GEM‐T2 is the latest in a series of Goddard Earth models of the terrestrial gravitational field. It is the second in a planned sequence of gravity models designed to improve both the modeling capabilities for determining the TOPEX/Poseidon satellite's radial position to an accuracy of 10‐cm RMS and for defining the long‐wavelength geoid to support many oceanographic and geophysical applications. GEM‐T2 includes more than 6OU coefficients above degree 36, the limit for GEM‐T1, and provides a dynamically determined model of the major tidal components which contains 90 terms. Like GEM‐T1, it was produced entirely from satellite tracking data. GEM‐T2 however, now uses nearly twice as many satellites (31 versus 17), contains 3 times the number of observations (2.4 million), and has twice the number of data arcs (1130). GEM‐T2 utilizes laser tracking from 11 satellites, Doppler data from four satellites, two‐ and three‐way range rate data from Landsat‐1, satellite‐to‐satellite tracking data between the geosynchronous ATS 6 and GEOS 3, and optical observations on 20 different orbits. This observation set effectively exhausts the inclination distribution available for gravitational field development from our historical data base. The recovery of the higher degree and order coefficients in GEM‐T2 was made possible through the application of a constrained least squares technique using the known spectrum of the Earth's gravity field as a priori information. The error calibration of the model was performed concurrently with its generation by comparing the complete model against test solutions which omit each individually identifiable data set in turn. The differences between the solutions isolate the contribution of a given data set, and the magnitudes of these differences are compared for consistency against their expected values from the respective solution covariances. The process yields near optimal data weights and assures that the model will be both self‐consistent and well calibrated. GEM‐T2 has benefitted by its application as demonstrated through comparisons using independently derived gravity anomalies from altimelry. Results for the GEM‐T2 error calibration indicate significant improvement over previous satellite‐only GEM models. The accuracy assessment of the lower degree and order coefficients of GEM‐T2 shows that their uncertainties have been reduced by 20% compared to GEM‐T1. The commission error of the geoid has been reduced from 160 cm for GEM‐T1 to 130 cm for GEM‐T2 for the 36 × 36 portion of the field. The orbital accuracies achieved using GEM‐T2 are likewise improved. This is especially true for the Starlette and GEOS 3 orbits where higher‐order resonance terms not present in GEM‐T1 (e.g., terms with m = 42,43) are now well represented in GEM‐T2. The improvement in orbital accuracy of GEM‐T2 over GEM‐T1 extends across all orbit inclinations. This confirms our conclusion that GEM‐T2 offers a significant advance in knowledge of the Earth's gravity field.

A major new computation of a terrestrial gravitational field model has been performed by the Geodynamics Branch of Goddard Space Flight Center (GSFC). In the development of this new model, designated Goddard Earth Model GEM‐T1, the design decisions of the past have been reassessed in light of the present state of the art in satellite geodesy. With GEM‐T1 a level of internal consistency has been achieved which is superior to any earlier Goddard Earth Model. For the first time a simultaneous solution has been made for spherical harmonic parameters of both invariant and tidal parts of the gravitational field. The solution of this satellite model to degree 36 is a major factor accounting for its improved accuracy. The addition of more precise and previously unused laser data and the introduction of consistent models were also accomplished with GEM‐T1. Another major factor allowing the creation of this model was the redesign and vectorization of our main software tools (GEODYN II and SOLVE) for the GSFC Cyber 205 computer. In particular, the high‐speed advantage (50:1), gained with the new SOLVE program, made possible an optimization of the weighting and parameter estimation scheme used in previous GEM models resulting in significant improvement in GEM‐T1. The solution for the GEM‐T1 model made use of the latest International Association of Geodesy reference constants, including the J2000 Reference System. It provided a simultaneous solution for (1) a gravity model in spherical harmonics complete to degree and order 36; (2) a subset of 66 ocean tidal coefficients for the long‐wavelength components of 12 major tides. This adjustment was made in the presence of 550 other fixed ocean tidal terms representing 32 major and minor tides and the Wahr frequency dependent solid earth tidal model; and (3) 5‐day averaged Earth rotation and polar motion parameters for the 1980 period onward. GEM‐T1 was derived exclusively from satellite tracking data acquired on 17 different satellites whose inclinations ranged from 15° to polar. In all, almost 800,000 observations were used, half of which were from third generation (<5 cm) laser systems. A calibration of the model accuracies has been performed showing GEM‐T1 to be a significant improvement over earlier GSFC “satellite‐only” models based purely on tracking data for both orbital and geoidal modeling applications. For the longest wavelength portion of the geoid (to 8×8), GEM‐T1 is a major advancement over all GEM models, even those containing altimetry and surface gravimetry. The radial accuracy for the anticipated TOPEX/POSEIDON orbit was estimated using the covariances of the GEM‐T1 model. The radial errors were found to be at the 25‐cm rms level as compared to 65 cm found using GEM‐L2. This simulation evaluated only errors arising from geopotential sources. GEM‐L2 was the best available model for TOPEX prior to the work described herein. A major step toward reaching the accuracy of gravity modeling necessary for the TOPEX/POSEIDON mission has been achieved.

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.

[1] Atmospheric rotational effects on Mars are computed and analyzed. Both axial (ÁLOD) and equatorial effects (polar motion) are evaluated. Surface values of stress and pressure from the NASA Ames general circulation model are used as inputs to compute the topographic, stress, and gravitational torques. Time series for the ice caps moments of inertia and the axial component of atmospheric angular momentum provide inputs for a separate computation of axial effects. Stress torque dominates the torque budget. This is different from the results obtained from Earth atmospheric models, in which pressure effects are paramount. Axial torque and ice caps yield annual and semiannual ÁLOD amplitudes of 0.747 and 0.121 ms, respectively. Torque-induced polar motion reaches a maximum of 16.26 mm in the second half of the Martian northern hemisphere winter. Changes in LOD using the angular momentum approach are 0.187 and 0.136 ms for the annual and semiannual harmonics. The expected precision of the planned NetLander Ionospheric and Geodesic Experiment (NEIGE) should detect the main harmonics in the ÁLOD time series. Annual and semiannual polar motion harmonics induced by atmospheric torque are below the level of NEIGE detectability.

[1] The NASA Ames general circulation model has been used to compute time series for atmospheric products of inertia and relative angular momentum terms. Model outputs were used also to compute time series representing the inertia terms due to CO 2 condensation and sublimation on the surface of Mars. Some of these terms were used to generate time series representing the forcing functions for the equatorial components of the linearized Liouville equations of rotational motion. These equations were then solved numerically for a period of a Martian year (669 sols) to obtain a time series for the position of the rotation pole on the surface of Mars. The results of the investigation indicate that mass variation in the atmosphere is as important as the formation and sublimation of ice caps on the surface of the planet. Numerical integration of the equations of rotational motion yields pole displacements as large as 30.9 cm (ice caps solution), 39.5 cm (atmospheric effects), or 33 cm (both effects combined). Fourier analysis of the time series corresponding to the equatorial components of pole displacement for the ice caps solution as well as the atmospheric effects solution shows that the (1/3)-annual harmonic has the largest coefficient in three cases, with magnitudes in the 7-9 cm range. Fourier analysis of the equatorial components of polar motion for the combined solution yields main harmonics of 5.12 cm (x), (1/3)-annual and 7.50 cm (y), annual.