Propellant-free station-keeping design of a solar sail around the Sun-Earth collinear equilibrium points

In this paper, we focus on the propellant-free station-keeping design of a solar sail spacecraft around the unstable Sun-Earth collinear equilibrium point L2. The dynamical model considered is the Sun-Earth restricted three-body problem, including the solar radiation pressure on a sail that depends on three parameters: its reflectivity and its attitude with respect to the Sun, expressed by means of two angles. In the libration zone, the solar sail maneuvers performed by means of changing the values of the sail parameters, can be understood as”jumps” in position instead of in velocity inside the phase space. The paper uses this fact to systematically analyze the impact of a maneuver (an instantaneous sail reorientation) on a spacecraft moving along a libration point Lissajous orbit. The station-keeping strategy periodically performs maneuvers to prevent the spacecraft to escape from a certain Lissajous orbit following its unstable manifold. Random errors in the execution of the maneuvers are also considered.