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NASA NTRS2019

Stability and Spin-Orbit Resonance Analysis of Low Altitude Martian Orbits

Orbit stability has been thoughtfully studied in various celestial bodies. In particular the focus has been placed on the Moon, due to the unstable natural perturbations of its gravity field. The increasing interest in Mars orbiters brings the question of the likelihood of natural decay in low altitude regimes. This paper studies the change in shape of low altitude Mars orbits by carrying out large sets of numerical high fidelity simulations. Results showed that various configurations of the orbital elements gave perturbations that result-ed in unstable orbits. The paper also studies the potential causes of the observed unstable regions. First by taking a close look at zonal and tesseral harmonics to find the implications of Mars mass concentrations of the used gravity fields, and second by computing theoretical spin-orbit resonances to study their implications in the stability at low altitudes.

gravity perturbations↗

NASA NTRSDate not supplied

Long-Term Orbit Operations for the Lunar Reconnaissance Orbiter

The Lunar Reconnaissance Orbiter (LRO) has been operating for 14 years at the Moon after it was launched on its original one-year mission on June 18, 2009. Along with the unprecedented scientific record, operating LRO has revealed many significant factors re-lated to orbit operations that can be used when designing future low-lunar orbit missions. Among other things, these factors include maintaining a low-lunar orbit, applications of a frozen orbit, observing a drift in the orbit inclination, compensating operations to survive through long lunar eclipses, and developing inventive new ways to execute maneuvers.

LRO Orbit Dynamics Operations↗

NASA NTRSDate not supplied

Long-Term Orbit Operations for the Lunar Reconnaissance Orbiter

LRO Orbit Dynamics Operations↗

DOE OSTI2021

Experimental evaluation of the stabilization of the COT orbitals by 4f orbitals in COT 2 Ce using a Hubbard model

Significant orbital mixing is rare in lanthanide complexes because of the limited radial extent of the 4f orbitals, which results in a generally small stabilization due to 4f orbital interactions. Nevertheless, even a small amount of additional stabilization could enhance lanthanide separations. One lanthanide complex in which orbital mixing has been extensively studied both experimentally and computationally is cerocene, COT 2 Ce, where COT is cyclooctatetraene. This compound has a singlet ground state with a low-lying, triplet excited state. Previous fluorescence studies on trimethylsilyl-substituted cerocenes indicate the triplet state is 0.4 eV higher in energy than the singlet state. In addition, computational studies predict that the triplet is 0.3 to 1 eV higher in energy than the singlet. The synthesis of highly pure COT 2 Ce by Walter and Andersen allowed its physical properties to be accurately measured. Using these measurements, we evaluate the stabilization of the 4f orbitals using two, independent approaches. A Hubbard model is used to evaluate the stabilization of the ground state due to orbital mixing. This stabilization, which is also the singlet–triplet gap, is –0.29 eV using this model. Furthermore, this gap was also from the temperature independent paramagnetism of COT 2 Ce, which yielded a value of –0.32 eV.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

NASA NTRS1974

Modification of an impulse-factoring orbital transfer technique to account for orbit determination and maneuver execution errors

A method has previously been developed to satisfy terminal rendezvous and intermediate timing constraints for planetary missions involving orbital operations. The method uses impulse factoring in which a two-impulse transfer is divided into three or four impulses which add one or two intermediate orbits. The periods of the intermediate orbits and the number of revolutions in each orbit are varied to satisfy timing constraints. Techniques are developed to retarget the orbital transfer in the presence of orbit-determination and maneuver-execution errors. Sample results indicate that the nominal transfer can be retargeted with little change in either the magnitude (Delta V) or location of the individual impulses. Additonally, the total Delta V required for the retargeted transfer is little different from that required for the nominal transfer. A digital computer program developed to implement the techniques is described.

Kibler, J. F.↗

NASA NTRS1978

New osculating orbits for 110 comets and analysis of original orbits for 200 comets

Osculating orbits are presented for 110 nearly parabolic comets. Combining these with selected orbit determinations from other sources, a total of 200 orbits are considered where the available observations yield a result of very good (first-class) or good (second-class) quality. For each of these, the original and future orbits (referred to the barycenter of the solar system) are calculated. The Oort effect (a tendency for original reciprocal semimajor axis values to range from zero to +100 millionths per AU) is clearly seen among the first-class orbits but not among the second-class orbits. Modifications in original reciprocal semimajor axis values due to the effects of nongravitational forces are considered.

Marsden, B. G.↗

NASA NTRS1981

Theory of satellite orbit-orbit resonance

On the basis of the strong mathematical and physical parallels between orbit-orbit and spin-orbit resonances, the dynamics of mutual orbit perturbations between two satellites about a massive planet are examined, exploiting an approach previously adopted in the study of spin-orbit coupling. Resonances are found to exist when the mean orbital periods are commensurable with respect to some rotating axis, which condition also involves the apsidal and nodal motions of both satellites. In any resonant state the satellites are effectively trapped in separate potential wells, and a single variable is found to describe the simultaneous librations of both satellites. The librations in longitude are 180 deg out-of-phase, with fixed amplitude ratio that depends only on their relative masses and semimajor axes. The theory is applicable to Saturn's resonant pairs Titan-Hyperion and Mimas-Tethys, and in these cases the calculated libration periods are in reasonably good agreement with the observed periods.

Blitzer, L.↗

NASA NTRS1987

Independent Orbiter Assessment (IOA): Analysis of the orbital maneuvering system

The results of the Independent Orbiter Assessment (IOA) of the Failure Modes and Effects Analysis (FMEA) and Critical Items List (CIL) are presented. The IOA approach features a top-down analysis of the hardware to determine failure modes, criticality, and potential critical items. To preserve independence, this analysis was accomplished without reliance upon the results contained within the NASA FMEA/CIL documentation. The independent analysis results for the Orbital Maneuvering System (OMS) hardware are documented. The OMS provides the thrust to perform orbit insertion, orbit circularization, orbit transfer, rendezvous, and deorbit. The OMS is housed in two independent pods located one on each side of the tail and consists of the following subsystems: Helium Pressurization; Propellant Storage and Distribution; Orbital Maneuvering Engine; and Electrical Power Distribution and Control. The IOA analysis process utilized available OMS hardware drawings and schematics for defining hardware assemblies, components, and hardware items. Each level of hardware was evaluted and analyzed for possible failure modes and effects. Criticality was asigned based upon the severity of the effect for each failure mode.

Prust, C. D.↗

NASA NTRS1989

An analytic development of orbit determination for a distant, planetary orbiter

With the advent of the Mariner '71 Mission, NASA has been sending spacecraft to orbit various distant bodies within the solar system. At present, there is still no adequate theory describing the inherent state estimation accuracy, based on two-way, coherent range-rate data. It is the purpose of this article to lay the groundwork for a general elliptic theory, and in addition to provide an analytic solution for the special case of circular orbits. It is shown that circular orbits about distant planets may suffer singularities in over-all position error estimation. These singularities are due to orbit inclination, placement of the line-of-nodes, and insignificant cross-velocity at the start and end of retrograde motion when orbiting a superior planet. Even though these conclusions appear to yield poor state estimation, one should not be unduly alarmed inasmuch as the stated conditions for singularity are not maintained for extended periods during typical mission scenarios. However, mission analysts should be aware of these potential pitfalls and realize that spuriously large results for circular orbiters can be obtained and are not the result of incorrect assumptions or faulty software. The general elliptic problem appears so involved that analytic inversion at this time is just not feasible, and in any case the resulting expression for the position error would likely be so lengthy that any understanding would be lost in the maze.

Russell, R. K.↗

NASA NTRS1993

Orbit determination support of the Ocean Topography Experiment (TOPEX)/Poseidon operational orbit

The Ocean Topography Experiment (TOPEX/Poseidon) mission is designed to determine the topography of the Earth's sea surface over a 3-year period, beginning shortly after launch in July 1992. TOPEX/Poseidon is a joint venture between the United States National Aeronautics and Space Administration (NASA) and the French Centre Nationale d'Etudes Spatiales. The Jet Propulsion Laboratory is NASA's TOPEX/Poseidon project center. The Tracking and Data Relay Satellite System (TDRSS) will nominally be used to support the day-to-day orbit determination aspects of the mission. Due to its extensive experience with TDRSS tracking data, the NASA Goddard Space Flight Center (GSFC) Flight Dynamics Facility (FDF) will receive and process TDRSS observational data. To fulfill the scientific goals of the mission, it is necessary to achieve and maintain a very precise orbit. The most stringent accuracy requirements are associated with planning and evaluating orbit maneuvers, which will place the spacecraft in its mission orbit and maintain the required ground track. To determine if the FDF can meet the TOPEX/Poseidon maneuver accuracy requirements, covariance analysis was undertaken with the Orbit Determination Error Analysis System (ODEAS). The covariance analysis addressed many aspects of TOPEX/Poseidon orbit determination, including arc length, force models, and other processing options. The most recent analysis has focused on determining the size of the geopotential field necessary to meet the maneuver support requirements. Analysis was undertaken with the full 50 x 50 Goddard Earth Model (GEM) T3 field as well as smaller representations of this model.

Schanzle, A. F.↗

NASA NTRS1992

Precise orbit determination of high-earth elliptical orbiters using differenced Doppler and ranging measurements

Recent advances in NASA's Deep Space Network station calibration methods have led to renewed interest in the use of differenced radiometric data types for interplanetary navigation, particularly differenced Doppler and range. An orbit determination error analysis which compares the performance of these differenced data types when used in concert with conventional two-way Doppler for precise navigation of high-earth orbiters is described. Three highly elliptical orbits are investigated, with apogee heights on the order of 20,000 km, 70,000 km, and 156,000 km. The analysis assumes that each orbiter's downlink antenna has no ground footprint limitation in the near apogee regime. Results indicate that the most significant navigational accuracy improvements are seen for the lowest-altitude orbit by using differenced Doppler measurements in conjunction with two-way Doppler. The results for the two higher-altitude orbits, although less dramatic, suggest that accuracy improvements can also be achieved when differenced range measurements are combined with two-way Doppler.

Estefan, Jeff A.↗

NASA NTRS1994

Some aspects of simultaneously flying Topex Follow-On in a Topex orbit with Geosat Follow-On in a Geosat orbit

The advantages of having Geosat Follow-On in a Geosat orbit flying simultaneously with Topex Follow-On in a Topex/Poseidon orbit are examined. The orbits are evaluated using two criteria. The first is the acute crossover angle. This angle should be at least 40 degrees in order to accurately resolve the slope of sea level at crossover locations. The second is tidal aliasing. In order to solve for tides, the largest constituents should not be aliased to a frequency lower than two cycles/year and should be at least one cycle discrete from one another and from exactly two cycles/year over the mission life. The results show that TFO and GFO in these orbits complement each other. Both satellites have large crossover angles over a wide latitude range. In addition, the Topex orbit has good aliasing characteristics for the M2 and P1 tides for which the Geosat orbit has difficulty.

Parke, Michael E.↗

NASA NTRS1995

The orbital characteristics of debris particle rings as derived from IDE observations of multiple orbit intersections with LDEF

During the first 346 days of the LDEF's almost 6 year stay in space, the metal oxide silicon detectors of the Interplanetary Dust Experiment (IDE) recorded over 15,000 impacts, most of which were separated in time by integer multiples of the LDEF orbital period (called multiple orbit event sequences, or MOES). Simple celestial mechanics provides ample reason to expect that a good deal of information about the orbits of the impacting debris particles can be extracted from these MOES, and so a procedure, based on the work of Greenberg, has been developed and applied to one of these events, the so-called 'May swarm'. This technique, the 'Method of Differential Precession,' allows for the determination of the geometrical elements of a particle orbit from the change in the position of the impact point with time. The application of this approach to the May swarm gave the following orbital elements for the orbit of the particles striking LDEF during this MOES: a = 6746.5 km; 0.0165 less than e less than 0.025; i = 66.55 deg; Omega(sub 0) = 179.0 deg plus or minus 0.2 deg; omega = 178.1 deg plus or minus 0.2 deg.

Cooke, William J.↗

NASA NTRS1999

Solar Sail Optimal Orbit Transfers to Synchronous Orbits

A constant outward radial thrust acceleration can be used to reduce the radius of a circular orbit of specified period. Heliocentric circular orbits are designed to match the orbital period of Earth or Mars for various radial thrust accelerations and are defined as synchronous orbits. Minimum-time solar sail orbit transfers to these synchronous heliocentric orbits are presented.

Powers, Robert B.↗

NASA NTRS2000

Beagle 2 and NASA's Mars 2003 Orbiter: A Unique Exobiology Opportunity with an Orbiter

With the exploration strategy for Mars undergoing reexamination, the opportunity exists for the incorporation of the 60 kg Beagle 2 lander, developed in the United Kingdom for inclusion on ESA's 2003 Mars Express mission, with NASA's Mars 2003 orbiter derived from the Mars Global Orbiter. The combination of Beagle 2 with a Mars orbiter would result in a unique mission which could obtain information on Mars' life, climate and resources both from orbit as well as on the surface of the planet. Beagle 2 has been developed in the LJK for ESA as a low-cost opportunity to study the exobiology of Mars and the spacecraft is in its final stages of manufacture. Only limited modifications to the Beagle 2 package would be required for inclusion on NASA's Mars 2003 orbiter. With the ESA Mars Express mission launch in 2003 and a potential NASA Mars orbiter in 2003, both Beagle 2 landers on Mars would offer a low-cost, decreased risk and increased science return opportunity for the exploration of Mars at two distinct geologically interesting sites.

Gibson, Everett K., Jr.↗

NASA NTRS2004

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

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

Folta, David↗

NASA NTRS2004

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

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

Roberts, Craig E.↗

NASA NTRS2005

Hardware in-the-Loop Demonstration of Real-Time Orbit Determination in High Earth Orbits

This paper presents results from a study conducted at Goddard Space Flight Center (GSFC) to assess the real-time orbit determination accuracy of GPS-based navigation in a number of different high Earth orbital regimes. Measurements collected from a GPS receiver (connected to a GPS radio frequency (RF) signal simulator) were processed in a navigation filter in real-time, and resulting errors in the estimated states were assessed. For the most challenging orbit simulated, a 12 hour Molniya orbit with an apogee of approximately 39,000 km, mean total position and velocity errors were approximately 7 meters and 3 mm/s respectively. The study also makes direct comparisons between the results from the above hardware in-the-loop tests and results obtained by processing GPS measurements generated from software simulations. Care was taken to use the same models and assumptions in the generation of both the real-time and software simulated measurements, in order that the real-time data could be used to help validate the assumptions and models used in the software simulations. The study makes use of the unique capabilities of the Formation Flying Test Bed at GSFC, which provides a capability to interface with different GPS receivers and to produce real-time, filtered orbit solutions even when less than four satellites are visible. The result is a powerful tool for assessing onboard navigation performance in a wide range of orbital regimes, and a test-bed for developing software and procedures for use in real spacecraft applications.

Moreau, Michael↗