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

Heiligers, Jeannette and Hiddink, Sander and Noomen, Ron and McInnes, Colin (2015) Solar sail Lyapunov and halo orbits in the Earth-Moon three-body problem. Acta Astronautica, 116. pp. 25-35. ISSN 0094-5765 (

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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.