On the coplanar eccentric non-restricted co-orbital dynamics
We study the phase space of eccentric coplanar co-orbitals in the non-restricted case. Departing from the quasi-circular case, we describe the evolution of the phase space as the eccentricities increase. We find that over a given value of the eccentricity, around 0.5 for equal mass co-orbitals, important topological changes occur in the phase space. These changes lead to the emergence of new co-orbital configurations and open a continuous path between the previously distinct trojan domains near the \(L_4\) and \(L_5\) eccentric Lagrangian equilibria. These topological changes are shown to be linked with the reconnection of families of quasi-periodic orbits of non-maximal dimension.
KeywordsTrojans Co-orbitals Lagrange Planetary problem Three-body problem High eccentricity Mean-motion resonance
The authors acknowledge financial support from the Observatoire de Paris Scientific Council, CIDMA strategic project UID/MAT/04106/2013, ENGAGE SKA POCI-01- 0145-FEDER-022217 (funded by COMPETE 2020 and FCT, Portugal), and the Marie Curie Actions of the European Commission (FP7-COFUND). Parts of this work have been carried out within the frame of the National Centre for Competence in Research PlanetS supported by the SNSF. This work was granted access to the HPC resources of MesoPSL financed by the Region Ile de France and the project Equip@Meso (Reference ANR-10-EQPX-29-01) of the programme Investissements dAvenir supervised by the Agence Nationale pour la Recherche. The authors thank the referees for useful suggestions that greatly improved the description of the results.
- Gascheau, G.: Examen d’une classe d’équations différentielles et application à un cas particulier du problème des trois corps. C. R. Acad. Sci. Paris 16(7), 393–394 (1843)Google Scholar
- Giuppone, C.A., Benitez-Llambay, P., Beaugé, C.: Origin and detectability of co-orbital planets from radial velocity data. MNRAS (2012)Google Scholar
- Leleu, A.: Dynamics of co-orbital exoplanets. PhD thesis (2016)Google Scholar
- Liouville, J.: Sur un cas particulier du problème des trois corps. C. R. Acad. Sci. Paris 14, 503–506 (1842)Google Scholar
- Morbidelli, A.: Modern Celestial Mechanics : Aspects of Solar System Dynamics. Taylor & Francis, London (2002). ISBN 0415279399Google Scholar
- Pousse, A., Robutel, P., Vienne, A.: On the co-orbital motion in the planar restricted three-body problem: the quasi-satellite motion revisited. Celest. Mech. Dyn. Astron. (2017)Google Scholar
- Sidorenko, V., Artemiev, A., Neishtadt, A., Zelenyi, L.: Quasi-satellite orbits in general context of dynamics at 1:1 mean motion resonance: a perturbative treatment (2014)Google Scholar