Lunar gravity: A long-term Keplerian Rate Method

Abstract

Recent reductions of Apollo subsatellite and Lunar Orbiter 5 data have determined the first plausible models for the fatside lunar gravity field. This paper presents a selenodesy method which estimates gravity by fitting to the long-term variations of the Kepler element rates. Raw Doppler tracking data taken over short arcs are reduced to estimate a best set of mean orbital elements for each orbit. A succession of such fits is performed to generate a history of mean elements. The element rates are determined from patched cubic spline fits to the elements. The rates are adjusted for n-body effects and along with the associated elements are used as input to a gravity estimator. This method eliminates certain of the dynamical aspects of long-term selenodesy, and consequently, the gravity inversion is a linear process. Since the rates are generated from a series of patched cubic spline fits, unmodeled spacecraft maneuvers contaminate at most only several data points, and there is no significant net integrated effect as in conventional long-term methods. Simulations petfotined demonsttate that farside gravity features can successfully be determined by fitting to mean elements derived from nearside tracking. Arguments are presented which conclude that a long-term gravity method of this type is the most plausible technique which can obtain realistic estimates for farside lunar gravity using the currently available data. Supplement is available with entire article on microfiche. Order from American Geophysical Union, 1909 K Street, N.W., Washington, D.C. 20006. Document J77-002; $1.00. Payment must accompany order.