Traveling between the Lagrange points and the moon

A detailed study is presented of the possible free-fall trajectories from the moon to the four Lagrangian points L1, L2, L4, L5, and back from these points to the moon. The Lagrangian point L3 has not been included in the study because it is considered of less practical interest in connection with travel from and to an eventual large space station or space colony. The problem of compromising between short transit times and small residual velocity at L1, which is proportional to the amount of fuel needed, is considered in detail. Several families of possible trajectories for each of the four Lagrangian points are represented. For L1 there is a family of slow indirect trajectories and a family containing both fast and slow direct trajectories. For L2 four different families are found, three of which having a slow and a fast branch. As for the triangular libration points, L4 and L5, a family of transfer orbits is described for each of them. Each family also has a slow and a fast branch. Finally, some relations between transfer orbits and the classical families of periodic solutions of the restricted three-body problem are discussed.