Generalized periodic orbits in some restricted three-body problems

TL;DR

This paper demonstrates the existence of numerous generalized periodic orbits in certain restricted three-body problems by framing them as periodically forced Kepler problems and applying existing results, especially for small mass ratios.

Contribution

It extends the application of periodic orbit existence results to restricted three-body problems with singularities, highlighting the role of small mass ratios.

Findings

Existence of many generalized periodic orbits for small mass ratios

Application of forced Kepler problem framework to three-body problems

Regularization of double collisions in periodic orbits

Abstract

We treat the circular and elliptic restricted three-body problems in inertial frames as periodically forced Kepler problems with additional singularities and explain that in this setting the main result of [4] is applicable. This guarantees the existence of an arbitrary large number of generalized periodic orbits (periodic orbits with possible double collisions regularized) provided the mass ratio of the primaries is small enough.