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At least 91 records · Page 5

Preliminary study of the application of the Timation 3 satellite to earth physics

The Timation 3 is a timing and navigation satellite originally planned for launch in December 1972 into a circular orbit at 98 deg inclination 14,000 km altitude with gravity gradient stabilization. An error analysis indicates a satellite position uncertainty of about one meter, 80 percent of which is attributable to the assumed gravity model errors. The remaining uncertainties have a period equal to that of the satellites and can be filtered out yielding an effective uncertainty of about 10 cm in the study of phenomena having different periodicities. The accomplishment of these results depends on a careful consideration of solar radiation pressure taking account of the spacecraft reflecting properties and variations in the presentation area. Consideration is also given to the displacement of the laser reflectors from the center of mass of the spacecraft and to the dynamic coupling of any libration in attitude with the orbital motion. The results indicate that a good set of well distribution laser observations of Timation 3 could yield determinations of polar motion, sea floor spreading, solid earth tides, and earth rotation at the 10 cm level.

Carpenter, L.↗

Orbit-orbit resonances in the solar system - Varieties and similarities

Descriptions of various orbit-orbit resonance mechanisms in the solar system are brought together in such a manner that the physical processes underlying the traditional mathematical presentations are apparent. A simple qualitative model based on the resonance between Saturn's satellites Titan and Hyperion is presented, the same resonance is analyzed quantitatively, and the small-eccentricity mechanism is examined. The following resonances are investigated in detail: Enceladus-Dione, Mimas-Tethys, Neptune-Pluto, and Rhea-Titan (secular resonance). Coupled librations of several asteroids near mean motions commensurable with Jupiter's are modeled, the Laplace relation involving Io, Europa, and Ganymede is studied, and the 1:1 resonance between the Trojan asteroids and Jupiter is discussed. Some higher-order commensurabilities involving asteroids are considered, including the 3:1 resonance between Alinda and Jupiter, the 13:5 resonance of Toro with Venus, the 8:5 resonance of Toro with earth, and the 11:28 resonance of Ivar with earth.

Greenberg, R.↗

Dust Trails of SP/Tuttle and the Unusual Outbursts of the Ursid Shower

Halley-type comets tend to have a series of dust trails that remain spatially correlated for extended periods of time, each dating from a specific return of the comet. Encounters with 1 - 9 revolution old individual dust trails of 55P/Tempel-Tuttle have led to well recognized Leonid shower maxim, the peak time of which was well predicted by recent models. Now. we used the same model to calculate the position of dust trails of comet Shuttle, a Halley-type comet in an (approximately) 13.6 year orbit passing just outside of Earth's orbit. We discovered that the meteoroids tend to be trapped in the 14:12 mean motion resonance with Jupiter, while the comet librates in a slightly shorter period orbit around the 13:15 resonance. It takes six centuries to change the orbit enough to intersect Earth's orbit. During that time, the meteoroids and comet separate in mean anomaly by six years. thus explaining the unusual aphelion occurrences of Ursid outbursts. The resonances also prevent dispersion, so that the dust trail encounters (specifically, from dust trails of AD 1378 - 1405) occur only in one year in each orbit. We predicted enhanced activity on December 22, 2000, at around 7:29 and 8:35 UT (universal time) from dust trails dating to the 1405 and 1392 return, respectively. This event was observed from California using video and photographic techniques. At the same time, five Global-MS-Net stations in Finland, Japan and Belgium counted meteors using forward meteor scatter. The outburst peaked at 8:06:07 UT, December 22, at Zenith Hourly Rate (approx.) 90 per hour. The Ursid rates were above half peak intensity during 4.2 hours. This is only the second Halley type comet for which a meteor outburst can be dated to a specific return of the parent comet, and traces their presence back form 9 to at least 45 revolutions of the comet. New orbital elements of Ursid meteoroids are presented. We find that most orbits do scatter around the anticipated positions, confirming the link with comet Shuttle and the epoch of ejection. The 1405 and.1392 dust trails appear to have contributed similar amounts to the activity profile. Some orbits provide a hint of much older debris being present as well. Some of the dispersion in the radiant position may reflect a true variation in inclinations, with two groupings at low and high values, which is not understood at present.

Jenniskens, Peter↗

Analysis of solar radiation pressure induced coupled librations of a gravity stabilized axisymmetric satellite

This paper presents an analysis of solar radiation pressure induced coupled librations of gravity stabilized cylindrical spacecraft with a special reference to geostationary communication satellites. The Lagrangian approach is used to obtain the corresponding equations of motion. The solar induced torques are assumed to be free of librational angles and are represented by their Fourier expansion. The response and periodic solutions are obtained through linear and nonlinear analyses, using the method of harmonic balance in the latter case. The stability conditions are obtained using Routh-Hurwitz criteria. To establish the ranges of validity the analytic response is compared with the numerical solution. Finally, values of the system parameters are suggested to make the satellite behave as desired. Among these is a possible approach to subdue the solar induced roll resonance. It is felt that the approximate analysis presented here should significantly reduce the computational efforts involved in the design and stability analysis of the systems.

Shrivastava, S. K.↗

Mapping the stability field of Jupiter Trojans

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

Levison, H. F.↗

Non-linear stability around the triangular libration points

The configuration space around the triangular libration points in the Earth-Moon system is partitioned according to the stability of the motion. The regions around L4 and L5 are established where particles placed with zero initial velocity will librate. The complexity of the partitioning is revealed.

Mckenzie, R.↗

Linear State-Space Representation of the Dynamics of Relative Motion, Based on Restricted Three Body Dynamics

Precision Formation Flying is an enabling technology for a variety of proposed space-based observatories, including the Micro-Arcsecond X-ray Imaging Mission (MAXIM) , the associated MAXIM pathfinder mission, Stellar Imager (SI) and the Terrestrial Planet Finder (TPF). An essential element of the technology is the control algorithm, requiring a clear understanding of the dynamics of relative motion. This paper examines the dynamics of relative motion in the context of the Restricted Three Body Problem (RTBP). The natural dynamics of relative motion are presented in their full nonlinear form. Motivated by the desire to apply linear control methods, the dynamics equations are linearized and presented in state-space form. The stability properties are explored for regions in proximity to each of the libration points in the Earth/Moon - Sun rotating frame. The dynamics of relative motion are presented in both the inertial and rotating coordinate frames.

Luquette,Richard J.↗

Linear State-Space Representation of the Dynamics of Relative Motion, Based on Restricted Three Body Dynamics

Precision Formation Flying is an enabling technology for a variety of proposed space- based observatories, including the Micro-Arcsecond X-ray Imaging Mission (MAXIM), Stellar Imager (SI) and the Terrestrial Planet Finder (TPF). An essential element of the technology is the control algorithm, requiring a clear understanding of the dynamics of relative motion. This paper examines the dynamics of relative motion in the context of the Restricted Three Body Problem (RTBP). The natural dynamics of relative motion are presented in their full nonlinear form. Motivated by the desire to apply linear control methods, the dynamics equations are linearized and presented in state-space form. The stability properties are explored for regions in proximity to each of the libration points in the Earth/Moon - Sun rotating frame. The dynamics of relative motion are presented in both the inertial and rotating coordinate frames.

Luquette, Richard J.↗

Investigations of Spacecraft Orbits Around the L(2) Sun-Earth Libration Point

Space agencies are planning missions to the vicinity of the Sun-Earth L sub 2 point, some involving a distributed system of telescope spacecraft, configured in a plane about a hub. An improved understanding is developed of their relative motion. First, the telescope equations of motion are written relative to L sub 2 in the context of the classical circular restricted three-body problem, and expanded in terms of the distance from L sub 2. A basic examination is presented of the spacecraft configuration requirements and effects of small orbit insertion errors. Next, the telescope equations of motion relative to the hub are written and further expanded in terms of the hub-L sub 2 and hub-telescope distances. An analytical solution is developed and a halo telescope orbit investigated, with appropriate initial conditions. Then, the force model is extended to include perturbations to an accuracy of 10 to 20 m, east as additive contributions to the circular restricted problem. Perturbations include Earth's orbital eccentricity, lunar motion, solar radiation pressure, and small thrusting forces. Simulations are presented, along with solution sensitivity to errors in hub position knowledge.

RELATIVE MOTION↗

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

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

Rhoden, Alyssa Rose↗

Lunar baselines and libration from differential VLBI observations of ALSEPs

Differential very-long-baseline interferometric observations of signals from Apollo Lunar Surface Experiment Package telemetry transmitters will yield the relative projected positions of the transmitters with uncertainty of only 1-3 m, set mainly by uncertainty of the lunar ephemeris. Noise and systematic instrumental errors which in the past affected similar observations have been reduced to the equivalent of a few centimeters on the lunar surface by the development of a new type of differential receiver. Continued observations should yield a determination of the motion of the moon about its center of mass with uncertainty less than 1 sec of selenocentric arc. Improvements (by other means) in our knowledge of the moon's orbital motion would allow a further order-of-magnitude refinement in the libration and relative position results obtainable by differential VLBI.

Counselman, C. C., III↗

A Solar System Survey of Forced Librations in Longitude

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

Cornstock, Robert L.↗

A Non-Linear Approach to Spacecraft Formation Control in the Vicinity of a Collinear Libration Point

An expanding interest in mission design strategies that exploit libration point regions demands the continued development of enhanced, efficient, control algorithms for station-keeping and formation maintenance. This paper discusses the development of a non-linear, formation maintenance, control algorithm for trajectories in the vicinity of a libration point. However, the formulation holds for any trajectory governed by the equations of motion for the restricted three body problem. The control law guarantees exponential convergence, based on a Lyaponov analysis. FreeFlyer and MATLAB provide the simulation environment for controller performance evaluation. The simulation, modeled after the MAXIM Pathfinder mission, maintains the relative position of a "follower" spacecraft with respect to a "leader" spacecraft, stationed near the L2 libration point in the Sun-Earth system. Evaluation metrics are fuel usage and tracking accuracy.

Luquette, Richard J.↗

Estimating the Libration of Mercury by Remote Sensing of Gravity and Altimetry

One of the most intriguing scientific questions about Mercury is whether the planet possesses a liquid core. One way that this can be ascertained is through the measurement of the longitudinal libration of Mercury about its rotation axis. The MESSENGER (Mercury Surface, Space, Environment, Geochemistry, and Ranging) mission to Mercury will attempt this measurement by deriving the rotation of the planet from remotely sensed observations of the Mercury gravity field and the planet's shape. For a fully fluid core the libration is expected to be an approximately 350-m-amplitude oscillation (at the equator) about the mean rotation of the planet. Thus, the shape of the planet undergoes a librational oscillation in the same way that features on the surface participate in the motion. In this sense altimetric topography can be considered analogous to imaging, with the important exception that for altimetry, the long wavelengths corresponding to low degrees and orders in a spherical harmonic expansion, can be precisely determined from orbital measurements. The rotation of the planet thus introduces a time dependence of the topographic image in an inertial (i.e. fixed) reference frame and the libration is a variation in the planetary rotation rate, manifest as an oscillation of the topographic image. Similarly, gravity measures the distribution of mass within a planet and as such can be viewed as providing a vertically integrated 'image' of the internal density structure. For a librating planet the gravitational field will also reveal a variation in the rotation rate, manifest as an oscillation of the field with respect to an inertial reference frame. While the long-wavelength gravity field contains contributions from the radial distribution of mass with depth, the long wavelength terms are most sensitive to the mass distribution of the deep interior. Thus, both the topography and the gravity independently can be used to determine the (irregular) rotation of a planet, although the topographical method measures the rotation of the crust while the gravity measures the rotation of the distributed mass, and these are not necessarily identical. For example, for a planet that contains a fluid outer core that is effectively decoupled from the mantle the gravity field will not librate in the manner of a solid body. The libration obtained from the variable rotation of the gravity field will represent a combination of contributions due to a librating mantle and a differentially rotating fluid core. Differential rotation of the Earth's inner core had been theoretically predicted from three dimensional geodynamical models and subsequently reported from seismic observations. A difference between the libration of the lithosphere as determined from altimetry and the deep interior as determined from gravity, if it could be detected, might provide further insight into the nature of core-mantle coupling. Additional information is contained in the original extended abstract.

Smith, D. E.↗

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

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

Luquette, Richard J.↗

Excitation and relaxation of the wobble, precession, and libration of the moon

The rate of meteorite-impact excitation of the free wobble, free precession, and free libration of the moon above a given amplitude is estimated for two crater-size scaling laws and is compared with the rate of damping by tidal and rotational distortion as well as by a possible core-mantle interaction. Criteria for the probable existence and the probable nonexistence of observable amplitudes of the free motions are developed in terms of upper bounds on the damping factor for the various motions and in terms of ranges for the kinematic viscosity of a possible core. It is shown that although observable amplitudes are compatible with reasonable values of the damping factor and kinematic viscosity, other reasonable values could keep the amplitudes below the observable level most of the time. It is found that the free libration is the least likely motion to be observed and that a lunar core with earthlike properties might keep some of the free motions damped, but not all of them. Uncertainties in some of the assumptions used in the analysis are discussed.

Peale, S. J.↗