Vectorial formulation for the propagation of average dynamics under gravitational effects

Abstract

General expressions for the vectorial formulation of the equations of motion under geopotential perturbations are provided. These expressions are based on the apsidal frame formulation, and ease the identification of the fast and slow components of the motion, as well as the consequent averaging of the potential over the mean anomaly. The mean variation equations of the eccentricity and angular momentum vector, while redundant, comprise a non-singular differential system that is efficiently integrated numerically, and naturally complements analogous vectorial formulations of the third-body and solar radiation pressure disturbing effects. Still, classical approaches in orbital elements may show better efficiency in the integration of moderate and high eccentricity orbits due to the almost linear character of the variations.