Determination of orbits of planetary artificial satellites and planetary gravitational fields.

Abstract

The state vector of a planetary artificial satellite is determined by using Earth-based rangerate measurements. The satellite velocity component in the direction from the planet center to Earth center instead of that from the satellite to an observation station is computed in a theoretical model. The relatively simple, least-squares estimation criterion thus obtained for the case of a planet at infinite distance facilitates the comparison study of numerical methods of solving a system of nonlinear equations. Simulation results obtained by programing in double precision show that the longitude of the ascending node of a planetary satellite can be determined to prescribed accuracy within a few days of tracking. The comparison study is made among 1) classical differential correction method, 2) Newton-Raphson method, 3) generalized differential correction method, and 4) generalized Newton-Raphson method. It indicates that the new generalized differential correction method has a convergence range of initial estimate wider than the other methods. The extension, in the convergence range of initial estimate, enhances the success of obtaining a preliminary state vector in a short tracking period and is particularly important in planetary missions. The effects of perturbations of noncentral forces on the satellite can be incorporated in the formulation without resorting to numerical integration.