Orbit Determination

An improved Earth geopotential model, complete to spherical harmonic degree and order 70, has been determined by combining the Joint Gravity Model 1 (JGM 1) geopotential coefficients, and their associated error covariance, with new information from SLR, DORIS, and GPS tracking of TOPEX/Poseidon, laser tracking of LAGEOS 1, LAGEOS 2, and Stella, and additional DORIS tracking of SPOT 2. The resulting field, JGM 3, which has been adopted for the TOPEX/Poseidon altimeter data rerelease, yields improved orbit accuracies as demonstrated by better fits to withheld tracking data and substantially reduced geographically correlated orbit error. Methods for analyzing the performance of the gravity field using high-precision tracking station positioning were applied. Geodetic results, including station coordinates and Earth orientation parameters, are significantly improved with the JGM 3 model. Sea surface topography solutions from TOPEX/Poseidon altimetry indicate that the ocean geoid has been improved. Subset solutions performed by withholding either the GPS data or the SLR/DORIS data were computed to demonstrate the effect of these particular data sets on the gravity model used for TOPEX/Poseidon orbit determination.

The TOPEX/POSEIDON (T/P) prelaunch Joint Gravity Model-1 (JGM-1) and the postlaunch JGM-2 Earth gravitational models have been developed to support precision orbit determination for T/P. Each of these models is complete to degree 70 in spherical harmonics and was computed from a combination of satellite tracking data, satellite altimetry, and surface gravimetry. While improved orbit determination accuracies for T/P have driven the improvements in the models, the models are general in application and also provide an improved geoid for oceanographic computations. The postlaunch model, JGM-2, which includes T/P satellite laser ranging (SLR) and Doppler orbitography and radiopositioning integrated by satellite (DORIS) tracking data, introduces radial orbit errors for T/P that are only 2 cm RMS with the commission errors of the marine geoid for terms to degree 70 being + 25 cm. Errors in modeling the nonconservative forces acting on T/P increase the total radial errors to only 3-4 cm RMS, a result much better than premission goals. While the orbit accuracy goal for T/P has been far surpassed, geoid errors still prevent the absolute determination of the ocean dynamic topography for wavelengths shorter than about 2500 km. Only a dedicated gravitational field satellite mission will likely provide the necessary improvement in the geoid. Lerch et al. [1993b]. Additional models which have been [Lerch et al., 1979] and GEM-L2 [Lerch et al., 1982], were developed outside of the T/P effort are GRIM4-C3 [Schwintzer et al., 1991], OSU89A/B [Rapp and Pavlis, 1990], and OSU91A [Rapp et aI., 1991]. Herein we describe the final results of this research effort, the prelaunch field Joint Gravity Model-1 (JGM-1, also in honor of our late colleague James G. Marsh), and the postlaunch field JGM-2, which differs from JGM-1 principally through the addition of T/P tracking data. Orbit determination can be simply stated as the adjustment of the orbit state, force, and measurement model parameters to minimize, in a least squares sense, the weighted difference between the actual tracking observations and their predicted values. Clearly, the accuracy of the computed orbit will depend on the accuracy and completeness of the force models, the measurement models, and the tracking data. In principle, T/P contains five tracking systems which can be used for determining its orbit [Nerem et al., 1993a]: (1) satellite laser ranging (SLR) [Degnan, 1993]; (2) Doppler orbitography and radiopo-24,421 24,422 NEREM ET AL: GRAVITY MODEL DEVELOPMENT FOR TOPEX/POSEIDON sitioning integrated by satellite (DORIS) tracking data [Nouel et at., 1988; Cazenave et at., 1992]; (3) Global Positioning System (GPS) tracking data [Bertiger et at., this issue; Melbourne et at.[Schanzte et at., 1992]; and (5) the satellite altimeter measurements themselves [e.g., Taptey et at., 1988; Nerem et at., 1990; Marsh et at., 1990b]. For the orbits which the National Aeronautics and Space Administration/Goddard Space Flight Center (NASA/GSFC) computes for the T/P altimeter geophysical data records (GDRs), only the well-tested and ocean-surfaceindependent SLR and DORIS data types are being used initially. The SLR and DORIS data are complementary; the SLR data provide precise slant-range information from a global set of tracking stations which are somewhat limited in geographic extent; the DORIS data provide precise line-of-sight velocity information from an extensive global network of stations which track the satellite nearly continuously. Both of these data types have in the past been very important for determining the gravity field; the use of these data types for T/P directly in the gravity solution provides extensive sensing of gravitational effects specific to the T/P orbit, such as long-term zonal, mdaily, and resonant perturbations [Kauta, 1966]. As indicated in the orbit determination error budget [Stewart et at., 1986; Taptey et at., this issue], precise modeling of the Earth's gravitational field was only one of many activities neeessary to meet the stringent requirements for T/P. The precise modeling of nonconservative forces due to solar/Earth radiation pressure, thermal imbalances, atmospheric drag, and spacecraft emissions required intensive parallel study [Marshall and Luthcke, 1994; Nerem et at., 1993a] and resulted in the development of a complex box-wing model describing the forces acting on each plate of a rectangular spacecraft model (the box) and the solar array (the wing). A subset of parameters describing the box-wing model were solved for simultaneously with the gravity field coefficients in the JGM-2 solution. The high-quality precision orbit determination results using SLR/DORIS tracking data, the box-wing nonconservative force model, and the JGM-2 gravity model are extensively discussed by Taptey et at. [this issue].

We demonstrate sensing of integrated slant-path water vapor (SWV) along ray paths between Global Positioning System (GPS) satellites and receivers. We use double differencing to remove GPS receiver and satellite clock errors and 85-cm diameter choke ring antennas to reduce ground-reflected multipath. We compare more than 17,000 GPS and pointed radiometer double difference observations above 20 o elevation and find 1.3 mm rms agreement. Potential applications for SWV data include local and regional weather modeling and prediction, correction for slant wet delay effects in GPS surveying and orbit determination, and synthetic aperture radar (SAR) imaging. The method is viable during all weather conditions.

The thermal and electrical conductivity probe (TECP), a component of the Microscopy, Electrochemistry, and Conductivity Analyzer (MECA), was included on the Phoenix Lander to conduct in situ measurements of the exchange of heat and water in the Martian polar terrain. TECP measured regolith thermal conductivity, heat capacity, temperature, electrical conductivity, and dielectric permittivity throughout the mission. A relative humidity sensor returned the first in situ humidity measurements from the Martian surface. The dry overburden above the ground ice is a good thermal insulator (average = 0.085 W m −1 K −1 and average Cr = 1.05 × 10 6 J m −3 K −1). Surface thermal inertia (I) calculated from these values agrees well with daytime orbital determinations, but differences in the spatial and temporal scale of heat transport lead to very different measurements at night. Electrical conductivity was consistent with open circuit throughout the mission; an upper limit conductivity of 2 nS cm −1 is derived. Bulk dielectric permittivity (" b) shows several puzzling signals but also a systematic increase overnight in the latter half of the mission, contemporaneous with H 2 O adsorption. The magnitude of the increase is difficult to reconcile with expected changes in unfrozen water. Atmospheric H 2 O averages around 1.8 Pa during the day, corresponding to a R H < 5%. At night, much of the H 2 O disappears from the atmosphere, and R H increases to ∼100%. Temperature and H 2 O partial pressure data suggest that adsorption on mineral surfaces plays a major role in scrubbing H 2 O, with a possible contribution from perchlorate salts.

Arecibo delay-Doppler measurements of (99942) Apophis in 2005 and 2006 resulted in a five standard-deviation trajectory correction to the optically predicted close approach distance to Earth in 2029. The radar measurements reduced the volume of the statistical uncertainty region entering the encounter to 7.3% of the pre-radar solution, but increased the trajectory uncertainty growth rate across the encounter by 800% due to the closer predicted approach to the Earth. A small estimated Earth impact probability remained for 2036. With standard-deviation planeof-sky position uncertainties for 2007-2010 already less than 0.2 arcsec, the best near-term ground-based optical astrometry can only weakly affect the trajectory estimate. While the potential for impact in 2036 will likely be excluded in 2013 (if not 2011) using ground-based optical measurements, approximations within the Standard Dynamical Model (SDM) used to estimate and predict the trajectory from the current era are sufficient to obscure the difference between a predicted impact and a miss in 2036 by altering the dynamics leading into the 2029 encounter. Normal impact probability assessments based on the SDM become problematic without knowledge of the object's physical properties; impact could be excluded while the actual dynamics still permit it. Calibrated position uncertainty intervals are developed to compensate for this by characterizing the minimum and maximum effect of physical parameters on the trajectory. Uncertainty in accelerations related to solar radiation can cause between 82 and 4720 Earth-radii of trajectory change relative to the SDM by 2036. If an actionable hazard exists, alteration by 2-10% of Apophis' total absorption of solar radiation in 2018 could be sufficient to produce a six standard-deviation trajectory change by 2036 given physical characterization; even a 0.5% change could produce a trajectory shift of one Earth-radius by 2036 for all possible spin-poles and likely masses. Planetary ephemeris uncertainties are the next greatest source of systematic error, causing up to 23 Earth-radii of uncertainty. The SDM Earth point-mass assumption introduces an additional 2.9 Earth-radii of prediction error by 2036. Unmodeled asteroid perturbations produce as much as 2.3 Earth-radii of error. We find no future small-body encounters likely to yield an Apophis mass determination prior to 2029. However, asteroid (144898) 2004 VD17, itself having a statistical Earth impact in 2102, will probably encounter Apophis at 6.7 lunar distances in 2034, their uncertainty regions coming as close as 1.6 lunar distances near the center of both SDM probability distributions. (J.D. Giorgini).

First results are presented from a newly developed meteoroid orbit survey, called CAMS -Cameras for Allsky Meteor Surveillance, which combines meteor detection algorithms for low-light video observations with traditional video surveillance tools. Sixty video cameras at three stations monitor the sky above 31°elevation. Goal of CAMS is to verify meteor showers in search of their parent comets among newly discovered near-Earth objects.

We present the results on precision orbit determination from the radio science investigation of the Lunar Reconnaissance Orbiter (LRO) spacecraft. We describe the data, modeling and methods used to achieve position knowledge several times better than the required 50-100 m (in total position), over the period from 13 July 2009 to 31 January 2011. In addition to the near-continuous radiometric tracking data, we include altimetric data from the Lunar Orbiter Laser Altimeter (LOLA) in the form of crossover measurements, and show that they strongly improve the accuracy of the orbit reconstruction (total position overlap differences decrease from ∼70 m to ∼23 m). To refine the spacecraft trajectory further, we develop a lunar gravity field by combining the newly acquired LRO data with the historical data. The reprocessing of the spacecraft trajectory with that model shows significantly increased accuracy (∼20 m with only the radiometric data, and ∼14 m with the addition of the altimetric crossovers). LOLA topographic maps and calibration data from the Lunar Reconnaissance Orbiter Camera were used to supplement the results of the overlap analysis and demonstrate the trajectory accuracy.

In this paper we assess the precision and accuracy of interstation vectors determined using the Global Positioning System (GPS) satellites. These vectors were between stations in California separated by 50-450 kin. Using data from tracking the seven block I satellites in campaigns from 1986 through 1989, we examine the precision of GPS measurements over time scales of a several days and a few years. We characterize GPS precision by constant and length dependent terms. The north-south component of the interstation vectors has a short-term precision of 1.9 mm + 0.6 parts in 10s; the east-west component shows a similar precision at the shortest distances, 2.1 ram, with a larger length dependence, 1.3 parts in 10 s. The vertical precision has a mean value of 17 ram, with no clear length dependence. For long-term precision, we examine interstation vectors measured over a period of 2.2 to 2.7 years. When we include the recent results of Davis et al.

The first ESA (European Space Agency) Earth explorer core mission GOCE (Gravity field and steady-state Ocean Circulation Explorer) was launched on 17 March 2009 into a sun-synchronous dusk-dawn orbit with an exceptionally low initial altitude of about 280 km. The onboard 12channel dual-frequency GPS (Global Positioning System) receiver delivers 1 Hz data, which provides the basis for precise orbit determination (POD) for such a very low orbiting satellite. As part of the European GOCE Gravity Consortium the Astronomical Institute of the University of Bern and the Department of Earth Observation and Space Systems are responsible for the orbit determination of the GOCE satellite within the GOCE High-level Processing Facility. Both quicklook (rapid) and very precise orbit solutions are produced with typical latencies of 1 day and 2 weeks, respectively. This article summarizes the special characteristics of the GOCE GPS data, presents POD results for about 2 months of data, and shows that both latency and accuracy requirements are met. Satellite Laser Ranging validation shows that an accuracy of 4 and 7 cm is achieved for the reduced-dynamic and kinematic Rapid Science Orbit solutions, respectively. The validation of the reduced-dynamic and kinematic Precise Science Orbit solutions is at a level of about 2 cm.

We present a new orbit determination method, termed statistical ranging, applicable to poorly observed single-apparition asteroids having two or more observations. We examine the Bayesian a posteriori probability density of the orbital elements using a Monte Carlo technique that maps an unbiased hypervolume in element phase space. We select two observations randomly from the full set, and after introducing random deviations to the observations and generating random topocentric ranges (distances), compute a sample orbit from the Cartesian positions available. Repeating the procedure allows us to obtain a large set of orbital elements compatible with the observations. To distinguish between realistic and unrealistic orbit solutions, we can incorporate the three-or four-dimensional distribution of semimajor axes, eccentricities, inclinations, and, in some cases, the absolute magnitudes of multi-apparition asteroids as a priori information in the Bayesian technique. The application of the method to both near-Earth and main-belt asteroids clearly indicates that there may exist a broad variety of orbits, all of which are compatible with the observations. The resulting distributions of the orbital elements allow recovery attempts for lost asteroids and linkage to existing observations of single-apparition asteroids. The Bayesian approach can prove useful in constraining the broad distribution of orbits for problematic newly discovered asteroids. c 2001 Elsevier Science (USA)

The objective of the Lunar Reconnaissance Orbiter (LRO) Laser Ranging (LR) system is to collect precise measurements of range that allow the spacecraft to achieve its requirement for precision orbit determination. The LR will make one-way range measurements via laser pulse time-of-flight from Earth to LRO, and will determine the position of the spacecraft at a sub-meter level with respect to ground stations on Earth and the center of mass of the Moon. Ranging will occur whenever LRO is visible in the line of sight from participating Earth ground tracking stations. The LR consists of two primary components, a flight system and ground system. The flight system consists of a small receiver telescope mounted on the LRO high-gain antenna that captures the uplinked laser signal, and a fiber optic cable that routes the signal to the Lunar Orbiter Laser Altimeter (LOLA) instrument on LRO. The LOLA instrument receiver records the time of the laser signal based on an ultrastable crystal oscillator, and provides the information to the onboard LRO data system for storage and/or transmittal to the ground through the spacecraft radio frequency link. The LR ground system consists of a network of satellite laser ranging stations, a data reception and distribution facility, and the LOLA Science Operations Center. LR measurements will enable the determination of a three-dimensional geodetic grid for the Moon based on the precise seleno-location of ground spots from LOLA.

The amplitude and variability of the total mass density of the Earth's atmosphere at altitudes between 200 and 475 km are analyzed for the period from June 1999 to January 2003, around the maximum of solar activity in cycle 23. The densities are derived with uncertainties of order ±6% from analysis of the approximately circular orbits of three Starshine spacecraft of known ballistic coefficients. Local densities averaged over all three Starshine missions are $4% lower than the corresponding NRLMSISE-00 model values, which may reflect a secular decrease from thermospheric cooling. Differences of order ±15% occur on timescales of days to weeks, and larger differences of as much as 30% can persist on timescales of several months. Some differences are traceable to the NRLMSIS model's use of the 10.7 cm proxy of EUV radiation, since they are reduced when NRLMSIS is evaluated using the Mg II index, which is a better proxy of variations in EUV irradiance that heats the thermosphere. Comparisons of 27-day density cycles extracted by complex demodulation indicate that NRLMSIS underestimates upper atmospheric density increases associated with solar rotational modulation of EUV radiation by as much as a factor of two.

This paper discusses the motivation and general design elements of a new fundamental physics experiment that will test relativistic gravity at the accuracy better than the effects of the second order in the gravitational field strength, ∝ G 2 . The Laser Astrometric Test Of Relativity (LATOR) mission uses laser interferometry between two micro-spacecraft whose lines of sight pass close by the Sun to accurately measure deflection of light in the solar gravity. The key element of the experimental design is a redundant geometry optical truss provided by a long-baseline (100 m) multi-channel stellar optical interferometer placed on the International Space Station (ISS). The spatial interferometer is used for measuring the angles between the two spacecraft and for orbit determination purposes. In Euclidean geometry, determination of a triangle's three sides determines any angle therein; with gravity changing the optical lengths of sides passing close by the Sun and deflecting the light, the Euclidean relationships are overthrown. The geometric redundancy enables LATOR to measure the departure from Euclidean geometry caused by the solar gravity field to a very high accuracy.

The TOPEX/Poseidon, Jason-1 and Jason-2 set of altimeter data now provide a time series of synoptic observations of the ocean that span nearly 17 years from the launch of TOPEX in 1992. The analysis of the altimeter data including the use of altimetry to monitor the global change in mean sea level requires a stable, accurate, and consistent orbit reference over the entire time span. In this paper, we describe the recomputation of a time series of orbits that rely on a consistent set of reference frames and geophysical models. The recomputed orbits adhere to the IERS 2003 standards for ocean and earth tides, use updates to the ITRF2005 reference frame for both the SLR and DORIS stations, apply GRACE-derived models for modeling of the static and time-variable gravity, implement the University College London (UCL) radiation pressure model for Jason-1, use improved troposphere modeling for the DORIS data, and apply the GOT4.7 ocean tide model for both dynamical ocean tide modeling and for ocean loading. The new TOPEX orbits have a mean SLR fit of 1.79 cm compared to 2.21 cm for the MGDR-B orbits. These new TOPEX orbits agree radially with independent SLR/crossover orbits at 0.70 cm RMS, and the orbit accuracy is estimated at 1.5-2.0 cm RMS over the entire TOPEX time series. The recomputed Jason-1 orbits agree radially with the Jason-1 GDR-C orbits at 1.08 cm RMS. The GSFC SLR/DORIS dynamic and reduced-dynamic orbits for Jason-2 agree radially with independent orbits from the CNES and JPL at 0.70-1.06 cm RMS. Applying these new orbits, and using the latest altimeter corrections for TOPEX, Jason-1, and Jason-2 from September 1992 to May 2009, we find a global rate in mean sea level of 3.0 ± 0.4 mm/yr. Published by Elsevier Ltd. on behalf of COSPAR.

Apart from the gradiometer as the core instrument, the first ESA Earth Explorer Core Mission GOCE (Gravity field and steady-state Ocean Circulation Explorer) will carry a 12-channel GPS receiver dedicated for precise orbit determination (POD) of the satellite. The EGG-C (European GOCE Gravity-Consortium), led by the Technical University in Munich, is building the GOCE HPF (High-level Processing Facility) dedicated to the Level 1b to Level 2 data processing. One of the tasks of this facility is the computation of the Precise Science Orbit (PSO) for GOCE. The PSO includes a reduced-dynamic and a kinematic orbit solution. The baseline for the PSO is a zero-difference procedure using GPS satellite orbits, clocks, and Earth Rotation Parameters (ERPs) from CODE (Center for Orbit Determination in Europe), one of the IGS (International GNSS Service) Analysis Centers. The scheme for reduced-dynamic and kinematic orbit determination is based on experiences gained from CHAMP and GRACE POD and is realized in one processing flow. Particular emphasis is put on maximum consistency in the analysis of day boundary overlapping orbital arcs, as well as on the higher data sampling rate with respect to CHAMP and GRACE and on differences originating from different GPS antenna configurations. We focus on the description of the procedure used for the two different orbit determinations and on the validation of the procedure using real data from the two GRACE satellites as well as simulated GOCE data.

This paper studies the relative orbital motion between arbitrary Keplerian trajectories. A closed-form vectorial solution to the nonlinear initial value problem that models this type of motion with respect to a noninertial reference frame is offered. Without imposing any particular conditions on the leader or the deputy satellites trajectories, exact expressions for the relative law of motion and relative velocity are obtained in a closed form. This solution allows the parameterization of the relative motion manifold and offers new methods to study its geometrical and topological properties. The result presented in this paper opens the way to obtain new classes of approximate solutions to the equations of relative motion with time, an eccentric or true anomaly as independent variables.

We describe the Multiple Solutions Method, a one-dimensional sampling of the six-dimensional orbital confidence region that is widely applicable in the field of asteroid orbit determination. In many situations there is one predominant direction of uncertainty in an orbit determination or orbital prediction, i.e., a "weak" direction. The idea is to record Multiple Solutions by following this, typically curved, weak direction, or Line Of Variations (LOV). In this paper we describe the method and give new insights into the mathematics behind this tool. We pay particular attention to the problem of how to ensure that the coordinate systems are properly scaled so that the weak direction really reflects the intrinsic direction of greatest uncertainty. We also describe how the multiple solutions can be used even in the absence of a nominal orbit solution, which substantially broadens the realm of applications. There are numerous applications for multiple solutions; we discuss a few problems in asteroid orbit determination and prediction where we have had good success with the method. In particular, we show that multiple solutions can be used effectively for potential impact monitoring, preliminary orbit determination, asteroid identification, and for the recovery of lost asteroids.

A long-term adaptive optics (AO) campaign of observing the double Asteroid (90) Antiope has been carried out in 2003-2005 using 8-10-m class telescopes, allowing prediction of the circumstances of mutual events occurring during the July 2005 opposition [Marchis, F., Descamps, P., Hestroffer, D., Berthier, J., . Bull. Am. Astron. Soc. 36, 1180. This is the first opportunity to use complementary lightcurve and AO observations to extensively study the (90) Antiope system, an interesting visualized binary doublet system located in the main belt. The orbital parameters derived from the AO observations have served as input quantities for the derivation of a whole set of other physical parameters (namely shapes, surface scattering, bulk density, and internal properties) from analysis of collected lightcurves. To completely model the observed lightcurves, we employed Roche figures to construct an overall shape solution. The combination of these complementary observations has enabled us to derive a reliable physical and orbital solution for the system. Our model is consistent with a system of slightly non-spherical components, having a size ratio of 0.95 (with R avg = 42.9 ± 0.5 km, separation = 171 ± 1 km), and exhibiting equilibrium figures for homogeneous rotating bodies. A comparison with grazing occultation event lightcurves suggests that the real shapes of the components do not depart from Roche equilibrium figures by more than 10%. The J2000 ecliptic coordinates of the pole of the system are λ n = 200 • ± 2 • and α n = 38 • ± 2 • . The orbital period was refined to P = 16.5051 ± 0.0001 h, and the density is found to be slightly lower than previous determinations, with a value of 1.25 ± 0.05 g/cm 3 , leading to a significant macro-porosity of 30%. Possible scenarios for the origin of the system are also discussed.

We present a new orbital model of Saturn's F ring core based on 93 occultations by the Cassini Ultraviolet Imaging Spectrograph (UVIS) and the Voyager radio and stellar occultations. We demonstrate that the core, despite its intrinsic variability, is well-described as an inclined, freely precessing ellipse. We find that post-fit residuals with a root-mean-square of 24 km are genuine, representing the well-known non-Keplerian features observed in the ring. Over the nearly 4 years of UVIS observations we find the residual variance to increase, coincident with the apse anti-alignment of Prometheus and F ring core in December 2009. This increase in dynamical F ring core temperature most likely reflects the ever-stronger perturbations by Prometheus. Our results are in good agreement with Earth-based and HST observations as well as Voyager imaging. Cassini UVIS stellar occultations resolve the F ring at unprecedented resolutions of a few meters and we identify the F ring core and inner and outer strands. We infer their normal optical depth and full width at half maximum (FWHM) and show that core and strands form distinct morphological groups. Typically, a strand is about ten times wider than the core (average FWHM is $10 km) while having a ten times smaller optical depth. Unlike in pre-Cassini occultations the F ring core displays significant optical depth with in some cases >3. In many cases we find a narrow optically thick component ($ few km and s > 0.5) embedded in the F ring core. Entertaining the possibility that this is the actual, ''true'' F ring core then UVIS results suggest that this ''true'' core is highly non-continuous. In addition, we report the detection of a previously unknown structure-dubbed the ''secondary'' as it visually resembles the F ring core. Its morphology is similar to that of the core in optical depth and FWHM and it displays individual opaque features. Despite its core-like appearance, we show that its kinematics is consistent with that of strands. We conclude that it is the most prominent strand seen to date. It represents a striking example of strand creation resulting in what could be called a morphological ''small-scale'' version of the F ring core. This extraordinary object should be one of the prime targets of future F ring studies.

A technique for the analysis of low-low intersatellite range-rate data in a gravity mapping mission is explored. The technique is based on standard tracking data analysis for orbit determination but uses a spherical coordinate representation of the 12 epoch state parameters describing the baseline between the two satellites. This representation of the state parameters is exploited to allow the intersatellite range-rate analysis to benefit from information provided by other tracking data types without large simultaneous multiple-datatype solutions. The technique appears especially valuable for estimating gravity from short arcs (e.g. less than 15 minutes) of data. Gravity recovery simulations which use short arcs are compared with those using arcs a day in length. For a high-inclination orbit, the short-arc analysis recovers low-order gravity coefficients remarkably well, although higher-order terms, especially sectorial terms, are less accurate. Simulations suggest that either long or short arcs of the Gravity Recovery and Climate Experiment (GRACE) data are likely to improve parts of the geopotential spectrum by orders of magnitude.

Using 8m-10m class telescopes and their Adaptive Optics (AO) systems, we conducted a long-term adaptive optics campaign initiated in 2003 focusing on four binary asteroid systems: (130) Elektra, (283) Emma, (379) Huenna, and (3749) Balam. The analysis of these data confirms the presence of their asteroidal satellite. We did not detect any additional satellite around these systems even though we have the capability of detecting a loosely-bound fragment (located at 1/4 × R Hill ) ~40 times smaller in diameter than the primary. The orbits derived for their satellites display significant eccentricity, ranging from 0.1 to 0.9, suggesting a different origin. Based on AO size estimate, we show that (130) Elektra and (283) Emma, G-type and P-type asteroids respectively, have a significant porosity (30-60% considering CI-CO meteorites as analogs) and their satellite's eccentricities (e~0.1) are possibly due to excitation by tidal effects. Huenna and (3749) Balam, two loosely bound binary systems, are most likely formed by mutual capture. (3749) Balam's possible high bulk density is similar to (433) Eros, another S-type asteroid, and should be poorly fractured as well. (379) Huenna seems to display both characteristics: the moonlet orbits far away from the primary in term of stability (20% × R Hill ), but the primary's porosity is significant (30-60%).

In the framework of its space debris research activities ESA established an optical survey program to study the space debris environment at high altitudes, in particular in the geostationary ring and in the geostationary transfer orbit region. The Astronomical Institute of the University of Bern (AIUB) performs these surveys on behalf of ESA using ESA's 1-m telescope in Tenerife. Regular observations were started in 1999 and are continued during about 120-140 nights per year. Results from these surveys revealed a substantial amount of space debris at high altitudes in the size range from 0.1 to 1 m. Several space debris populations with different dynamical properties were identified in the geostationary ring. During the searches for debris in the geostationary transfer orbit region a new population of objects in unexpected orbits, where no potential progenitors exist, was found. The orbital periods of these objects are clustered around one revolution per day; the eccentricities, however, are scattered between 0 and 0.6. By following-up some of these objects using the ESA telescope and AIUB's 1-m telescope in Zimmerwald, Switzerland, it was possible to study the properties of this new population. One spectacular finding from monitoring the orbits over time spans of days to months is the fact that these objects must have extreme area-to-mass ratios, which are by several orders of magnitudes higher than for 'normal-type' debris. This in turn supports the hypothesis that the new population actually is debris generated in or near the geostationary ring and which is in orbits with periodically varying eccentricity and inclination due to perturbations by solar radiation pressure. In order to further study the nature of these debris, multi-color and temporal photometry (light curves) were acquired with the Zimmerwald telescope. The light curves show strong variations over short time intervals, including signals typical for specular reflections. Some objects exhibit distinct periodic variations with periods ranging from 10 to several 100 s. All this is indicative for objects with complicated shapes and some highly reflective surfaces.

An artificial satellite, flying in a purely gravitational field is a natural probe, such that, by a very accurate orbit determination, would allow a perfect estimation of the field. A true satellite experiences a number of perturbational, non-gravitational forces acting on the shell of the spacecraft; these can be revealed and accurately measured by a spaceborne accelerometer. If more accelerometers

Astrometric uncertainty is a crucial component of the asteroid orbit determination process. However, in the absence of rigorous uncertainty information, only very crude weighting schemes are available to the orbit computer. This inevitably leads to a correspondingly crude characterization of the orbital uncertainty and in many cases to less accurate orbits. In this paper we describe a method for carefully assessing the statistical performance of the various observatories that have produced asteroid astrometry, with the ultimate goal of using this statistical characterization to improve asteroid orbit determination. We also include a detailed description of our previously unpublished automatic outlier rejection algorithm used in the orbit determination, which is an important component of the fitting process.To start this study we have determined the best fitting orbits for the first 17,349 numbered asteroids and computed the corresponding OC astrometric residuals for all observations used in the orbit fitting. We group the residuals into roughly homogeneous bins and compute the root mean square (RMS) error and bias in declination and right ascension for each bin. Results are tabulated for each of the 77 bins containing more than 3000 observations; this comprises roughly two thirds of the data, but only 2% of the bins. There are several interesting results, including substantial bias from several observatories, and some distinct non-Gaussian characteristics that are difficult to explain. Several limitations of our approach and possible future improvements are discussed.The correlation of errors among observations taken closely together in time is in many cases an important issue that has rarely been considered. We have computed the mean correlation between observations with varying time separations and obtained empirical functions that model the results. This has been done for several observatories with very large data sets (the remainder has been lumped into a single mixed batch). These functions could be used for estimating correlation coefficients among different observations of the same observatory, supplying a new observation weighting scheme based upon an empirically tested observational error model.

Precise microwave tracking of interplanetary spacecraft has been a crucial tool in solar system exploration. Range and range rate measurements, the main observable quantities in spacecraft orbit determination and navigation, have been widely used to refine the dynamical model of the solar system and to probe planetary interiors. Thanks to the use of Ka-band and multifrequency radio links, a significant improvement in microwave tracking systems has been demonstrated by the radio science experiments of the Cassini mission to Saturn. The Cassini radio system has been used to carry out the most accurate test of general relativity to date. Further developments in the radio instrumentation have been recently started for the Mercury Orbiter Radio Experiment (MORE), selected for the ESA mission to Mercury, BepiColombo. MORE addresses the mission's scientific goals in geodesy, geophysics and fundamental physics. In addition, MORE will carry out a navigation experiment, aiming to a precise assessment of the orbit determination accuracies attainable with the use of the novel instrumentation. The key instrument is a Ka/Ka band digital transponder enabling a high phase coherence between uplink and downlink carriers and supporting a wideband ranging tone. The onboard instrumentation is complemented by a ground system based upon the simultaneous transmission and reception of multiple frequencies at X-and Ka-band. The new wideband ranging system is designed for an end-to-end accuracy of 20 cm using integration times of a few seconds. Two-way range rate measurements are expected to be accurate to 3 m/s, thanks to nearly complete cancellation or calibration of the propagation noise from interplanetary plasma and troposphere. We review the experimental configuration of the experiment and outline its scientific goals and expected results.

We study the orbital structure in a series of self-consistent N-body configurations simulating rotating barred galaxies with spiral and ring structures. We perform frequency analysis in order to measure the angular and the radial frequencies of the orbits at two different time snapshots during the evolution of each N-body system. The analysis is done separately for the regular and the chaotic orbits. We thereby identify the various types of orbits, determine the shape and percentages of the orbits supporting the bar and the ring/spiral structures, and study how the latter quantities change during the secular evolution of each system. Although the frequency maps of the chaotic orbits are scattered, we can still identify concentrations around resonances. We give the distributions of frequencies of the most important populations of orbits. We explore the phase space structure of each system using projections of the 4D surfaces of section. These are obtained via the numerical integration of the orbits of test particles, but also of the real N-body particles. We thus identify which domains of the phase space are preferred and which are avoided by the real particles. The chaotic orbits are found to play a major role in supporting the shape of the outer envelope of the bar as well as the rings and the spiral arms formed outside corotation.

When the observational data available are not enough to compute a meaningful orbit for an asteroid/comet we can represent the data with an attributable (containing two angles and their time derivatives); then the undetermined variables range and range rate span an admissible region of solar system orbits, which can be represented by a set of Virtual Asteroids (VAs) selected by means of an optimal triangulation ]. The attributable 4 coordinates are themselves the result of a fit and they have an uncertainty, represented by a covariance matrix. Thus the predictions of future observations can be described by a quasi-product structure (admissible region times confidence ellipsoid), which can be approximated by a triangulation with each node surrounded by a confidence ellipsoid.

DORIS is a French precise orbit determination system. However, in the past four years, through the creation of the International DORIS Service, a larger international cooperation was involved. Furthermore, the precision of its scientific applications (geodesy, geophysics) gradually improved and expanded to new fields (atmospheric sciences), leading, for example, to the publication of a special issue of the Journal of Geodesy. The goal of this manuscript is to present and explain these changes and to put them in perspective with current results obtained with other space geodetic techniques, such as GPS or Satellite Laser Ranging. To cite this article: P. Willis et al., C. R. Geoscience 339 . # 2007 Académie des sciences. Published by Elsevier Masson SAS. All rights reserved.

available online at http://meteoritics.org 1005 Abstract-The properties and history of the parent meteoroid of the Morávka H5-6 ordinary chondrites have been studied by a combination of various methods. The pre-atmospheric mass of the meteoroid was computed from fireball radiation, infrasound, seismic signal, and the content of noble gases in the meteorites. All methods gave consistent results. The best estimate of the pre-atmospheric mass is 1500 ± 500 kg. The fireball integral bolometric luminous efficiency was 9%, and the acoustic efficiency was 0.14%. The meteoroid cosmic ray exposure age was determined to be (6.7 ± 1.0) × 10 6 yr. The meteorite shows a clear deficit of helium, both 3 He and 4 He. This deficit can be explained by solar heating. Numerical backward integration of the meteoroid orbit (determined in a previous paper from video records of the fireball) shows that the perihelion distance was probably lower than 0.5 AU and possibly as low as 0.1 AU 5 Ma ago. The collision which excavated Morávka probably occurred while the parent body was on a near-Earth orbit, as opposed to being confined entirely to the main asteroid belt. An overview of meteorite macroscopic properties, petrology, mineralogy, and chemical composition is given. The meteorites show all mineralogical features of H chondrites. The shock level is S2. Minor deviations from other H chondrites in abundances of trace elements La, Ce, Cs, and Rb were found. The ablation crust is enriched with siderophile elements.