Computational and Applied Mathematics

, Volume 37, Supplement 1, pp 65–71 | Cite as

Coorbital capture at arbitrary inclination

  • Fathi NamouniEmail author
  • Helena Morais


The process of capture in the coorbital region of a solar system planet is studied. Absolute capture likelihood in the 1:1 resonance is determined by randomly constructed statistical ensembles numbering \(7.24\times 10^5\) of massless asteroids that are set to migrate radially from the outer to the inner boundaries of the coorbital region of a Jupiter-mass planet. Orbital states include coorbital capture, ejection, collisions with the Sun and the planet and free-crossing of the coorbital region. The relative efficiency of retrograde capture with respect to prograde capture is confirmed as an intrinsic property of the coorbital resonance. Half the asteroids cross the coorbital region regardless of eccentricity and for any inclination less than \(120^\circ \). We also find that the recently discovered retrograde coorbital of Jupiter, asteroid 2015 BZ509, lies almost exactly at the capture efficiency peak associated with its orbital parameters.


Orbital dynamics Resonance Asteroids Centaurs 

Mathematics Subject Classification

70F07 70F15 



The authors thank two anonymous reviewers for their comments. F. N. thanks the 2016 Colóquio Brasileiro de Dinâmica Orbital Organizing Committee for their kind invitation to the conference where part of this work was presented. The authors acknowledge support from Grant 2015/17962-5 of São Paulo Research Foundation (FAPESP). The numerical simulations in this work were performed at the Centre for Intensive Computing ‘Mésocentre sigamm’ hosted by the Observatoire de la Côte dAzur.


  1. Kozai Y (1962) Secular perturbations of asteroids with high inclination and eccentricity. Astron J 67:591. doi: 10.1086/108790 MathSciNetCrossRefGoogle Scholar
  2. Lidov ML (1962) The evolution of orbits of artificial satellites of planets under the action of gravitational perturbations of external bodies. Plan Space Sci 9:719–759. doi: 10.1016/0032-0633(62)90129-0 CrossRefGoogle Scholar
  3. Morais MHM, Namouni F (2013a) Asteroids in retrograde resonance with Jupiter and Saturn. Mon Not R Astron Soc 436:L30–L34. doi: 10.1093/mnrasl/slt106. arXiv:1308.0216
  4. Morais MHM, Namouni F (2013b) Retrograde resonance in the planar three-body problem. Celest Mech Dyn Astron 117:405–421. doi: 10.1007/s10569-013-9519-2. arXiv:1305.0016
  5. Morais MHM, Namouni F (2016) A numerical investigation of coorbital stability and libration in three dimensions. Celest Mech Dyn Astron 125:91–106, doi: 10.1007/s10569-016-9674-3. arXiv:1602.04755
  6. Morais MHM, Namouni F (2017) Reckless orbiting in the solar system. Nature 543:635–636CrossRefGoogle Scholar
  7. Murray CD, Dermott SF (1999) Solar system dynamics. Cambridge University Press, CambridgezbMATHGoogle Scholar
  8. Namouni F (1999) Secular interactions of coorbiting objects. Icarus 137:293–314. doi: 10.1006/icar.1998.6032 CrossRefGoogle Scholar
  9. Namouni F, Morais MHM (2015) Resonance capture at arbitrary inclination. Mon Not R Astron Soc 446:1998–2009. doi: 10.1093/mnras/stu2199. arXiv:1410.5383
  10. Namouni F, Morais MHM (2017) Resonance capture at arbitrary inclination: Effect of the radial drift rate. Mon Not R Astron Soc 467:2673–2683, doi: 10.1093/mnras/stx290. arXiv:1702.00236
  11. Namouni F, Christou AA, Murray CD (1999) Coorbital dynamics at large eccentricity and inclination. Phys Rev Lett 83:2506–2509. doi: 10.1103/PhysRevLett.83.2506 CrossRefGoogle Scholar
  12. Wiegert P, Connors M, Veillet C (2017) A retrograde co-orbital asteroid of Jupiter. Nature 543:687–689CrossRefGoogle Scholar
  13. Wisdom J (1980) The resonance overlap criterion and the onset of stochastic behavior in the restricted three-body problem. Astron J 85:1122–1133. doi: 10.1086/112778 CrossRefGoogle Scholar

Copyright information

© SBMAC - Sociedade Brasileira de Matemática Aplicada e Computacional 2017

Authors and Affiliations

  1. 1.Université Côte d’Azur, CNRS, Observatoire de la Côte d’AzurNiceFrance
  2. 2.Instituto de Geociências e Ciências ExatasUniversidade Estadual Paulista (UNESP)Rio ClaroBrazil

Personalised recommendations