Exact dynamic of satellite relative motion under arbitrary zonal harmonic perturbations

To expand the exact dynamic model of satellite relative motion under J₂ perturbation, a new model is established which is exactly up to arbitrary zonal harmonic perturbations. Moreover, a set of differential equations in terms of Reference Satellite Variables (RSV) are obtained to describe the satellite motion around the Earth accurately under arbitrary zonal harmonic perturbations. Since no simplification is applied during the derivation, the result is valid for arbitrary eccentric orbits.