On quasi-satellite periodic motion in asteroid and planetary dynamics

TL;DR

This paper investigates quasi-satellite periodic orbits in the three-body problem using analytical continuation, identifying new families of orbits and analyzing their stability, which could explain long-lived co-orbital objects.

Contribution

It extends the understanding of quasi-satellite orbits by identifying and analyzing new families of periodic solutions in the three-body problem, including their stability properties.

Findings

Identification of critical orbits in family f

Existence of a new spatial orbit family

Stable periodic orbits indicating regular motion regimes

Abstract

Applying the method of analytical continuation of periodic orbits, we study quasi-satellite motion in the framework of the three-body problem. In the simplest, yet not trivial model, namely the planar circular restricted problem, it is known that quasi-satellite motion is associated with a family of periodic solutions, called family $f$, which consists of 1:1 resonant retrograde orbits. In our study, we determine the critical orbits of family $f$ that are continued both in the elliptic and in the spatial model and compute the corresponding families that are generated and consist the backbone of the quasi-satellite regime in the restricted model. Then, we show the continuation of these families in the general three-body problem, we verify and explain previous computations and show the existence of a new family of spatial orbits. The linear stability of periodic orbits is also studied. Stable periodic orbits unravel regimes of regular motion in phase space where 1:1 resonant angles librate. Such regimes, which exist even for high eccentricities and inclinations, may consist dynamical regions where long-lived asteroids or co-orbital exoplanets can be found.