In-plane satellite formations in eccentric orbits under J₂ perturbation

Formation design considering the eccentricity and the J₂ perturbation is significant for a practical satellite formation flying mission. The linear solution of satellite relative motion proves that, by setting all satellites having the same mean orbit elements of semi-major axis, eccentricity, inclination and right ascension of ascending node, a passive in-plane formation is periodic and stable in J₂ perturbed eccentric orbits. Especially, a special in-plane formation named as Almost Constant Separation Formation is achieved by suitably designing the differential secular elements of the argument of perigee and the mean anomaly. Further analysis shows that the separation distances between satellites in this special in-plane formation can be specified at will and are almost invariant if the eccentricity is smaller than 0.3.