Mean rates of the orbital elements of a satellite perturbed by a lens shaped mass concentration
Long arc gravity analysis of lunar orbiter tracking data in the past has been carried out with the help of averaged equations of motion, in which short period effects have been suppressed. This procedure has required that the harmonic terms in the gravity potential be averaged over an orbital period. In the present paper, this technique is extended to mass points and mass disks in the gravity field. This requires the evaluation of expressions for the mean rates of the orbit elements for a satellite perturbed by a lens shaped mass concentration. Corresponding expressions for the perturbations due to a mass point are obtained in the limit as the lens radius goes to zero. The derived equations have been programmed on the UNIVAC 1108 computer, and the results checked by numerical differencing.