Designing solar sail formations in sun-synchronous orbits for geomagnetic tail exploration

•Solar sail formation flying with a common apse-line precessing control is studied.•A condition leading to in-plane quasi-periodic relative motion is derived.•The condition is applied in the design of two-craft and three-craft formations.•Two formation geometries are proposed that lead to quasi-periodic relative motion.•Lunar-solar gravity effects are included to study the formations׳ stability.

Exploration of the Earth׳s magnetosphere using solar sails has advantages over the use of traditional spacecraft in inertially fixed orbits because of the solar sails׳ capability to stay in the geomagnetic tail for longer periods. In this paper, solar sail formation flying in Earth-centered slightly inclined orbits is investigated, with each solar sail employing a simple sun-pointing steering law that precesses the orbit apse-line sun-synchronously. An analytic condition for determining target states that lead to in-plane quasi-periodic relative motion under solar radiation pressure is derived, assuming all sails use the same steering law. Even though active control is required to achieve these target states, only the simple steering law is required for flying the formation upon achieving the target states. The condition is verified in the design of two-craft and three-craft formations. The effects of Earth׳s nonsphericity, lunar gravity, and solar gravity are included to determine the stability of the designed formations under these perturbations.