Trajectories to and from the Lagrange points and the primary body surfaces

This paper investigates ballistic trajectories to and from the vicinity of the Lagrange points L1 and L2 and the surfaces of the primaries in the circular restricted three-body problem. The study focuses on trajectories from the Lagrange points and their Lyapunov orbits that can access the entire surfaces of the primary bodies for the sun-Earth and Earth-moon systems. By a symmetry property, trajectories leaving the surface of the primary bodies and reaching the Lagrange points and their Lyapunov orbits can also be found. The lowest velocity increment providing such whole-surface coverage from the Lagrange points and the lowest-energy Lyapunov orbit providing whole-surface coverage are found. Applications of such trajectories are to be found in sample return missions and future crewed missions that use the Lagrange points as exploration staging posts.