the motivation of our ansatz is to transform the previously presented system of equations to the convenient form, in which the minimum of numerical calculations are required to obtain the final solutions. Preferably, it should be the analytical solutions; we have presented the solution as a set of quasi- periodic cycles via re-inversing of the proper ultra- elliptical integral. It means a quasi-periodic character of the evolution of the eccentricity, of the semi-major axis for the satellite orbit as well as of the quasi-periodic character of the tidal dissipation in the Planet.

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

Mitri, F. G., E-mail: F.G.Mitri@ieee.org

This paper presents two key contributions; the first concerns the development of analytical expressions for the axial and transverse acoustic radiation forces exerted on a 2D rigid elliptical cylinder placed in the field of plane progressive, quasi-standing, or standing waves with arbitrary incidence. The second emphasis is on the acoustic radiation torque per length. The rigid elliptical cylinder case is important to be considered as a first-order approximation of the behavior of a cylindrical fluid column trapped in air because of the significant acoustic impedance mismatch at the particle boundary. Based on the rigorous partial-wave series expansion method in cylindricalmore » coordinates, non-dimensional acoustic radiation force and torque functions are derived and defined in terms of the scattering coefficients of the elliptic cylinder. A coupled system of linear equations is obtained after applying the Neumann boundary condition for an immovable surface in a non-viscous fluid and solved numerically by matrix inversion after performing a single numerical integration procedure. Computational results for the non-dimensional force components and torque, showing the transition from the progressive to the (equi-amplitude) standing wave behavior, are performed with particular emphasis on the aspect ratio a/b, where a and b are the semi-axes of the ellipse, the dimensionless size parameter, as well as the angle of incidence ranging from end-on to broadside incidence. The results show that the elliptical geometry has a direct influence on the radiation force and torque, so that the standard theory for circular cylinders (at normal incidence) leads to significant miscalculations when the cylinder cross section becomes non-circular. Moreover, the elliptical cylinder experiences, in addition to the acoustic radiation force, a radiation torque that vanishes for the circular cylinder case. The application of the formalism presented here may be extended to other 2D surfaces of arbitrary shape, such as Chebyshev cylindrical particles with a small deformation, stadiums (with oval shape), or other non-circular geometries.« less

Comets: Very Eccentric Characters

NASA Technical Reports Server (NTRS)

Kwok, Enoch; Fisher, Diane

1999-01-01

Astronomical distances, even within our own solar system, are very difficult for anyone, let alone children, to imagine. In this month's space-program-related activity, students have the opportunity to create a visual and kinesthetic model of the solar system on a scale that may begin to inspire an awed comprehension of how big space is and how small Earth is. In addition, they will learn a little basic geometry in demonstrating for themselves the difference between a circular planetary orbit and an elongated elliptical cometary orbit. As a space exploration first the Jet Propulsion Laboratory (JPL), under contract to the National Aeronautics and Space Administration (NASA), is planning to send a spacecraft to rendezvous with and land on a comet. The Space Technology 4/Champollion mission is part of NASA's New Millennium Program, the primary goal of which is to test new technologies for use in 21st century planetary and earth observing missions.

Delta-90 Interplanetary Monitoring Platform-H (IMP-H) flash flight report

NASA Technical Reports Server (NTRS)

1972-01-01

The Delta-90 launch vehicle and the IMP-H spacecraft were successfully launched from Pad B, Complex 17, Cape Kennedy Air Force Station, Florida, at 2120:00.559 EDT on September 22, 1972. The countdown proceeded smoothly to liftoff with no major difficulties or unscheduled holds. The Delta-90/IMP-H were launched on a pad azimuth of 115 degrees, the vehicle ten rolled to 95 degrees from the north placing the spacecraft in a highly elliptical transfer orbit. Firing the spacecraft kickmotor at 1136 EDT, September 25, 1972, injected the spacecraft into its final desirable near-circular orbit approximately half way between the planet earth and its moon. Vehicle performance of all stages appeared nominal with all sequenced events occurring at the expected times. Data acquisition from all range stations was very good. Damage to the launch pad caused by liftoff was nominal.

A test of the massive binary black hole hypothesis - Arp 102B

NASA Technical Reports Server (NTRS)

Helpern, J. P.; Filippenko, Alexei V.

1988-01-01

The emission-line spectra of several AGN have broad peaks which are significantly displaced in velocity with respect to the host galaxy. An interpretation of this effect in terms of orbital motion of a binary black hole predicts periods of a few centuries. It is pointed out here that recent measurements of the masses and sizes of many low-luminosity AGN imply orbital periods much shorter than this. In particular, it is found that the elliptical galaxy Arp 102B is the most likely candidate for observation of radial velocity variations; its period is expected to be about 3 yr. The H-alpha line profile of Arp 102B has been measured for 5 yr without detecting any change in velocity, and it is thus found that a rather restrictive observational test of the massive binary black hole hypothesis already exists, albeit for this one object.

An Anomalous External Force on the MAP Spacecraft

NASA Technical Reports Server (NTRS)

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

2002-01-01

A common theme in discussions of the Microwave Anisotropy Probe (MAP) is the attainment of mission goals for minimal cost. One area of cost savings was a reduction in the fuel budget required. To reach orbit around the L2 notation point of the Earth-Sun system, the MAP spacecraft was guided very close to the Moon, allowing a gravity-assisted trajectory out to L2. In order to property time the lunar swing-by, MAP followed a trajectory of three-and-a-half highly elliptical phasing loops. At each perigee of this trajectory MAP executed a thruster maneuver to increase orbit velocity; maneuvers were required at one or both clothe first two perigees (called P1 and P2) and at the third and final perigee (P-final). The preference was for successful maneuvers at all three perigees because this scheme provided a small, additional fuel savings.

Inflatable lenses for space photovoltaic concentrator arrays

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

O`Neill, M.J.; Piszczor, M.F.

1997-12-31

For 12 years, ENTECH and NASA Lewis have been developing Fresnel lens concentrator technology for space power applications. ENTECH provided the point-focus mini-dome lenses for the PASP+ array, launched in 1994. These silicone lenses performed well on orbit, with only about 3% optical performance loss after 1 year in elliptical orbit, with high radiation, atomic oxygen, and ultraviolet exposure. The only protection for these silicone lenses was a thin-film coating provided by OCLI. ENTECH also provided the line-focus lenses for the SCARLET 1 and SCARLET 2 arrays in 1995 and 1997, respectively. These lenses are laminated assemblies, with protective ceriamore » glass superstrates over the silicone lens. In March 1997, ENTECH and NASA Lewis began development of inflatable Fresnel lenses, to achieve lower weight, smaller launch volume, reduced cost, less fragility, and other advantages. This paper summarizes the new concentrator approach, including key program results to date.« less

Parametric control of maneuver of a space tether system

NASA Astrophysics Data System (ADS)

Bezglasnyi, S. P.; Piyakina, E. E.

2015-07-01

Planar motion of a space tether system (STS) simulated by a massless rod with two masses fixed on its edges and a third mass moving along the rod is considered. An equation of the pendulum-controlled motion of the system in an elliptical orbit is obtained. Problems of parametric control that takes the STS from one stable radial equilibrium state to another and stabilizes it with respect to planar excitations of two diametrically opposite positions of the relative equilibrium of the STS in a circular orbit are investigated. The control is a continuous law of motion for a moving mass along the tether on the swing principle. The solution is obtained in a closed form based on the second method of the classical stability theory by the construction of the corresponding Lyapunov functions. Asymptotic convergence of solutions is confirmed by the results of numerical modeling of the system motion.

GRAIL TCM-5 Go/No-Go: Developing Lunar Orbit Insertion Criteria

NASA Technical Reports Server (NTRS)

Chung, Min-Kun J.

2013-01-01

The Gravity Recovery and Interior Laboratory (GRAIL) mission successfully completed mapping the Moon's gravity field to an unprecedented level. The mission success was critically dependent on the success of the Lunar Orbit Insertion (LOI). It was somewhat unfamiliar as it involved an elliptical approach from a low-energy trans-lunar cruise trajectory via Sun-Earth three-body region rather than a more conventional hyperbolic approach from a direct Earth-to-Moon transfer. In addition, how its delivery dispersion affected the science formation of the two spacecraft was not well understood. In this paper we establish a set of LOI criteria to meet all the requirements and we use these criteria to establish Go/No-Go boundaries of the last, statistical Trajectory Correction Maneuvers (TCM-5s) for operations. In the end both spacecraft were found to be within the established boundaries and TCM-5s of both spacecraft were cancelled.

KSC-2013-4065

NASA Image and Video Library

2013-11-18

CAPE CANAVERAL, Fla. -- Dr. Jim Green, director of the Planetary Science Division at NASA Headquarters, participates in a post-launch news conference in NASA's Press Site TV auditorium following the successful launch of NASA’s Mars Atmosphere and Volatile EvolutioN, or MAVEN, spacecraft. Launch was on schedule at 1:28 p.m. EST Nov. 18 at the opening of a two-hour launch window. After a 10-month journey to the Red Planet, MAVEN will study its upper atmosphere in unprecedented detail from orbit above the planet. Built by Lockheed Martin in Littleton, Colo., MAVEN will arrive at Mars in September 2014 and will be inserted into an elliptical orbit with a high point of 3,900 miles, swooping down to as close as 93 miles above the planet's surface. For more information, visit: http://www.nasa.gov/mission_pages/maven/main/index.html. Photo credit: NASA/Kim Shiflett

Intertwining solutions for magnetic relativistic Hartree type equations

NASA Astrophysics Data System (ADS)

Cingolani, Silvia; Secchi, Simone

2018-05-01

We consider the magnetic pseudo-relativistic Schrödinger equation where , m  >  0, is an external continuous scalar potential, is a continuous vector potential and is a convolution kernel, is a constant, , . We assume that A and V are symmetric with respect to a closed subgroup G of the group of orthogonal linear transformations of . If for any , the cardinality of the G-orbit of x is infinite, then we prove the existence of infinitely many intertwining solutions assuming that is either linear in x or uniformly bounded. The results are proved by means of a new local realization of the square root of the magnetic laplacian to a local elliptic operator with Neumann boundary condition on a half-space. Moreover we derive an existence result of a ground state intertwining solution for bounded vector potentials, if G admits a finite orbit.

Image Mission Attitude Support Experiences

NASA Technical Reports Server (NTRS)

Ottenstein, N.; Challa, M.; Home, A.; Harman, R.; Burley, R.

2001-01-01

The spin-stabilized Imager for Magnetopause to Aurora Global Exploration (IMAGE) is the National Aeronautics and Space Administration's (NASA's) first Medium-class Explorer Mission (MIDEX). IMAGE was launched into a highly elliptical polar orbit on March 25, 2000 from Vandenberg Air Force Base, California, aboard a Boeing Delta II 7326 launch vehicle. This paper presents some of the observations of the flight dynamics analyses during the launch and in-orbit checkout period through May 18, 2000. Three new algorithms - one algebraic and two differential correction - for computing the parameters of the coning motion of a spacecraft are described and evaluated using in-flight data from the autonomous star tracker (AST) on IMAGE. Other attitude aspects highlighted include support for active damping consequent upon the failure of the passive nutation damper, performance evaluation of the AST, evaluation of the Sun sensor and magnetometer using AST data, and magnetometer calibration.

Arbitrary spin-to-orbital angular momentum conversion of light.

PubMed

Devlin, Robert C; Ambrosio, Antonio; Rubin, Noah A; Mueller, J P Balthasar; Capasso, Federico

2017-11-17

Optical elements that convert the spin angular momentum (SAM) of light into vortex beams have found applications in classical and quantum optics. These elements-SAM-to-orbital angular momentum (OAM) converters-are based on the geometric phase and only permit the conversion of left- and right-circular polarizations (spin states) into states with opposite OAM. We present a method for converting arbitrary SAM states into total angular momentum states characterized by a superposition of independent OAM. We designed a metasurface that converts left- and right-circular polarizations into states with independent values of OAM and designed another device that performs this operation for elliptically polarized states. These results illustrate a general material-mediated connection between SAM and OAM of light and may find applications in producing complex structured light and in optical communication. Copyright © 2017, American Association for the Advancement of Science.

Self-Consistent Chaotic Transport in a High-Dimensional Mean-Field Hamiltonian Map Model

DOE PAGES

Martínez-del-Río, D.; del-Castillo-Negrete, D.; Olvera, A.; ...

2015-10-30

We studied the self-consistent chaotic transport in a Hamiltonian mean-field model. This model provides a simplified description of transport in marginally stable systems including vorticity mixing in strong shear flows and electron dynamics in plasmas. Self-consistency is incorporated through a mean-field that couples all the degrees-of-freedom. The model is formulated as a large set of N coupled standard-like area-preserving twist maps in which the amplitude and phase of the perturbation, rather than being constant like in the standard map, are dynamical variables. Of particular interest is the study of the impact of periodic orbits on the chaotic transport and coherentmore » structures. Furthermore, numerical simulations show that self-consistency leads to the formation of a coherent macro-particle trapped around the elliptic fixed point of the system that appears together with an asymptotic periodic behavior of the mean field. To model this asymptotic state, we introduced a non-autonomous map that allows a detailed study of the onset of global transport. A turnstile-type transport mechanism that allows transport across instantaneous KAM invariant circles in non-autonomous systems is discussed. As a first step to understand transport, we study a special type of orbits referred to as sequential periodic orbits. Using symmetry properties we show that, through replication, high-dimensional sequential periodic orbits can be generated starting from low-dimensional periodic orbits. We show that sequential periodic orbits in the self-consistent map can be continued from trivial (uncoupled) periodic orbits of standard-like maps using numerical and asymptotic methods. Normal forms are used to describe these orbits and to find the values of the map parameters that guarantee their existence. Numerical simulations are used to verify the prediction from the asymptotic methods.« less

Apollo-Lunar Orbital Rendezvous Technique

NASA Technical Reports Server (NTRS)

1963-01-01

The film shows artists rendition of the spacecrafts, boosters, and flight of the Apollo lunar missions. The Apollo spacecraft will consist of three modules: the manned Command Module; the Service Module, which contains propulsion systems; and the Lunar Excursion Module (LEM) to carry astronauts to the moon and back to the Command and Service Modules. The spacecraft will be launched via a three-stage Saturn booster. The first stage will provide 7.5 million pounds of thrust from five F-1 engines for liftoff and initial powered flight. The second stage will develop 1 million pounds of thrust from five J-2 engines to boost the spacecraft almost into Earth orbit. Immediately after ignition of the second stage, the Launch Escape System will be jettisoned. A single J-2 engine in the S4B stage will provide 200,000 pounds of thrust to place the spacecraft in an earth parking orbit. It also will be used to propel the spacecraft into a translunar trajectory, then it will separate from the Apollo Modules. Onboard propulsion systems will be used to insert the spacecraft into lunar orbit. Two astronauts will enter the LEM, which will separate from the command and service modules. The LEM will go into elliptical orbit and prepare for landing. The LEM will lift off of the Moon's surface to return to the Command and Service Modules, and most likely be left in lunar orbit. After leaving the Moon's orbit, and shortly before entering Earth's orbit, the Service Module will be ejected. The Command Module will be oriented for reentry into the Earth's atmosphere. A drogue parachute will deploy at approximately 50,000 feet, followed by the main parachute system for touchdown.

Self-Consistent Chaotic Transport in a High-Dimensional Mean-Field Hamiltonian Map Model

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

Martínez-del-Río, D.; del-Castillo-Negrete, D.; Olvera, A.

We studied the self-consistent chaotic transport in a Hamiltonian mean-field model. This model provides a simplified description of transport in marginally stable systems including vorticity mixing in strong shear flows and electron dynamics in plasmas. Self-consistency is incorporated through a mean-field that couples all the degrees-of-freedom. The model is formulated as a large set of N coupled standard-like area-preserving twist maps in which the amplitude and phase of the perturbation, rather than being constant like in the standard map, are dynamical variables. Of particular interest is the study of the impact of periodic orbits on the chaotic transport and coherentmore » structures. Furthermore, numerical simulations show that self-consistency leads to the formation of a coherent macro-particle trapped around the elliptic fixed point of the system that appears together with an asymptotic periodic behavior of the mean field. To model this asymptotic state, we introduced a non-autonomous map that allows a detailed study of the onset of global transport. A turnstile-type transport mechanism that allows transport across instantaneous KAM invariant circles in non-autonomous systems is discussed. As a first step to understand transport, we study a special type of orbits referred to as sequential periodic orbits. Using symmetry properties we show that, through replication, high-dimensional sequential periodic orbits can be generated starting from low-dimensional periodic orbits. We show that sequential periodic orbits in the self-consistent map can be continued from trivial (uncoupled) periodic orbits of standard-like maps using numerical and asymptotic methods. Normal forms are used to describe these orbits and to find the values of the map parameters that guarantee their existence. Numerical simulations are used to verify the prediction from the asymptotic methods.« less

First-Order System Least-Squares for Second-Order Elliptic Problems with Discontinuous Coefficients

NASA Technical Reports Server (NTRS)

Manteuffel, Thomas A.; McCormick, Stephen F.; Starke, Gerhard

1996-01-01

The first-order system least-squares methodology represents an alternative to standard mixed finite element methods. Among its advantages is the fact that the finite element spaces approximating the pressure and flux variables are not restricted by the inf-sup condition and that the least-squares functional itself serves as an appropriate error measure. This paper studies the first-order system least-squares approach for scalar second-order elliptic boundary value problems with discontinuous coefficients. Ellipticity of an appropriately scaled least-squares bilinear form of the size of the jumps in the coefficients leading to adequate finite element approximation results. The occurrence of singularities at interface corners and cross-points is discussed. and a weighted least-squares functional is introduced to handle such cases. Numerical experiments are presented for two test problems to illustrate the performance of this approach.

A resilient domain decomposition polynomial chaos solver for uncertain elliptic PDEs

NASA Astrophysics Data System (ADS)

Mycek, Paul; Contreras, Andres; Le Maître, Olivier; Sargsyan, Khachik; Rizzi, Francesco; Morris, Karla; Safta, Cosmin; Debusschere, Bert; Knio, Omar

2017-07-01

A resilient method is developed for the solution of uncertain elliptic PDEs on extreme scale platforms. The method is based on a hybrid domain decomposition, polynomial chaos (PC) framework that is designed to address soft faults. Specifically, parallel and independent solves of multiple deterministic local problems are used to define PC representations of local Dirichlet boundary-to-boundary maps that are used to reconstruct the global solution. A LAD-lasso type regression is developed for this purpose. The performance of the resulting algorithm is tested on an elliptic equation with an uncertain diffusivity field. Different test cases are considered in order to analyze the impacts of correlation structure of the uncertain diffusivity field, the stochastic resolution, as well as the probability of soft faults. In particular, the computations demonstrate that, provided sufficiently many samples are generated, the method effectively overcomes the occurrence of soft faults.

Decoupling antennas in printed technology using elliptical metasurface cloaks

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

Bernety, Hossein M., E-mail: hmehrpou@go.olemiss.edu, E-mail: yakovlev@olemiss.edu; Yakovlev, Alexander B., E-mail: hmehrpou@go.olemiss.edu, E-mail: yakovlev@olemiss.edu

2016-01-07

In this paper, we extend the idea of reducing the electromagnetic interactions between transmitting radiators to the case of widely used planar antennas in printed technology based on the concept of mantle cloaking. Here, we show that how lightweight elliptical metasurface cloaks can be engineered to restore the intrinsic properties of printed antennas with strip inclusions. In order to present the novel approach, we consider two microstrip-fed monopole antennas resonating at slightly different frequencies cloaked by confocal elliptical metasurfaces formed by arrays of sub-wavelength periodic elements, partially embedded in the substrate. The presence of the metasurfaces leads to the drasticmore » suppression of mutual near-field and far-field couplings between the antennas, and thus, their radiation patterns are restored as if they were isolated. Moreover, it is worth noting that this approach is not limited to printed radiators and can be applied to other planar structures as well.« less

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

NASA Astrophysics Data System (ADS)

Barkin, Yu. V.

2008-09-01

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