Semi-Analytical Perturbative Approaches to Third Body Resonant Trajectories

TL;DR

This paper compares three perturbative methods to predict spacecraft trajectories affected by third-body gravitational influences, especially during close approaches, enhancing understanding of their accuracy in multi-body dynamics.

Contribution

It provides a comparative analysis of averaged dynamics, Opik's theory, and Keplerian map approaches for modeling third-body perturbations in various encounter scenarios.

Findings

Averaged dynamics best for distant encounters

Opik's theory effective for close approaches

Keplerian map offers a balance between methods

Abstract

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.