Epicyclic motion of satellites about an oblate planet

An analytic formulation is presented of a near circular orbit of a satellit e about nrl axisymmetric potential, The model has a simple analytic form th at is capable of describing all of the gravitational perturbative effects, Unlike more rigorous treatments, our approach has a simple geometric interp retation and greater mathematical simplicity than conventional descriptions of the perturbed motion, yet is sufficiently accurate to describe the moti on 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 geopotenti al can be incorporated into the same formulation is demonstrated. Also cons idered are second-order effects arising front the J(2) term, which provides sufficient accuracy in the modeling for most satellite applications. Some simulation results are presented to establish the accuracy of the predictiv e model over time.