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NASA NTRS1992

TOPEX/Poseidon orbit acquisition maneuver design

The current baseline injection orbit for the jointly sponsored NASA/CNES TOPEX/Poseidon mission is near-circular, approximately 30 km below the desired operational orbit altitude and at the operational orbit inclination. A baseline maneuver sequence to retarget from this injection orbit to the desired operational orbit has been designed based upon the expected worst-case 3-sigma injection and maneuver execution errors. The sequence requires seven maneuvers, including an initial calibration burn, and achieves the operational orbit with the desired ground track pattern in 30 days. A delay sensitivity analysis has been conducted to estimate the allowable operational delay for each maneuver without increasing the total orbit acquisition period. The baseline sequence provides back-ups for a one-revolution delay for each maneuver and one-day delay for most maneuvers. It is also shown that a higher injection orbit allows the maneuver sequence to achieve the operational orbit in 26 days under a worst-case scenario.

Bhat, Ramachandra S.↗
NASA NTRS1992

Long-term orbital evolution of short-period comets found in Project Cosmo-DICE

Orbital evolutions of about 160 short-period (SP) comets are numerically integrated for 4400 years in the framework of a realistic dynamical model. By the round-trip error in closure test, a reliable time space of the integrated orbits is estimated for each comet. Majority of the SP comets with their Tisserand's constant(J) between 2.8 and 3.1 are found to evolve within the past 1000-2000 years from the orbits whose perihelia are near the Jovian orbit to the orbits with perihelia of 1-2 AU. This evolution is much more rapid than that expected from Monte Carlo simulations based on symmetric distribution of planetary perturbations, thus suggesting that asymmetry of perturbation distribution play an important role in cometary evolution. Several comets are shown to evolve from the near-Saturn orbits and then to be handed over under the control of Jupiter. We also find that a few comets were captured from long-period orbits (a = 75-125 AU) via only a few close encounters with Jupiter. It is confirmed that the captured SP comets of low-inclination with 2.7 less than J less than 3.1 show more or less strong chaotic behavior. On the other hand, comets with longer orbital period and/or of high inclination reveal slow or quasi-periodic orbital evolution.

Nakamura, Tsuko↗
NASA NTRS1991

The design of two-stage-to-orbit vehicles

Two separate student design groups developed conceptual designs for a two-stage-to-orbit vehicle, with each design group consisting of a carrier team and an orbiter team. A two-stage-to-orbit system is considered in the event that single-stage-to-orbit is deemed not feasible in the foreseeable future; the two-stage system would also be used as a complement to an already existing heavy lift vehicle. The design specifications given are to lift a 10,000-lb payload 27 ft long by 10 ft diameter, to low Earth orbit (300 n.m.) using an air breathing carrier configuration that will take off horizontally within 15,000 ft. The staging Mach number and altitude were to be determined by the design groups. One group designed a delta wing/body carrier with the orbiter nested within the fuselage of the carrier, and the other group produced a blended cranked-delta wing/body carrier with the orbiter in the more conventional piggyback configuration. Each carrier used liquid hydrogen-fueled turbofanramjet engines, with data provided by General Electric Aircraft Engine Group. While one orbiter used a full-scale Space Shuttle Main Engine (SSME), the other orbiter employed a half-scale SSME coupled with scramjet engines, with data again provided by General Electric. The two groups conceptual designs, along with the technical trade-offs, difficulties, and details that surfaced during the design process are presented.

Source record↗
NASA NTRS1994

Improved solution accuracy for TDRSS-based TOPEX/Poseidon orbit determination

Orbit determination results are obtained by the Goddard Space Flight Center (GSFC) Flight Dynamics Division (FDD) using a batch-least-squares estimator available in the Goddard Trajectory Determination System (GTDS) and an extended Kalman filter estimation system to process Tracking and Data Relay Satellite (TDRS) System (TDRSS) measurements. GTDS is the operational orbit determination system used by the FDD in support of the Ocean Topography Experiment (TOPEX)/Poseidon spacecraft navigation and health and safety operations. The extended Kalman filter was implemented in an orbit determination analysis prototype system, closely related to the Real-Time Orbit Determination System/Enhanced (RTOD/E) system. In addition, the Precision Orbit Determination (POD) team within the GSFC Space Geodesy Branch generated an independent set of high-accuracy trajectories to support the TOPEX/Poseidon scientific data. These latter solutions use the geodynamics (GEODYN) orbit determination system with laser ranging and Doppler Orbitography and Radiopositioning integrated by satellite (DORIS) tracking measurements. The TOPEX/Poseidon trajectories were estimated for November 7 through November 11, 1992, the timeframe under study. Independent assessments were made of the consistencies of solutions produced by the batch and sequential methods. The batch-least-squares solutions were assessed based on the solution residuals, while the sequential solutions were assessed based on primarily the estimated covariances. The batch-least-squares and sequential orbit solutions were compared with the definitive POD orbit solutions. The solution differences were generally less than 2 meters for the batch-least-squares and less than 13 meters for the sequential estimation solutions. After the sequential estimation solutions were processed with a smoother algorithm, position differences with POD orbit solutions of less than 7 meters were obtained. The differences among the POD, GTDS, and filter/smoother solutions can be traced to differences in modeling and tracking data types, which are being analyzed in detail.

Doll, C. E.↗
NASA NTRS1995

GPS as an orbit determination subsystems

This paper evaluates the use of Global Positioning System (GPS) receivers as a primary source of tracking data for low-Earth orbit satellites. GPS data is an alternative to using range, azimuth, elevation, and range-rate (RAER) data from the Air Force Satellite Control Network antennas, the Space Ground Link System (SGLS). This evaluation is applicable to missions such as Skipper, a joint U.S. and Russian atmosphere research mission, that will rely on a GPS receiver as a primary tracking data source. The Detachment 2, Space and Missile Systems Center's Test Support Complex (TSC) conducted the evaluation based on receiver data from the Space Test Experiment Platform Mission O (STEP-O) and Advanced Photovoltaic and Electronics Experiments (APEX) satellites. The TSC performed orbit reconstruction and prediction on the STEP-0 and APEX vehicles using GPS receiver navigation solution data, SGLS RAER data, and SGLS anglesonly (azimuth and elevation) data. For the STEP-O case, the navigation solution based orbits proved to be more accurate than SGLS RAER based orbits. For the APEX case, navigation solution based orbits proved to be less accurate than SGLS RAER based orbits for orbit prediction, and results for orbit reconstruction were inconclusive due to the lack of a precise truth orbit. After evaluating several different GPS data processing methods, the TSC concluded that using GPS navigation solution data is a viable alternative to using SGLS RAER data.

Fennessey, Richard↗
NASA NTRS1993

A demonstration of TDRS orbit determination using differential tracking observables from GPS ground receivers

A Global Positioning System (GPS) flight receiver provides a means of precisely determining orbits for satellites in low to moderate altitude orbits. Above 5000 km altitude, however, relatively few GPS satellites are visible. We present a new approach to orbit determination for satellites at higher altitudes. Modification of GPS ground receivers enables a beacon from the orbiter to be tracked simultaneously with GPS data. The orbit accuracy expected from this GPS-like tracking (GLT) technique in principle could be comparable to accuracies of GPS orbits. Present-day GPS orbit quality from a daily semi-automated analysis system at the Jet Propulsion Laboratory is at the 30 - 50 cm level: expected accuracies for orbiters with GLT are calculated to be in the few-meter range for altitudes up to 100000 km. For geosynchronous satellites, however, there are unique challenges due to geometrical limitations and to the lack of strong dynamical signature in tracking data. We examine two approaches for tracking Tracking and Data Relay Satellites (TDRS) geostationary orbiters. One uses GLT with a global network; the other relies on a small `connected element' ground network with a distributed clock for short baseline differential carrier phase (SB Delta Phi). In priciple, both could meet 50-m TDRS operational requirements. However there are practical difficulties with either pure GLT or SB Delta Phi tracking schemes for present-day TDRS satellites. We describe an experiment planned for late 1993 which will combine aspects of both GLT and SB Delta Phi to demonstrate a new approach for tracking TDRS which offers a number of operationally convenient and attractive features. The TDRS demo will in effect ba a proof of concept experiment for both the GLT and SB Delta Phi approaches to tracking spacecraft.

Lichten, Stephen M.↗
NASA NTRS1995

Asteroid orbit evolution due to thermal drag

Thermal drag, a variant of the Yarkovsky effect, may act on small asteroids with sizes from a few meters to a few tens of meters. Yarkovsky thermal drag comes from an asteroid's absorbing sunlight in the visible and reradiating it in the infrared. Since the infrared photons have momentum, by action-reaction, they kick the asteroid when they leave its surface. The reradiation, which is asymmetric in latitude over the asteroid, gives a net force along the asteroid's pole. Due to the asteroid's thermal inertia, averaging this force over one orbital period produces a net drag if the spin axis has a component in the orbital plane. Thermal drag tends to circularize orbits. It can increase or decrease orbital inclinations. An object whose spin axis points in random directions over its lifetime displays little change in orbital inclination. Thermal drag appears to have little to do with the delivery of chondrites from the asteroid belt; the thermal drag timescale (10(exp 8) years for meter-sizzed objects) is long compared with their cosmic ray exposure ages, and aphelia in the asteroid belt are not expected for mature thermal drag orbits. However, Yarkovsky thermal drag may act on the recently discovered near-Earth asteroids, which have radii of 10-30 m. Asteroid 1992 DA, for instance, might have its orbit shrunk by 0.1 AU in 3 x 10(exp 7) years, removing it from an Earth-crossing orbit. The near-Earth asteroids also tend to have small to moderate orbital eccentricities, as expected for highly evolved thermal drag objects. However, the time needed to bring them in from the asteroid belt (about 10(exp 9) years) is long compared with the collisonal and dynamical lifetimes (both about 10(exp 8) years) for Earth-crossing objects, arguing against their emplacement by thermal drag.

Rubincam, David Parry↗
NASA NTRS1993

Orbital Resonances in the Solar Nebula: Strengths and Weaknesses

A planetesimal moving in the Solar Nebula experiences an aerodynamic drag which causes its orbit to circularize and shrink. However, resonant perturbations from a protoplanet interior to the planetesimal's orbit can counteract both the orbital decay and the damping of the eccentricity: the planetesimal can be captured into an orbital resonance and its eccentricity pumped up to a modestly high equilibrium value. Thus, orbital resonances constitute (partial) barriers to the delivery of planetesimals into the feeding zone of the protoplanet. We have established the characteristics of the phenomenon of resonance capture by gas drag in the circular restricted three-body approximation. We have determined the strengths of the equilibrium resonant orbits with respect to impulsive velocity perturbations. We conclude that planetesimals captured in orbital resonances are quite vulnerable to being dislocated from these orbits by mutual planetesimal interactions, but that the resonances are effective in slowing down the rate of orbital decay of planetesimals. Only very small bodies, less than or equal to 100 m, are able to reach a approx. 1 Earth mass protoplanet without being slowed down by resonances.

Malhotra, Renu↗
NASA NTRS1993

Orbital Resonances in the Solar Nebula: Strengths and Weaknesses

A planetesimal moving in the Solar Nebula experiences an aero- dynamic drag which causes its orbit to circularize and shrink. However, resonant perturbations from a protoplanet interior to the planetesimal's orbit ran counteract both the orbital decay and the damping of the eccentricity: the planetesimal can be captured into an orbital resonance and its eccentricity pumped up to a modestly high equilibrium value. Thus, orbital resonances constitute (partial) barriers to the delivery of planetesimals into the feeding zone of the protoplanet. We have established the characteristics of the phenomenon of resonance capture by gas drag in the circular restricted three-body approximation. We have determined the strengths of the equilibrium resonant orbits with respect to impulsive velocity perturbations. We conclude that planetesimals captured in orbital resonances are quite vulnerable to being dislocated from these orbits by mutual planetesimal interactions, but that the resonances are effective in slowing down the rate of orbital decay of planetesimals. Only very small bodies, less or approx. equal to 100 m, are able to reach a approx. 1 mass of the earth protoplanet without being slowed down by resonances.

Malhotra, Renu↗
NASA NTRS1999

The Lunar Prospector Mission: Final Results of Trajectory Design, Quasi-Frozen Orbits, Extended Mission Targeting, and Lunar Topography and Potential Models

The National Aeronautics and Space Administration (NASA) selected Lunar Prospector (LP) as one of the discovery missions to conduct solar system exploration science investigations. The mission was NASA's first lunar voyage to investigate key science objectives since Apollo and was launched in January 1998. In keeping with discovery program requirements to reduce total mission cost and utilize new technology, Lunar Prospector's mission design and control will focus on the use of innovative and proven trajectory analysis programs. As part of this effort, the Goddard Space Flight Center and the Ames Research Center became partners in the Lunar Prospector trajectory team to provide the trajectory analysis and orbit determination support. At the end of 1998, Lunar Prospector completed its one-year primary mission at 100-km altitude above the lunar surface. On December 19, 1998, Lunar Prospector entered its extended mission phase. The mission orbit was lowered from 100 km to a mean altitude of 40 km. Due to lunar potential effects, the altitude of Lunar Prospector varied from 25 to 55 km above the mean lunar geoid. After one month at 40 km, the lunar potential model was updated based upon the new tracking data at 40 km. On January 15, 1999, the altitude was lowered again to a mean altitude of 30 km. The spherical altitude varied between 15 km and 45 km above the mean lunar geoid while the topographical altitude varied between 10 km and 50 km. Various means were employed to get accurate lunar surface elevation including Clementine altimetry and LOS analysis. Based upon the best available terrain maps, Lunar Prospector reached actual altitudes of 8 km above lunar mountains in the southern polar region. This extended mission phase of six months will enable LP to obtain science data up to 3 orders of magnitude better than at the mission orbit. At the end of the operations mission, LP was targeted for impact at a chosen location that allowed optical observation of the lunar ejecta as LP ended its mission at 1.6 km/sec. This paper details the trajectory design and orbit determination planning and actual results of the Lunar Prospector nominal and extended mission including maneuver design, eccentricity vs. argument of perigee evolution, topographical altitude estimation, and lunar potential modeling. This paper provides understanding of the quasi-frozen orbit design of the LP mission, the optimization process of lunar orbit targets, the impacts that the selected lunar potential models play, and discusses the feasibility of meeting the mission goals. Observed evolution of the Keplerian orbit elements are compared to the theoretical predictions using the latest lunar potential model available which incorporates the Lunar Prospector Doppler data. Mapping orbit maintenance maneuver design along with results of the actual maneuvers to maintain the orbital requirements are also presented.

Folta, David↗
NASA NTRS1993

Mars Observer Lecture: Mars Orbit Insertion

The Mars Observer mission spacecraft was primarily designed for exploring Mars and the Martian environment. The Mars Observer was launched on September 25, 1992. The spacecraft was lost in the vicinity of Mars on August 21, 1993 when the spacecraft began its maneuvering sequence for Martian orbital insertion. This videotape shows a lecture by Suzanne R. Dodd, the Mission Planning Team Chief for the Mars Observer Project. Ms Dodd begins with a brief overview of the mission and the timeline from the launch to orbital insertion. Ms Dodd then reviews slides showing the trajectory of the spacecraft on its trip to Mars. Slides of the spacecraft being constructed are also shown. She then discusses the Mars orbit insertion and the events that will occur to move the spacecraft from the capture orbit into a mapping orbit. During the trip to Mars, scientists at JPL had devised a new strategy, called Power In that would allow for an earlier insertion into the mapping orbit. The talk summarizes this strategy, showing on a slide the planned transition orbits. There are shots of the Martian moon, Phobos, taken from the Viking spacecraft, as Ms Dodd explains that the trajectory will allow the orbiter to make new observations of that moon. She also explains the required steps to prepare for mapping after the spacecraft has achieved the mapping orbit around Mars. The lecture ends with a picture of Mars from the Observer on its approach to the planet.

Dodd, Suzanne R.↗
NASA NTRS2001

A Cryogenic Propellant Production Depot for Low Earth Orbit

The cost of access to space beyond low Earth orbit can be lowered if vehicles can refuel in orbit. The power requirements for a propellant depot that electrolyzes water and stores cryogenic oxygen and hydrogen can be met using technology developed for space solar power. A propellant depot is described that will be deployed in a 400 km circular equatorial orbit, receive tanks of water launched into a lower orbit from Earth by gun launch or reusable launch vehicle, convert the water to liquid hydrogen and oxygen, and store Lip to 500 metric tonnes of cryogenic propellants. The propellant stored in the depot can support transportation from low Earth orbit to geostationary Earth orbit, the Moon, LaGrange points, Mars, etc. The tanks are configured in an inline gravity-gradient configuration to minimize drag and settle the propellant. Temperatures can be maintained by body-mounted radiators; these will also provide some shielding against orbital debris. Power is supplied by a pair of solar arrays mounted perpendicular to the orbital plane, which rotate once per orbit to track the Sun. In the longer term, cryogenic propellant production technology can be applied to a larger LEO depot, as well as to the use of lunar water resources at a similar depot elsewhere.

Potter, Seth D.↗
NASA NTRS2002

Evaluation of GEOSAT Follow-On Precise Orbit Ephemeris

The GEOSAT Follow-On spacecraft (GFO-l), launched in 1998, began continuous radar altimeter coverage of the oceans in 2000, and after an extensive series of calibration campaigns in 1999 and 2000 was finally accepted by the US Navy on November 29, 2000. By providing high quality altimeter data, GFO can supplement TOPEX/POSEIDON(T/P), ERS-1, and ERS-2 data, providing a different synoptic sampling of the oceans with its 17-day ground track repeat cycle. Altimeter analysis suggests GFO is capable of POSEIDON class altimetry, with orbit error the largest contributor to the GFO altimeter error budget. Satellite laser ranging (SLR), especially in combination with altimeter crossover data, offer the only means of determining high-quality precise orbits. SLR tracking is also augmented by Doppler (Tranet style) beacons. These data were used to tune the gravity field and macromodel (3D representation of the spacecraft geometry and surface properties). Beginning with January 2000 GSFC has produced a 2.5 year span of the Precision Orbit Ephemeris (POE) intended for use on the GFO GDR and for the Pathfinder Project. Using GFO GDR and IGDR altimeter data from NOAA, a two year span of POE orbits are evaluated with respect to the TOPEX orbits by adjusting the GFO data into the TOPEX frame with the help of TOPEX/GFO altimeter crossovers. A 2.5 year span of orbits are also evaluated using tracking data residual analysis, GFO altimeter crossover residual analysis, and direct orbit comparison. In an effort to improve the current POE orbit several ideas are considered, including using recent gravity models which include CHAMP data, the reduced-dynamic approach, and including TOPEX/GFO altimeter crossover data in the orbit solution.

Lemoine, Frank G.↗
NASA NTRS2005

Synergy Between Entry Probes and Orbiters

We identify two catagories of probe-orbiter interactions which benefit the science return from a particular mission. The first category is termed "Mission Design Aspects". This category is meant to describe those aspects of the mission design involving the orbiter that affect the science return from the probe(s). The second category of probe-orbiter interaction is termed "Orbiter-Probe Science Interactions", and is meant to include interactions between oribter and probe(s) that directly involve science measurements made from each platform. Two mission related aspects of probe-orbiter interactions are delivery of a probe(s) to the entry site(s) by an orbiter, and communication between each probe and the orbiter. We consider four general probe-orbiter science interactions that greatly enhance, or in certain cases are essential for, the mission science return. The four topics are, global context of the probe entry site(s), ground truth for remote sensing observations of an orbiter, atmospheric composition measurements, and wind measurements.

Young, Richard E.↗
NASA NTRS2007

Titan Orbiter with Aerorover Mission (TOAM)

We propose to develop a new mission to Titan called Titan Orbiter with Aerorover Mission (TOAM). This mission is motivated by the recent discoveries of Titan, its atmosphere and its surface by the Huygens Probe, and a combination of in situ, remote sensing and radar mapping measurements of Titan by the Cassini orbiter. Titan is a body for which Astrobiology (i.e., prebiotic chemistry) will be the primary science goal of any future missions to it. TOAM is planned to use an orbiter and balloon technology (i.e., aerorover). Aerobraking will be used to put payload into orbit around Titan. One could also use aerobraking to put spacecraft into orbit around Saturn first for an Enceladus phase of the mission and then later use aerocapture to put spacecraft into orbit around Titan. The Aerorover will probably use a hot air balloon concept using the waste heat from the MMRTG approx. 1000 watts. Orbiter support for the Aerorover is unique to our approach for Titan. Our strategy to use an orbiter is contrary to some studies using just a single probe with balloon. Autonomous operation and navigation of the Aerorover around Titan will be required, which will include descent near to the surface to collect surface samples for analysis (i.e., touch and go technique). The orbiter can provide both relay station and GPS roles for the Aerorover. The Aerorover will have all the instruments needed to sample Titan's atmosphere, surface, possible methane lakes-rivers, use multi-spectral imagers for surface reconnaissance; to take close up surface images; take core samples and deploy seismometers during landing phase. Both active and passive broadband remote sensing techniques will be used for surface topography, winds and composition measurements.

Sittler, E. C., Jr.↗
NASA NTRS2007

Optimisation of the Future Routine Orbit for Mars Express

Mars Express (MEX), the first planetary mission of the European Space Agency (ESA), reached Mars on December 25th 2003. Since then it is performing routine operations. Its operational phase had to cover one Martian year, with the possibility of an extension for a second Martian year (i.e. until November 2007). The end of the mission extension is approaching but, given the good health of the payload instruments and the high science return of the mission, there is a strong will to achieve further extensions. Mars Express is also seen as an important asset, capable to provide relay functions for future Martian missions. The ESA Science Program Committee has recently approved a second extension of the MEX mission until May 2009 and even further extensions are possible. Mars Express has an eccentric quasi-polar orbit with a period of approximately 6.72 hours and a pericentre height of about 300 km. Science observations are mainly performed at pericentre (but not only). In addition the orbit has a resonance of 11 revolutions per 3 Martian days. This means that ground tracks corresponding to orbits separated by 11 revolutions are adjacent, such that a given area can be covered by the on-board camera without leaving gaps. The J2 effect of Mars causes a drift of both ascending node and argument of pericentre. The drift of argument of pericentre makes it possible to observe periodically all Mars latitudes from close distance. Illumination conditions at pericentre are influenced by both the drift of the argument of pericentre and the drift of ascending node, as well as by the rotation of Mars around the Sun. The original MEX routine orbit was optimized for the duration of the nominal mission and extension, such that it produced a balanced share of day-side observations (for the optical instruments) and night-side observations (for the radar). The orbit was thus not optimized for the time beyond the assumed extension. Indeed, the evolution of the ascending node and argument of pericentre would cause in the following years a drift of the pericentre towards night-side observation conditions, hence uninteresting for the optical instruments. In order to prevent this an optimisation process for the future routine orbit has taken place. The share between day-side and night-side observations can be controlled by adjusting the drift of argument of pericentre and ascending node. This can in particular be achieved by changing the semimajor axis, eccentricity and/or inclination. A change of inclination is inefficient compared to a change in semimajor axis and eccentricity, and has therefore been discarded. An in-plane maneuvre can be performed to change both semi-major axis and eccentricity, and thus the period of the orbit. Although an apocentre manoeuvre is cheaper in terms of deltaV, it would result in raising the pericentre height, which is unfavourable for close observations. Hence a pericentre manoeuvre is proposed, which will increase the apocentre height. A repeat cycle is still required to allow mapping areas with adjacent ground tracks, so the change of semimajor axis must result in a new resonance. Resonances 18:5, 25:7 and 7:2 have been considered as potential candidates. The resulting long term evolution of the observation conditions has been analysed. Finally it has been decided to perform a change of orbit to reach the 18:5. Another aspect of the optimisation process is the control of the ground track. The previous MEX reference trajectory included regular maneuvres at every apocentre in order to adjust the orbital period, such that the separation of the ground tracks would be optimal, regardless of the latitude of pericentre. The implementation of the actual delatVs on-board was done partly by optimizing the attitude of reaction-wheel desaturation activities. Despite of it, this strategy has a significant propellant cost, because it prevents to optimize reaction wheel de-saturation activities to minimize propellant consumption. Therore, with the aim at preserving propellant resources for a long time extension it has been agreed to stop the ground-track control. This requires now a more accurate science operation planning, with improved attitude pointing control. Finally, the approach to phase Mars Express to provide back-up relay functions for NASA Phoenix landing is explained. In the context of the routine trajectory optimisation a new requirement for close fly-bys at Phobos, with different observation geometries, has been specified. The approach to fulfill this requirement is explained.

Carranza, Manuel↗
NASA NTRS2007

Spaceborne Autonomous and Ground Based Relative Orbit Control for the TerraSAR-X/TanDEM-X Formation

TerraSAR-X (TSX) and TanDEM-X (TDX) are two advanced synthetic aperture radar (SAR) satellites flying in formation. SAR interferometry allows a high resolution imaging of the Earth by processing SAR images obtained from two slightly different orbits. TSX operates as a repeat-pass interferometer in the first phase of its lifetime and will be supplemented after two years by TDX in order to produce digital elevation models (DEM) with unprecedented accuracy. Such a flying formation makes indeed possible a simultaneous interferometric data acquisition characterized by highly flexible baselines with range of variations between a few hundreds meters and several kilometers [1]. TSX has been successfully launched on the 15th of June, 2007. TDX is expected to be launched on the 31st of May, 2009. A safe and robust maintenance of the formation is based on the concept of relative eccentricity/inclination (e/i) vector separation whose efficiency has already been demonstrated during the Gravity Recovery and Climate Experiment (GRACE) [2]. Here, the satellite relative motion is parameterized by mean of relative orbit elements and the key idea is to align the relative eccentricity and inclination vectors to minimize the hazard of a collision. Previous studies have already shown the pertinence of this concept and have described the way of controlling the formation using an impulsive deterministic control law [3]. Despite the completely different relative orbit control requirements, the same approach can be applied to the TSX/TDX formation. The task of TDX is to maintain the close formation configuration by actively controlling its relative motion with respect to TSX, the leader of the formation. TDX must replicate the absolute orbit keeping maneuvers executed by TSX and also compensate the natural deviation of the relative e/i vectors. In fact the relative orbital elements of the formation tend to drift because of the secular non-keplerian perturbations acting on both satellites. The goal of the ground segment is thus to regularly correct this configuration by performing small orbit correction maneuvers on TDX. The ground station contacts are limited due to the geographic position of the station and the costs for contact time. Only with a polar ground station a contact visibility is possible every orbit for LEO satellites. TSX and TDX use only the Weilheim ground station (in the southern part of Germany) during routine operations. This station allows two scheduled contact per day for the nominal orbit configuration, meaning that the satellite conditions can be checked with an interval of 12 hours. While this limitation is usually not critical for single satellite operations, the visibility constraints drive the achievable orbit control accuracy for a LEO formation if a ground based approach is chosen. Along-track position uncertainties and maneuver execution errors affect the relative motion and can be compensated only after a ground station contact.

Ardaens, J. S.↗
NASA NTRS2008

Optical Studies of Orbital Debris at GEO Using Two Telescopes

Beginning in March, 2007, optical observations of debris at geosynchronous orbit (GEO) were commenced using two telescopes simultaneously at the Cerro Tololo Inter-American Observatory (CTIO) in Chile. The University of Michigan's 0.6/0.9-m Schmidt telescope MODEST (for Michigan Orbital DEbris Survey Telescope) was used in survey mode to find objects that potentially could be at GEO. Because GEO objects only appear in this telescope's field of view for an average of 5 minutes, a full six-parameter orbit can not be determined. Interrupting the survey for follow-up observations leads to incompleteness in the survey results. Instead, as objects are detected on MODEST, initial predictions assuming a circular orbit are done for where the object will be for the next hour, and the objects are reacquired as quickly as possible on the CTIO 0.9-m telescope. This second telescope then follows-up during the first night and, if possible, over several more nights to obtain the maximum time arc possible, and the best six parameter orbit. Our goal is to obtain an initial orbit for all detected objects fainter than R = 15th in order to estimate the orbital distribution of objects selected on the basis of two observational criteria: magnitude and angular rate. Objects fainter than 15th are largely uncataloged and have a completely different angular rate distribution than brighter objects. Combining the information obtained for both faint and bright objects yields a more complete picture of the debris environment rather than just concentrating on the faint debris. One objective is to estimate what fraction of objects selected on the basis of angular rate are not at GEO. A second objective is to obtain magnitudes and colors in standard astronomical filters (BVRI) for comparison with reflectance spectra of likely spacecraft materials. This paper reports on results from two 14 night runs with both telescopes: in March and November 2007: (1) A significant fraction of objects fainter than R = 15th have eccentric orbits (e > 0.1) (2) Virtually all objects selected on the basis of angular rate are in the GEO and GTO regimes. (3) Calibrated magnitudes and colors in BVRI were obtained for many objects fainter than R = 15th magnitude. This work is supported by NASA's Orbital Debris Program Office, Johnson Space Center, Houston, Texas, USA.

Seitzer, P.↗