High Degree and Order Spherical Harmonic Models for the Moon From Clementine and Historic S-Band Data

Abstract

A spherical harmonic model complete to degree and order seventy has been developed from Doppler tracking of the Lunar Orbiters, the Apollo 15 and 16 subsatellites, and the Clementine spacecraft. The model combines 361,000 observations from Clementine with 347,000 historical observations. The model was developed using the method of Lerch [1991] in order to derive a more realistic realization of the uncertainties associated with this model. An a priori power law of the form 15 × 10⁻⁵/1², where l is the spherical harmonic degree, was applied in this model. The Clementine data provide a powerful constraint on the low degree harmonics, and the sectoral terms through degree twenty, by virtue of the spacecraft orbit geometry, and the excellent quality of the tracking data. The gravity anomalies in our model, GLGM-2 (Goddard Lunar Gravity Model-2), have a dynamic range of −294 to +358 mGals when evaluated on the lunar surface at a reference radius of 1738 km. The error predicted from the GLGM-2 covariance ranges from 14 mGals on the equatorial near side to 44 mGals over the high latitude regions of the lunar far side. The model resolves the mascon basins first deduced from Lunar Orbiter tracking [Muller and Sjogren,1968]. Mare Orientale is resolved as a horseshoe-shaped low with an amplitude of −225 mGals centered on the inner and outer Rook rings. Although direct tracking is not available over substantial regions of the lunar farside, the model still resolves far side basins such as South-Pole Aitken, Hertzsprung, Korolev, Moscoviens, and Tsiolkovsky.