Epicyclic Motion of Satellites About an Oblate Planet

Abstract

An analytic formulation is presented of a near circular orbit of a satellite about an axisymmetric potential. The model has a simple analytic form that is capable of describing all of the gravitational perturbative effects. Unlike more rigorous treatments, our approach has a simple geometric interpretation and greater mathematical simplicity than conventionaldescriptions of the perturbedmotion,yet is sufŽ ciently accurate to describe themotion of a satellite over its lifetime. The formulation of the orbit, based on epicyclic motion, is presented, and how all of the terms in the geopotential can be incorporated into the same formulation is demonstrated. Also considered are second-order effects arising from the J2 term, which provides sufŽ cient accuracy in the modeling for most satellite applications. Some simulation results are presented to establish the accuracy of the predictive model over time.