A harmonic analysis of lunar gravity

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Abstract
An improved model of lunar global gravity has been obtained by fitting a sixteenth‐degree harmonic series to a combination of Doppler tracking data from Apollo missions 8, 12, 15, and 16, and Lunar Orbiters 1, 2, 3, 4, and 5, and laser ranging data to the lunar surface. To compensate for the irregular selenographic distribution of these data, the solution algorithm has also incorporated a semi‐empirical a priori covariance function. Maps of the free‐air gravity disturbance and its formal error are presented, as are free‐air anomaly and Bouguer anomaly maps. The lunar gravitational variance spectrum has the form V(G; n) = O(n−4), as do the corresponding terrestrial and martian spectra. The variance spectra of the Bouguer corrections (topography converted to equivalent gravity) for these bodies have the same basic form as the observed gravity (V(ΔG; n) = O(n−4)), and, in fact, the spectral ratios σn (ΔG )/σn(G) are nearly constant throughout the observed spectral range for each body. Despite this spectral compatibility, the correlation between gravity and topography is generally quite poor on a global scale.