Relative motion equation for perturbed elliptical reference orbit formation

The variation equation of the satellite orbit elements under both J₂ and drag perturbations was derived based on the Gauss perturbation equation. Introducing the concept of virtual reference satellite, by expanding the real satellite dynamics to the first order around the virtual one, the relative motion of the real satellite with respect to the virtual one was analyzed to build a model for the linear time-varying relative motion between formation satellites under both the J₂ and drag perturbations The comparison of the simulated results with the STK high precision orbit prediction module shows that for the elliptical reference orbit formation (its size no more than 10 km), the proposed algorithm can quite precisely predict the change of the formation, thus the effectiveness of the given algorithm was verified.