Two-impulse transfer to multi-revolution halo orbits in the Earth-Moon elliptic restricted three body problem framework

For the design of transfer trajectories in the Earth-Moon system, the manifolds theory is popularly used in the existing literature. Because the manifolds in the Earth-Moon system do not pass close to the Earth, the transfers leveraging manifolds theory involves a bridge maneuver that transfers the space vehicle from the trans-halo trajectory to the stable manifold originating from the halo orbit. The transfer involves two segments, and the bridge impulse makes the number of velocity impulses three wherein, however, the third one is a very small one for halo orbit insertion. Alternately, a direct technique that generates two-impulse transfer trajectories to multi-revolution (MR) halo orbits around Lagrangian point L-1 in the Earth-Moon system under elliptic restricted three body problem framework is proposed. Unlike in the other direct transfer techniques, which divide the transfer trajectory into multiple segments, the proposed technique designs the transfer trajectory in a single segment. In the proposed technique, the first maneuver injects the space vehicle directly into the single segment transfer trajectory from an Earth parking orbit and the space vehicle reaches the MR halo orbit. The second maneuver inserts the space vehicle into the MR halo orbit. The location of insertion into the MR halo orbit and the components of the insertion velocity are treated as unknowns and obtained using differential evolution, an evolutionary optimization technique. The optimal solutions indicate that there exist trajectories with lower cost and for significantly lower time of flight than those reported in the literature for similar problems.