Moon transfer design using Weak Stability Boundary

The aim of this work is to analyze the feasibility of Earth-Moon transfers using weak stability boundary, in order to reach a Halo orbit around L2. The analysis is firstly conducted in the CR3BP (Circular Restricted 3 Body Problem) and afterwards perturbations are introduced. The objective of such transfer is to reduce the mission cost by lowering the propellant requirements compared to a traditional Hohmann transfer, aiming for a ballistic capture at Moon arrival. Such capture is possible using region in space in which the gravitation forces of the influencing bodies tend to balance each other, called weak stability boundary. Firstly a suitable destination Halo orbit is computed using differential correction in a single shooting method, with an attention to the stability of the Halo orbit in order to reduce station keeping costs. Afterwards, with the aid of invariant manifolds, the trajectory connecting a circular low Earth orbit to the selected Halo is obtained in the CR3BP. Two trajectory are proposed, using weak stability boundaries around L2 in the Earth-Moon system and around either L1 or L2 in the Sun-Earth system in order to achieve the required transfer. The analysis is conducted for different Moon phases at arrival. Secondly perturbations to the baseline trajectory calculated are introduced and a perturbed trajectory is computed, using multiple-shooting method, considering a Moon arrival window of a year. Lastly consideration on the effect of Moon phase are reported, followed by a comparison of the two transfer options in the CR3BP and the perturbed system, and on the variability of the transfer cost and time throughout an year. Finally some conclusive remarks on the convenience of such transfer and the reliability of the CR3BP model are presented.