Numerical Methods to Design Low-Energy, Low-Thrust Sun-Perturbed Transfers to the Moon

In this work we merge together the low-thrust propulsion and the invariant manifold technique to design transfer trajectories from GTO to equatorial orbits around the Moon. The dynamical framework is the Sun-perturbed Earth-Moon-spacecraft restricted three-body problem. The problem is formulated in an optimal control fashion, and it is solved using a direct transcription approach. Two different direct methods have been investigated: multiple shooting and collocation; in the latter the dynamics is discretized over an uniform time grid using a 6th-order linear multi-point method. Optimal transfers are made up by three different phases: a spiral arc, hyperbolic transit orbit shadowing the invariant manifolds associated to L 1, and a low-thrust arc that places the spacecraft on its final orbit around the Moon. Results show the feasibility of this kind of transfers requiring both moderate propellant mass fractions and reasonable times of flight. Considerations are made on the solutions found with respect to numerical methods adopted.