Study on escaping energy in circular restricted three-body problem

Escaping trajectories are investigated using a Poincare map method in the circular restricted three body problem consisting of spacecraft, planet and moon. On the condition that Jacobi constant is fixed, the escaping trajectories are integrated back to the first periapsis from vicinity of L1 and L2 and the escaping velocity of moon is obtained. The results show that the optimal escaping velocities through the vicinity of L1 and L2 are different. Compared with the Kepler method it saves 46.5 m/s and 42.3 m/s ΔV escaping from the moon. It is more precision than the result of 38.9 m/s which is obtained by Villac in the Hill problem model. The optimal escaping velocities of the primary planetary moon in the solar system are also presented.