Earth-moon low-energy transfer trajectory by patching with the invariant manifold tubes

In this paper, an Earth-Moon low-energy transfer trajectory design method in the planar circular restricted three-body problem is proposed. This proposed method patches two trajectories by a modified Poincaré section, with equal and nonequal Jacobi constant. One trajectory emanates from the stable invariant manifold tube of the Lyapunov orbit associated with the libration point, and another trajectory is from the period orbit around the Earth. The velocity is changed at the patching point by two ways, by adjusting the velocity direction with an equal Jacobi constant or the velocity magnitude along with the varying Jacobi constant. Several candidate low-energy transfer trajectories could be obtained by this proposed method, among which a suitable trajectory could be selected via the trade-off between fuel and flight time. Finally, extensive numerical simulations are implemented to demonstrate the effectiveness of the proposed method.