Computations of low energy escaping/capturing trajectories in hill's region via an extended Poincaré map

In this paper, low energy escaping trajectories in Hill's region are investigated via an extended Poincare map. The extended Poincaré map in this paper needs two (not one) surfaces of sections transversal to the flow in phase space, i.e., relates the crossing of a plane containing one of the collinear libration points back to the periapsis passage. Meanwhile, the map is calculated numerically using the Total-Variation-Diminishing Runge-Kutta integration method to get a good description of the Poincaré sections. The capturing trajectories can be achieved straightforwardly by considering the symmetry of the Hill three-body problem which is the underlying model we focused on. Finally, the 2D and 3D escaping and capturing trajectories of the Rhea orbiter are successfully simulated which verify the desired efficiency and robustness of our method.