Low-energy transfers to cislunar periodic orbits visiting triangular libration points

Abstract This paper investigates the cislunar periodic orbits that pass through triangular libration points of the Earth–Moon system and studies the techniques on design low-energy transfer trajectories. In order to compute periodic orbits, families of impulsive transfers between triangular libration points are taken to generate the initial guesses of periodic orbits, and multiple shooting techniques are applied to solving the problem. Then, varieties of periodic orbits in cislunar space are obtained, and stability analysis shows that the majority of them are unstable. Among these periodic orbits, an unstable periodic orbit in near 3:2 resonance with the Moon is taken as the nominal orbit of an assumed mission. As the stable manifolds of the target orbit could approach the Moon, low-energy transfer trajectories can be designed by combining lunar gravity assist with the invariant manifold structure of the target orbit. In practice, both the natural and perturbed invariant manifolds are considered to obtain the low-energy transfers, which are further refined to the Sun-perturbed Earth–Moon system. Results indicate that (a) compared to the case of natural invariant manifolds, the optimal transfers using perturbed invariant manifolds could reduce flight time at least 50 days, (b) compared to the cheapest direct transfer, the optimal low-energy transfer obtained by combining lunar gravity assist and invariant manifolds could save on-board fuel consumption more than 200 m/s, and (c) by taking advantage of the gravitational perturbation of the Sun, the low-energy transfers could save more fuel consumption than the corresponding ones obtained in the Earth–Moon system.