The gravity fields of planetary bodies other than the Earth have been determined almost exclusively from Earth-based tracking of robotic spacecraft. Our knowledge of the gravity fields of the outer planets is limited to estimates of their mass and a few of the low degree geopotential coefficients determined from planetary flybys. Thomas [1991] gives a good summary of these results. However, for the Moon, Venus, and Mars, fairly detailed gravity models have been developed using Doppler tracking of spacecraft inserted into elliptical orbits about these bodies. This is more difficult than determining the gravity field of the Earth because the tracking stations are not attached to the planet in question. In addition, the orbits of these planetary spacecraft were usually highly elliptical which further complicates the differentiation of gravitational signals and nongravitational signals caused by forces such as atmospheric drag. As a result, substantial improvements in the gravity models for these bodies has been gained by reprocessing the historical tracking data using improved solution techniques.
One reason for the improvement of these models has been the use of a technique for constraining the gravity models in regions where they are poorly observed. Models computed in the 1980s were generally complete in spherical harmonics to only about degree 18 since larger solutions were ill-behaved due to the poor spatial distribution of the tracking data (caused by the highly elliptical orbits generally employed). However, a considerable amount of gravitational signal remained in the tracking data using these models. This situation was improved in the 1990s as scientists applied a constraint technique long used in developing models for the Earth's gravity field [ Lerch et al., 1993b; 1993c]. Essentially, this technique consists of using a priori information in the least squares estimation process defining the a priori value of a spherical harmonic coefficient to be zero and its a priori error to be 100% as given by an approximation for the power of the gravity field. This technique allows solutions to be computed to very high degree (generally 50-60), thereby extracting much more of the gravitational signal, thus providing solution detail in regions overflown at periapse. The application of the a priori constraints (which biases poorly observed coefficients towards zero) allows the short wavelength features of the gravity field to be resolved where the tracking data permit and does not introduce significant aliasing at shorter wavelengths where the field is not well observed.