Combined Optimal Low‐Thrust and Stable‐Manifold Trajectories to the Earth‐Moon Halo Orbits

In this paper we incorporate the low‐thrust propulsion in the stable manifold technique to design transfer trajectories to the halo orbits around L1 and L2 of the Earth‐Moon system. The problem is stated in an optimal control scheme and solved using direct transcription and collocation; the dynamics is discretized over an uniform time grid using a sixth‐order linear multi‐point method. The resulting transfers are made up by a spiral arc that targets a piece of the stable manifold associated to the final orbit. Thanks to the generality of this approach, halo‐to‐Moon transfers are also computed combining unstable manifolds and low‐thrust. Furthermore, complete Earth‐to‐Moon transfers via halos can also be constructed. Results show the feasibility of this kind of transfers requiring moderate propellant mass fractions and feasible times of flight.