The dependence of the r.m.s. geoid height error on the degree of the first term in the zonal harmonics expansion of the kernel in Stokes's integration formula is examined. It is shown that kernels with the lower degree terms removed have some advantage over the conventional kernel when a significant error in the zeroth term of the gravity anomaly expansion is present. Numerical estimates of r.m.s. geoid height error vs integration cap size are obtained for several kernels.

A surface‐layer representation of the lunar gravitational field has been derived dynamically from the analysis of Doppler observations on both polar and equatorial lunar orbiters. The force model contained 600 discrete masses located on the mean lunar surface between the approximate boundaries of ±60° latitude and ±95° longitude. The derived major mascons were generally in agreement with a model based on polar orbits alone. A technique for combining the discrete mass gravitational field for the front side with a spherical harmonics expansion for the back side is described. Harmonic analysis of the resultant field shows that the higher end of the power spectrum roughly follows the decay rule predicted by W. M. Kaula in Nicolaides et al. [1963].

The magnitudes of 92 surface mass points at designated locations were estimated from the radio tracking data of the Mariner Mars 1971 (M9) orbiter. This result is the first mass point model of a global field. The derived surface mass distribution correlates positively with the visible topography. The Hellas basin contains a mass deficiency, in contrast to some of the lunar basins which contain mass excesses. The Mars gravity field represented by the four parameters of an optimally located mass point (superimposed on an oblate spheroid) has third‐ and fourth‐degree harmonics comparable to those of the Complete model.

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