Satellite relative dynamic in terms of mean motion on a zone harmonic perturbed elliptical orbit

The equations of satellite relative dynamics described by mean orbital elements are derived under LVLH coordinates. The primary gravitational perturbation that results from the equatorial bulge term J₂ is considered. In this paper, the short and long-periodic variations of J₂ perturbation are neglected, only show the effect of a secular term . The first-order Taylor series expansion is employed to linearize the equations. Finally, the accurate description of satellite relative motion under the eccentric orbit is obtained.