On quasi-satellite periodic motion in asteroid and planetary dynamics

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.

arXiv commentAccepted for publication in Celestial Mechanics and Dynamical Astronomy

References in corpus (18)

• On the co-orbital motion of two planets in quasi-circular orbits
• Origin and Detectability of coorbital planets from radial velocity data
• Quasi-satellite orbits in the general context of dynamics in the 1:1 mean motion resonance. Perturbative treatment
• Dynamics of two planets in co-orbital motion
• 2/1 resonant periodic orbits in three dimensional planetary systems
• An interstellar origin for Jupiter's retrograde co-orbital asteroid
• Tidal evolution of close-in exoplanets in co-orbital configurations
• The orbit of 2010 TK7. Possible regions of stability for other Earth Trojan asteroids
• The TROY project: Searching for co-orbital bodies to known planets. I. Project goals and first results from archival radial velocity
• The nature of the giant exomoon candidate Kepler-1625 b-i
• Detection of co-orbital planets by combining transit and radial-velocity measurements
• The 1:1 resonance in Extrasolar Systems: Migration from planetary to satellite orbits
• On the co-orbital motion in the planar restricted three-body problem: the quasi-satellite motion revisited
• The dynamics of the elliptic Hill problem : Periodic orbits and stability regions
• Inclined asymmetric librations in exterior resonances
• On the bifurcation and continuation of periodic orbits in the three-body problem
• 1/1 resonant periodic orbits in three dimensional planetary systems
• The rectilinear three body problem as a basis for studying highly-eccentric systems

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