The TOPEX/POSEIDON (T/P) prelaunch Joint Gravity Model‐1 (JGM‐I) 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.

An improved model of Earth's gravitational field, GEM‐T3, has been developed from a combination of satellite tracking, satellite altimeter, and surface gravimetric data. GEM‐T3 provides a significant improvement in the modeling of the gravity field at half wavelengths of 400 km and longer. This model, complete to degree and order 50, yields more accurate satellite orbits and an improved geoid representation than previous Goddard Earth Models. GEM‐T3 uses altimeter data from GEOS 3 (1975–1976), Seasat (1978) and Geosat (1986–1987). Tracking information used in the solution includes more than 1300 arcs of data encompassing 31 different satellites. The recovery of the long‐wavelength components of the solution relies mostly on highly precise satellite laser ranging (SLR) data, but also includes TRANET Doppier, optical, and satellite‐to‐satellite tracking acquired between the ATS 6 and GEOS 3 satellites. The main advances over GEM‐T2 (beyond the inclusion of altimeter and surface gravity information which is essential for the resolution of the shorter wavelength geoid) are some improved tracking data analysis approaches and additional SLR data. Although the use of altimeter data has greatly enhanced the modeling of the ocean geoid between 65°N and 60°S latitudes in GEM‐T3, the lack of accurate detailed surface gravimetry leaves poor geoid resolution over many continental regions of great tectonic interest (e.g., Himalayas, Andes). Estimates of polar motion, tracking station coordinates, and long‐wavelength ocean tidal terms were also made (accounting for 6330 parameters). GEM‐T3 has undergone error calibration using a technique based on subset solutions to produce reliable error estimates. The calibration is based on the condition that the expected mean square deviation of a subset gravity solution from the full set values is predicted by the solutions' error covariances. Data weights are iteratively adjusted until this condition for the error calibration is satisfied. In addition, gravity field tests were performed on strong satellite data sets withheld from the solution (thereby ensuring their independence). In these tests, the performance of the subset models on the withheld observations is compared to error projections based on their calibrated error covariances. These results demonstrate that orbit accuracy projections are reliable for new satellites which were not included in GEM‐T3.

We have estimated monthly values of the J2 and J3 Earth gravitational coefficients using LAGEOS satellite laser ranging (SLR) data collected between 1980 and 1989. For the same time period, we have also computed corresponding estimates of the variations in these coefficients caused by atmospheric mass redistribution using surface atmospheric pressure estimates from the European Center for Medium Range Weather Forecasts (ECMWF). These data were processed both with and without a correction for the “inverted barometer effect,” the ocean's isostatic response to atmospheric loading. While the estimated zonal harmonics in the orbit analysis accommodate gravitational changes at a reduced level arising from all other higher degree zonal effects, the LAGEOS and atmospheric time series for J2 compare quite well and it appears that the non‐secular variation in J2 can be largely attributed to the redistribution of the atmospheric mass. While the observed changes in the “effective” J3 parameters are not well predicted by the third degree zonal harmonic changes in the atmosphere, both odd zonal time series display strong seasonality. The LAGEOS J3 estimates are very sensitive to as yet unmodeled forces acting on the satellite and these effects must be better understood before determining the dominant geophysical signals contributing to the estimate of this time series.

Orbit error projections based on the error covariance estimates of Goddard Earth Model (GEM)‐T3 have been shown to be reliable through their projection on observation residuals within independent data sets. Special geopotential solutions were developed based upon the same data set and weighting used in the GEM‐T3 gravity model, but with a significant satellite data set eliminated from the solution. These subset gravity models are then used to compute the observation residuals within orbital solutions for the omitted satellite and the results are compared to their predicted values based on the error covariance of these models. To ensure meaningful results, the tests were designed so that the observation residuals are dominated by geopotential modeling errors. This yields a reliable test of the error estimates of the subset solutions and hence tests the data weighting used in the construction of these models (GEM‐T3 and subset solutions alike). The error estimates for GEM‐T3 are based upon an optimal data weighting method and have been obtained in a separate calibration process. The test results shown here indicate that the GEM‐T3 error estimates for the gravity parameters are calibrated and that the predicted orbit errors correspond well with actual orbit accuracies. Test results of the complete GEM‐T3 model with totally independent high precision DORIS Doppler tracking data acquired on the French SPOT‐2 satellite confirms these conclusions.

The Mars Observer (MO) Mission, in a near-polar orbit at 360-410 km altitude for nearly a 2-year observing period, will greatly improve our understanding of the geophysics of Mars including its gravity field. To assess the expected improvement of the gravity field, we have conducted an error analysis based upon the mission plan for the Mars Observer radio tracking data from the Deep Space Network. Our results indicate that it should be possible to obtain a high-resolution model (spherical harmonics complete to degree and order 50 corresponding to a 200-km horizontal resolution) for the gravitational field of the planet. This model, in combination with topography from MO altimetry, should provide for an improved determination of the broad scale density structure and stress state of the Martian crust and upper mantle. The mathematical model for the error analysis is based on the representation of doppler tracking data as a function of the Martian gravity field in spherical harmonics, solar radiation pressure, atmospheric drag, angular momentum desaturation residual acceleration (AMDRA) effects, tracking station biases, and the MO orbit parameters. Two approaches are employed. In the first case, the error covariance matrix of the gravity model is estimated including the effects from all the nongravitational parameters (noise-only case). In the second case, the gravity recovery error is computed as above but includes unmodelled systematic effects from atmospheric drag, AMDRA, and solar radiation pressure (biased case). The error spectrum of gravity shows an order of magnitude of improvement over current knowledge based on doppler data precision from a single station of 0.3 1 mm s-noise for 1-min integration intervals during three 60-day periods. This first approach of noise only yielded an estimated total accuracy (omission plus commission) for a 200 km block size of 5.4 m for geoid undulations and 31 mGal for gravity anomalies. For the second case, corresponding to the unmodelled systematic effects, an additional error of 5% in the above statistics was obtained. Although the degradation in the accuracy of the mean gravity anomalies and mean geoid undulations is not very pronounced, significant degradation in the recovery of the harmonic coefficients was observed due to the unmodelled systematic nongravitational effects (mainly atmospheric drag). A worst result occurred for an individual 60-day period, corresponding to maximum atmospheric drag, which gave significant degradation for the low-degree terms out through degree 20. However, the overall accuracy for the combined solution of the three 60-day periods for the second case of systematic effects gave only a small difference from the noise-only solution. The results suggest that the spacecraft orbit could possibly be raised in altitude without significant loss of gravitational signal, because the atmospheric drag is the dominant error source. A change in altitude could also alleviate the large effects seen in the spectrum of the satellite resonant orders. A conser...