Circular and Elliptic Restricted Three Body Problems -- A Comparison

TL;DR

This paper introduces a new formulation of the elliptic restricted three body problem using a constant rotation rate coordinate system, facilitating direct comparison with the circular problem.

Contribution

It presents a novel approach with a fixed rotation rate coordinate system to compare elliptic and circular restricted three body problems more effectively.

Findings

Enables straightforward comparison between elliptic and circular models

Simplifies analysis by using a constant rotation rate

Facilitates future research on three body problem dynamics

Abstract

The elliptic restricted three body problem has been well studied. However, the previous formulations of the problem have used a rotating coordinate system to keep the positions of the primary and secondary on the x-axis. This requires the rotation rate of the rotating coordinate system to speed up and slow down. The approach here uses a rotating coordinate system with constant rotation rate. This formulation allows one to conveniently compare solutions of the elliptic problem with solutions of the circular restricted three body problem.