Free Return Trajectories in Lunar Missions

Four types of symmetric free return trajectories in the planar circular restricted three-body problem are computed and compared with each other. One of these four types is most applicable in practice. Concentrating ourselves on this special type of free return trajectory, the corresponding planar asymmetric cases are studied. Then the studies are generalized to the three-dimensional case. The restrictions on the inclination angle of the probe at the perilune are discussed. It is found that the maximum inclination at the perilune between the probe's orbit plane and the Moon's orbit plane is restricted by the heights of the perigee and the perilune of the free return trajectory. However, the inclination at the perigee is nearly not affected by them. At last, a strategy to design free return trajectories in the real Earth-Moon system is proposed. Some numerical simulations are done to show the feasibility of this orbit design strategy. The discussions from the planar case to the spatial case and then to the real force model can also be applied to the other three types of planar free return trajectories.