Optimal low-thrust transfer trajectories from Earth to Earth-Moon L2 point halo orbits

The restricted three-body problem deals with the motion of a secondary body (spacecraft) of negligible mass under the influence of two large primary bodies (Earth and Moon). Since there can be no analytic solution to the problem, numerical solutions are used to study and optimize the motion of the secondary body in the primary system. The collinear L2 point of the Earth-Moon system lends a unique opportunity to future lunar missions to the far-side of the Moon. These missions will require direct communications with the Earth and a relay placed in a halo orbit about the L2 point could provide this service. Development of the optimal low-thrust transfer trajectories required between Earth and the L2 halo orbit is the primary goal of the work. A general optimal solution method is constructed using sequential nonlinear programming to find minimum-propellant spacecraft transfers. Only a single thrust phase of the trajectory (using tangential steering) is optimized with the spacecraft traveling the remaining time-of-flight on the stable manifold of the halo insertion point. The solution method is demonstrated for a number of insertion points on two different reference halos (7,000 km x 7,000 km diameter circular orbit and 70,000 km x 25,000 km diameter elliptic orbit) for both the circular and the elliptic restricted three-body problems. Depending on the reference halo chosen, typical optimal thrust trajectories require a time-of-flight of approximately 150 days and 580 kg of ammonia gas propellant.