Review Article: Resonant Families of Periodic Orbits in the Restricted Three-body Problem* *Supported by the National Natural Science Foundation of China.

Abstract

The restricted three-body problem (RTBP) is a fundamental model in celestial mechanics. Periodic orbits in the synodic frame play a very important role in understanding the dynamics of the RTBP model. Most of these periodic orbits, when interpreted in the sidereal frame, are actually resonant periodic orbits. As a result, numerical computation of the periodic orbits is also one approach for researchers to understand the orbital resonances of the three-body problem. Extensive studies have been carried out on this topic, concerning either the circular case or the elliptic case of this model. In this paper, we make a brief review of the history and current status of the studies on resonant periodic orbits in the RTBP model. Starting from the unperturbed two-body problem, we organize the review paper by the two cases of this model—the circular restricted three-body problem and the elliptic restricted three-body problem.