Keeping a Solar Sail near the Triangular Libration Point of a Dumbbell-Shaped or Binary Asteroid

The possibility of keeping a spacecraft with a solar sail near an unstable triangular libration point of a minor planet or a binary asteroid is studied under the assumption that only the gravitation and the solar radiation influence the spacecraft motion. The case where the solar sail orientation remains unchanged with respect to the frame of reference of the heliocentric orbit of the asteroid mass center is considered. This means that the angle between the solar sail normal and ecliptic, as well as the angle between this normal and the solar rays at the current point, does not change during the motion. The spacecraft equations of motion are deduced under assumptions of V.V. Beletsky’s generalized restricted circular problem of three bodies, but taking into account the Sun radiation. The existence of a manifold of initial conditions for which it is possible to choose the normal direction that guarantees the spacecraft bounded motion near the libration point is established. Moreover, the dimension of this manifold coincides with that of the phase space of the problem at which the libration point belongs to the manifold boundary. In addition, some proposals for stabilization of the spacecraft motions are formulated for trajectories beginning in the manifold.