Examples of the nonlinear dynamics of ballistic capture and escape in the earth-moon system

An example of a trajectory is given which is initially captured in an elliptic resonant orbit about the Earth and then ballistically escapes the Earth-Moon system. This is demonstrated by a numerical example in three-dimensions using a planetary ephemeris. Another example shows a mechanism of how an elliptic orbit about the Earth can increase its energy by performing a complex nonlinear transition to an elliptic orbit of a larger semi-major axis. Capture is also considered. An application of ballistic capture at the Moon via an unstable periodic orbit using the four-body Sun-Earth-Moon-SIC interaction is described.