Periodic and quasi-periodic motions of a solar sail close to SL 1 in the Earth-Sun system

Solar sails are a proposed form of spacecraft propulsion using large membrane mirrors to propel a satellite taking advantage of the solar radiation pressure. To model the dynamics of a solar sail we have considered the Earth-Sun Restricted Three Body Problem including the Solar radiation pressure (RTBPS). This model has a 2D surface of equilibrium points parametrised by the two angles that define the sail orientation. In this paper we study the non-linear dynamics close to an equilibrium point, with special interest in the bounded motion. We focus on the region of equilibria close to SL (1), a collinear equilibrium point that lies between the Earth and the Sun when the sail is perpendicular to the Sun-sail direction. For different fixed sail orientations we find families of planar, vertical and Halo-type orbits. We have also computed the centre manifold around different equilibria and used it to describe the quasi-periodic motion around them. We also show how the geometry of the phase space varies with the sail orientation. These kind of studies can be very useful for future mission applications.