Periodic orbits of solar sails in the Sun-Earth system

Abstract This paper studies the periodic orbits of solar sails using reflectivity control devices (RCDs) in the circular Sun-Earth system. Significantly, the dynamical equations about the solar sail are given separately in the rotational coordinate system and adjoint coordinate system. Analytical solutions about the periodic orbits of solar sails are given. So as to gain the periodic orbits of solar sails, we discuss the conditions of the attitude angles and reflectivity modulation ratio of solar sails. This paper simulates some periodic orbits of solar sails and analyzes the stability of a periodic orbit of a solar sail by using the Floquet theory. The outcomes show that it is unstable for the periodic orbit of a solar sail. Based on the linear quadratic regulator (LQR), this paper designs a control algorithm to achieve tracking in the target orbit of solar sails.