J_2 invariant perturbation conditions for the relative movement for satellites in formation flying

The earth's non-spherical shape greatly affects the relative movement of satellites in formation flying. This shape perturbation makes the satellites rotate or drift in the forward direction. The J2 invariant perturbation conditions were developed to describe the relative movement of satellites in formation with small eccentricities. The results showed that the J2 perturbation can not affect the relative movement of satellites in formation when the satellites have equal orbital nodal periods and nodal precession rates; thus, the satellites can maintain their formation for a long time. The first order approximate expressions of the J2 invariant perturbation conditions were developed using small orbital elements for the satellites. The simulation results show that the first-order approximation of the J2 invariant perturbation conditions can effectively reduce the drift of the relative orbital configurations.