AN APPROXIMATE SOLUTION FOR SHORT-TERM MOTION OF A LUNAR SATELLITE

The expressions developed by Kaula for the primary and third-body disturbing functions in terms of the classical orbit elements are used to develop a modified first-order perturbation solution to the differential equations for a set of nonsingular orbit elements. The resulting solution includes the short-period, long- period, and secular effects of the primary and third-body disturbing functions, and is valid for all circular and elliptical motion. Results obtained by evaluating this solution for a near-lunar satellite orbit were compared with results obtained by numerical integration. After eight days, the value of the range differed by less than 200 ft, whereas the velocities differed by less than 0. 2 fps.