Analytical and Numerical Approaches to Study the Gravitational Capture in the Four-Body Problem

The objective of this paper is to study the problem of gravitational capture in the bicircular restricted four-body problem. A gravitational capture occurs when a massless particle changes its two-body energy around one celestial body from positive to negative without the use of non-gravitational forces. It is mainly studied the effect of the fourth-body included in the dynamics. The Earth-Moon system with the inclusion of the Sun is used for the numerical simulations. The results show the savings obtained in this more realistic model when compared with the more traditional restricted three-body problem model. It is clear that large savings are obtained thanks to the effect of the Sun, if a proper geometry is used for the maneuver.