Transfer to long term distant retrograde orbits around the Moon

• A numerical algorithm for finding DRO without approximations is investigated.
• The launch window and the zone of a long term DRO are proposed.
• Two different types of transfers to a long term DRO around the Moon are designed.
• Interior transfers can also achieve low energy transfers like exterior transfers.

Distant retrograde orbit (DRO), serving for future astrophysical observatories and communications, has received much attention, including those around the Moon. Instead of high-order analytical approximate solutions, a numerical algorithm is deduced to find DRO, with a given Jacobi value or given amplitude. The goal is to determine the DRO around the Moon and the Lyapunov orbits which are tangential to the DRO. Considering the force of Sun׳s gravity, the long term DRO remains bounded at some moments which are expropriated as the launch window. After determining the launch window of a long term DRO, two different types of transfers to the DRO are obtained, namely interior transfers and exterior transfers. Numerical results indicate that exterior transfers need less fuel consumption while interior transfers always achieve quicker transfers. By the comparison of these transfer strategies, the interior transfers with non-tangential injection can be accomplished with as less fuel consumption as the exterior transfers approximately, about 549 m/s less than the transfers in the previous works.