Equations of satellite relative motion in low earth orbit under lunar perturbation

Aimed at the low earth satellites under lunar perturbation, this paper derived two sets of dynamic equations based on the Reference Satellite Variable (RSV). One is for orbital motion of the reference satellite and another one is for relative motion between satellites. Both sets of equations are simple and accurate and expressed explicitly. Because of clear physical meaning of the selected Reference Satellite Variables, the equations are also suitable to analyze the effect of satellite motion under lunar perturbation qualitatively.