Lunar gravity - A long-term Keplerian rate method

Nearside tracking data from Apollo subsatellites and Lunar Orbiter 5 are used to construct a model of the farside lunar gravity field. An indirect method of calculating the average effect of all the gravity anomalies which affect spacecraft orbits is reduced to a linear estimation problem by eliminating the integration of spacecraft dynamics. Doppler frequency shifts between the lunar satellite and earth-based tracking station are used to measure the line of sight velocity component between the orbiter and the tracker; gravity determination is then performed in a weighted least squares estimator which employs the orbital rates as data and formulates the normal equations using the associated Keplerian state. Simulations performed demonstrate that farside gravity features can be economically determined by use of gravity estimates obtained from long-period models of nearside orbiting tracks.