Analytical solution of perturbed circular motion: application to satellite geodesy

Abstract

Starting from the analytical theory of perturbed␣circular motions presented in Celestial Mechanics (Bois 1994) and from specific extended formulations of the perturbations in a uniformly rotating plane of constant inclination, this paper presents an extended formulation of the solution. The actual gain made through this extension is the establishment of a first-order predictive theory written in spherical coordinates and thus free of singularities, whose perturbations are directly expressed in the local orbital frame generally used in satellite geodesy. This new formulation improves the generality, the precision and the field of applications of the theory. It is particularly devoted to the analysis of satellite position perturbations for satellites in low eccentricity orbits usually used for many Earth observation applications. An application to the TOPEX/Poseidon (T/P) orbit is performed. In particular, contour maps are provided which show the geographical location of orbit differences coming from geopotential coefficient differences of two recent gravity field models. Comparison of predicted radial and along-track orbit differences with respect to numerical results provided by the French group (CNES, in Toulouse) in charge of the T/P orbit are convincing.