Escaping Trajectories in the Hill Three-Body Problem and Applications

Low-energy escaping trajectories in the Hill three-body problem are investigated numerically using a Poincare map that relates the crossing of a plane containing one of the collinear libration points back to the first periapsis passage. This set of periapsis points is confined in a small region that determines some conditions for escape from any planetary satellite. In particular, the minimum energy to escape from a given circular orbit is obtained together with restrictions on the initial conditions (inclination, argument of periapsis, and longitude of the ascending node). This leads to a new optimal transfer criterion for the class of directly escaping trajectories. Savings on the order of 130 m/s in the case of Europa are obtained when compared to a classic two-body model. The results are also extended to the problem of low-energy capture. Numerical applications are given for the cases of Miranda, Europa, Titan, and Triton.