F. J. Lerch’s research while affiliated with Johnson Space Center and other places

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.

High-degree (Nmax=360) gravitational models require surface gravity data to resolve the fine structure of the field. Given a global gravity anomaly data set, one can extract this information using either quadrature formulæ (orthogonality relations) or by solving a system of observation equations. Under certain conditions such a system yields a normal matrix of block-diagonal structure. To determine accurately the lower part of the spectrum requires the least-squares combination of the surface gravity information with a satellite-only gravity model. Depending on the technique employed to develop the surface gravity solution, the estimation of a combined model can be performed in different ways. We have used a global set of 30’ mean gravity anomalies and a satellite-only model to produce combination solutions using both quadratures and the block-diagonal adjustment technique. In both cases the complete covariance matrix of the satellite-only model was used. Global geoid height difference (to Nmax=360) between the two types of solution is at the ± 20 cm level. The error spectra obtained from the two techniques are in excellent agreement. The models from the two techniques perform equally well in orbit fit tests. Absolute comparisons with GPS/Leveling-derived undulations over British Columbia and the US indicated that the block-diagonal technique yields slightly better results. However, relative GPS/Leveling undulation comparisons seem to indicate a problem with the higher degree harmonics obtained from the block-diagonal technique which requires further study.

Tracking data from the Tracking and Data Relay Satellite System (TDRSS) are used to determine operational orbits for a variety of user spacecraft. These data are not routinely used for precise orbit determination because the Tracking and Data Relay Satellite (TDRS) orbits, derived from Bilateration Ranging Transponder System (BRTS) tracking, are of insufficient accuracy (40-60 m). Therefore, we have investigated alternative orbit determination techniques to improve our knowledge of TDRS and user satellite trajectories. These techniques include incorporating ground based tracking of the user satellite, exploiting the enhanced tracking geometry provided by the user satellite, and improving the force and measurement modeling. Results from analysis of TDRSS-TOPEX/POSEIDON (T/P) data demonstrate that the TDRSS data are powerful, that computed TDRS orbits have 3-5 m total position accuracies, and that the corresponding T/P ephemerides have 25-40 cm accuracies.

The NASA Goddard Space Flight Center (GSFC) and the U.S. Defense Mapping Agency (DMA) with the aid of other organizations such as The Ohio State University are cooperating in a joint effort to determine a significantly improved degree 360 spherical harmonic model representing the Earth’s gravitational potential. This new model will be of immediate use in defining an undulation model that will be the basis for an enhanced WGS-84 geoid, but the model will be general in use and will provide enhancements for a wide range of applications. The development of the new model is driven, in part, by the need to determine an accurate geoid undulation model that will be the vertical reference surface for WGS-84. In addition, the new geoid model will help satisfy increasingly important studies in ocean circulation (sea surface topography) and geodetic positioning through GPS.

Precision orbit determination on the TOPEX/Poseidon (T/P) altimeter satellite is now being routinely achieved with sub-5cm radial and sub-15 cm total positioning accuracy using state-of-the-art modeling with precision tracking provided by a combination of: (a) global Satellite Laser Ranging (SLR) and Doppler Orbitography and Radiopositioning Integrated by Satellite (DORIS), or (b) the Global Positioning System (GPS) Constellation which provides pseudo-range and carrier phase observations. The geostationary Tracking and Data Relay Satellite System (TDRSS) satellites are providing the operational tracking and communication support for this mission. The TDRSS Doppler data are of high precision (0.3 mm/s nominal noise levels). Unlike other satellite missions supported operationally by TDRSS, T/P has high quality independent tracking which enables absolute orbit accuracy assessments. In addition, the T/P satellite provides extensive geometry for positioning a satellite at geostationary altitude, and thus the TDRSS-T/P data provides an excellent means for determining the TDRS orbits. Arc lengths of 7 and 10 days with varying degrees of T/P spacecraft attitude complexity are studied. Sub-meter T/P total positioning error is achieved when using the TDRSS range-rate data, with radial orbit errors of 10.6 cm and 15.5 cm RMS for the two arcs studied. Current limitations in the TDRSS precision orbit determination capability include mismodeling of numerous TDRSS satellite-specific dynamic and electronic effects, and in the inadequate treatment of the propagation delay and bending arising from the wet troposphere and ionosphere.

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 root mean square (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.

Orbital sensitivity of the gravity field for high degree terms (greater than 30) is analyzed on satellites employed in a Goddard Mars Model GMM-1, complete in spherical harmonics through degree and order 50. The model is obtained from S-band Doppler data on Mariner 9 (M9), Viking Orbiter 1 (VO1), and Viking Orbiter 2 (VO2) spacecraft, which were tracked by the NASA Deep Space Network on seven different highly eccentric orbits. The main sensitivity of the high degree terms is obtained from the VO1 and VO2 low orbits (300 km periapsis altitude), where significant spectral sensitivity is seen for all degrees out through degree 50. The velocity perturbations show a dominant effect at periapsis and significant effects out beyond the semi-latus rectum covering over 180 degrees of the orbital groundtrack for the low altitude orbits. Because of the wideband of periapsis motion covering nearly 180 degrees in w and +39 degrees in latitude coverage, the VO1 300 km periapsis altitude orbit with inclination of 39 degrees gave the dominant sensitivity in the GMM-1 solution for the high degree terms. Although the VO2 low periapsis orbit has a smaller band of periapsis mapping coverage, it strongly complements the VO1 orbit sensitivity for the GMM-1 solution with Doppler tracking coverage over a different inclination of 80 degrees.

A high-precision radiometric satellite tracking system, Doppler Orbitography and Radio-positioning Integrated by Satellite system (DORIS), has recently been developed by the French space agency, Centre National d'Etudes Spatiales (CNES). DORIS was designed to provide tracking support for missions such as the joint United States/French TOPEX/Poseidon. As part of the flight testing process, a DORIS package was flown on the French SPOT 2 satellite. A substantial quantity of geodetic quality tracking data was obtained on SPOT 2 from an extensive international DORIS tracking network. These data were analyzed to assess their accuracy and to evaluate the gravitational modeling enhancements provided by these data in combination with the Goddard Earth Model-T3 (GEM-T3) gravitational model. These observations have noise levels of 0.4 to 0.5 mm/s, with few residual systematic effects. Although the SPOT 2 satellite experiences high atmospheric drag forces, the precision and global coverage of the DORIS tracking data have enabled more extensive orbit parameterization to mitigate these effects. As a result, the SPOT 2 orbital errors have been reduced to an estimated radial accuracy in the 10-20 cm RMS range. The addition of these data, which encompass many regions heretofore lacking in precision satellite tracking, has significantly improved GEM-T3 and allowed greatly improved orbit accuracies for Sun-synchronous satellites like SPOT 2 (such as ERS 1 and EOS). Comparison of the ensuing gravity model with other contemporary fields (GRIM-4C2, TEG2B, and OSU91A) provides a means to assess the current state of knowledge of the Earth's gravity field. Thus, the DORIS experiment on SPOT 2 has provided a strong basis for evaluating this new orbit tracking technology and has demonstrated the important contribution of the DORIS network to the success of the TOPEX/Poseidon mission.

Last year we published the GMM-1 (Goddard Mars Model-1) gravity model for Mars. We have completely re-analyzed the Viking and Mariner 9 tracking data in the development of the new field, designated GMM-2. The model is complete to degree and order 70. Various aspects of the model are discussed.