Mars gravity derived from long-period motion of Mariner 9

The spherical harmonic coefficients in the gravity field of Mars are determined using a two stage filtering process. In the first stage, a weighted least squares orbit determination processor is applied to Mariner 9 Doppler tracking data to estimate Kepler elements and rates. In the second stage, the Kepler element rates are used as input to another weighted least squares processor that estimates gravity coefficients using the Lagrange perturbation equations. The novelty in this method is the fitting of element rates rather than the elements themselves. This procedure decouples the results from the effects of internal spacecraft dynamics.