  In the framework of multi-body dynamics, successive encounters with a third
body, even if well outside of its sphere of influence, can noticeably alter the
trajectory of a spacecraft. Examples of these effects have already been
exploited by past missions such as SMART-1, as well as are proposed to benefit
future missions to Jupiter, Saturn or Neptune, and disposal strategies from
Earth's High Eccentric or Libration Point Orbits. This paper revises three
totally different descriptions of the effects of the third body gravitational
perturbation. These are the averaged dynamics of the classical third body
perturbing function, the Opik's close encounter theory and the Keplerian map
approach. The first two techniques have respectively been applied to the cases
of a spacecraft either always remaining very far or occasionally experiencing
extremely close approaches to the third body. However, the paper also seeks
solutions for trajectories that undergo one or more close approaches at
distances in the order of the sphere of influence of the third body. The paper
attempts to gain insight into the accuracy of these different perturbative
techniques into each of these scenarios, as compared with the motion in the
Circular Restricted Three Body Problem.
