Solar sail periodic orbits in the elliptic restricted three-body problem

The periodic orbits of a solar sail in the elliptic restricted three-body problem are designed in this paper. The dynamical equation of a solar sail is derived in a non-uniformly rotating and pulsating coordinate frame, where out-of-plane artificial equilibria do not exist. Two families of displaced periodic orbits in the vicinity of the out-of-plane fixed points are generated by adjusting the solar sail parameters and the motion in the out-of-plane direction to satisfy the equilibrium equations. The analytical solutions to the linearized equations are obtained with average method. The stability of these orbits is studied, and the results indicate that they are always unstable. Finally, the controllability of these orbits is discussed and a typical time-varying linear quadratic regulator is used to stabilize the system.