A hybrid method based on invariant manifold and chaos control for earth-moon low-energy transfer

In this paper, a new hybrid method based on invariant manifold and chaos control is presented to design Earth-Moon low-energy transfer trajectory in the planar circular restricted three-body problem. In the proposed method, one segment trajectory emanates from the period orbit around the Earth to Lyapunov orbit associated with the Lagrange points L₁, which is designed by chaos control method to reduce the transfer time wandering in the chaotic region. Another segment starts from the Lyapunov orbit and reaches the Moon orbit, which is designed by the invariant manifold method. The two segments are patched with varying Jacobi constant by utilizing a Poincaré section, which is determined by the pericenter relative to the Earth. Several candidate low-energy transfer trajectories can be obtained by the proposed method, among which a suitable trajectory could be selected via the trade-off between fuel and flight time. Extensive numerical simulations are implemented to demonstrate the effectiveness of the proposed method.