Solar sail formation flying on an inclined Earth orbit

The versatility of solar sail propulsion can be utilized in the exploration of Earth's magnetotail. An inclined periodic orbit with respect to ecliptic is possible for a solar sail with its orbital plane in synchronous rotation with the sun. Solar sail evolving on such an inclined orbit is free of Earth shadow. Formation flying of a cluster of sails around such an inclined periodic orbit is investigated in this paper. The solution of the first-order approximation to the linear relative motion is used to qualitatively analyze the configurations of relative orbits. Since the relative motion is unstable, active control is necessary to keep a periodic relative motion. A typical LQR method is employed to stabilize the relative motion. The design method is validated by numerical examples.