Small-amplitude periodic orbit around sun-earth L₁/L₂ Controlled by solar radiation pressure

The L₁ and L₂ points of the Sun-Earth system attract much attention for various space uses, such as observation and communication. Deploying the spacecraft just on L₁/L₂ is, however, not convenient, because L₁ always overlaps with the Sun as seen from the Earth and L2 is hidden behind the shadow of the Earth. Adopting a small-amplitude periodic orbit around the L₁/L₂ points is one option to solve this problem. The orbit can be achieved by low continuous maneuvering. The required magnitude of acceleration is at a level that can be managed by solar radiation pressure. Utilizing solar radiation pressure has the possibility of saving maneuvering to keep the spacecraft near a L₁/L₂ orbit. Acceleration due to solar radiation pressure depends on the surface area of the spacecraft and thus the spacecraft should be equipped with a large flat surface. A spacecraft equipped with a solar sail is appropriate. This paper presents two station-keeping examples of solar sails in the vicinity of SE L₁/L₂ using acceleration resulting from solar radiation pressure. The orbit control laws are built into the linear system about the equilibrium, and we confirm that they are applicable in the non-linear system through numerical calculation.