Escape criterion for restricted three-body problem

In this study, we investigate escape criterion suitable for the restricted three-body problem. First, the Earth-Moon planar circular restricted three-body problem is used as an example, and the escape criteria developed in previous works are presented and analyzed. Next, the energy of a test body is introduced as a key indicator for escape. A condition for identifying escape trajectories in the Earth-Moon planar circular restricted three-body problem is theoretically derived, based on an approximate relationship between the energy of the test body and the two-body energy with respect to the Earth-Moon barycenter. The proposed criterion is then transformed into numerical conditions for trajectory simulations. Numerical simulations verify that the proposed criterion can identify escape trajectories more accurately than those developed in previous works. Finally, the application of this criterion in identifying the natural and artificial escape trajectories is presented.