Solar sail Lyapunov and Halo orbits in the Earth–Moon three-body problem

Solar sailing has been proposed for a range of novel space applications, including hovering above the ecliptic for high-latitude observations of the Earth and monitoring the Sun from a sub-L1 position for space weather forecasting. These applications, and many others, are all defined in the Sun–Earth three-body problem, while little research has been conducted to investigate the potential of solar sailing in the Earth–Moon three-body problem. This paper therefore aims to find solar sail periodic orbits in the Earth–Moon three-body problem, in particular Lagrange-point orbits. By introducing a solar sail acceleration to the Earth–Moon three-body problem, the system becomes non-autonomous and constraints on the orbital period need to be imposed. In this paper, the problem is solved as a two-point boundary value problem together with a continuation approach: starting from a natural Lagrange-point orbit, the solar sail acceleration is gradually increased and the result for the previous sail performance is used as an initial guess for a slightly better sail performance. Three in-plane steering laws are considered for the sail, two where the attitude of the sail is fixed in the synodic reference frame (perpendicular to the Earth–Moon line) and one where the sail always faces the Sun. The results of the paper include novel families of solar sail Lyapunov and Halo orbits around the Earth–Moon L1 and L2 Lagrange points, respectively. These orbits are double-revolution orbits that wind around or are off-set with respect to the natural Lagrange-point orbit. Finally, the effect of an out-of-plane solar sail acceleration component and that of the Sun-sail configuration is investigated, giving rise to additional families of solar sail periodic orbits in the Earth–Moon three-body problem.