Review Article: Resonant Families of Periodic Orbits in the Restricted Three-body Problem

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.