Skip to main content
SpringerLink
Log in

Regular and chaotic orbits in the dynamics of exoplanets

  • Review
  • Session A: Reviews
  • Published:
The European Physical Journal Special Topics Aims and scope Submit manuscript

Abstract

Many of exoplanetary systems consist of more than one planet and the study of planetary orbits with respect to their long-term stability is very interesting. Furthermore, many exoplanets seem to be locked in a mean-motion resonance (MMR), which offers a phase protection mechanism, so that, even highly eccentric planets can avoid close encounters. However, the present estimation of their initial conditions, which may change significantly after obtaining additional observational data in the future, locate most of the systems in chaotic regions and consequently, they are destabilized. Hence, dynamical analysis is imperative for the derivation of proper planetary orbital elements. We utilize the model of spatial general three body problem, in order to simulate such resonant systems through the computation of families periodic orbits. In this way, we can figure out regions in phase space, where the planets in resonances should be ideally hosted in favour of long-term stability and therefore, survival. In this review, we summarize our methodology and showcase the fact that stable resonant planetary systems evolve being exactly centered at stable periodic orbits. We apply this process to co-orbital motion and systems HD 82943, HD 73526, HD 128311, HD 60532, HD 45364 and HD 108874.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. J. Laskar, A.C.M. Correia, A&A 496, L5 (2009)

    Article  ADS  Google Scholar 

  2. A.C.M. Correia, J. Couetdic, J. Laskar, X. Bonfils, M. Mayor, J.-L. Bertaux, F. Bouchy, X. Delfosse, T. Forveille, C. Lovis, F. Pepe, C. Perrier, D. Queloz, S. Udry, A&A 511, A21 (2010)

    Article  ADS  Google Scholar 

  3. H. Rein, J.C.B. Papaloizou, W. Kley, A&A 510, A4 (2010)

    Article  ADS  Google Scholar 

  4. C. Lovis, D. Ségransan, M. Mayor, S. Udry, W. Benz, J.-L. Bertaux, F. Bouchy, A.C.M. Correia, J. Laskar, G. Lo Curto, C. Mordasini, F. Pepe, D. Queloz, N.C. Santos, A&A 528, A112 (2011)

    Article  ADS  Google Scholar 

  5. G. Campanella, R.P. Nelson, C.B. Agnor, MNRAS 433, 3190 (2013)

    Article  ADS  Google Scholar 

  6. R.A. Wittenmyer, S. Wang, J. Horner, C.G. Tinney, R.P. Butler, H.R.A. Jones, S.J. O’Toole, J. Bailey, B.D. Carter, G.S. Salter, D. Wright, J.-L. Zhou, ApJS 208, 2 (2013)

    Article  ADS  Google Scholar 

  7. K.I. Antoniadou, G. Voyatzis, H. Varvoglis, IAUS 310, 82 (2014)

    Article  ADS  Google Scholar 

  8. J. Lillo-Box, D. Barrado, L. Mancini, T. Henning, P. Figueira, S. Ciceri, N. Santos, A&A 576, A88 (2015)

    Article  ADS  Google Scholar 

  9. F. Marzari, S.J. Weidenschilling, Icarus 156, 570 (2002)

    Article  ADS  Google Scholar 

  10. S. Chatterjee, E.B. Ford, S. Matsumura, F.A. Rasio, ApJ 686, 580 (2008)

    Article  ADS  Google Scholar 

  11. E.W. Thommes, J.J. Lissauer, ApJ 597, 566 (2003)

    Article  ADS  Google Scholar 

  12. M.H. Lee, E.W. Thommes, ApJ 702, 1662 (2009)

    Article  ADS  Google Scholar 

  13. A.C.M. Correia, J. Laskar, F. Farago, G. Boué, CeMDA 111, 105 (2011)

    Article  ADS  Google Scholar 

  14. S. Ferraz-Mello, C. Beaugé, T.A. Michtchenko, CeMDA 87, 99 (2003)

    Article  ADS  Google Scholar 

  15. M.H. Lee, ApJ 611, 517 (2004)

    Article  ADS  Google Scholar 

  16. C. Beaugé, T.A. Michtchenko, S. Ferraz-Mello, MNRAS 365, 1160 (2006)

    Article  ADS  Google Scholar 

  17. J.D. Hadjidemetriou, G. Voyatzis, CeMDA 107, 3 (2010)

    Article  ADS  MathSciNet  Google Scholar 

  18. J.D. Hadjidemetriou, G. Voyatzis, IJBC 21, 2195 (2011)

    ADS  MathSciNet  Google Scholar 

  19. G. Voyatzis, K.I. Antoniadou, K. Tsiganis, CeMDA 119, 221 (2014)

    Article  ADS  MathSciNet  Google Scholar 

  20. T.A. Michtchenko, C. Beaugé, S. Ferraz-Mello, CeMDA 94, 411 (2006)

    Article  ADS  Google Scholar 

  21. G. Voyatzis, T. Kotoulas, J.D. Hadjidemetriou, MNRAS, 395, 2147 (2009)

    Article  ADS  Google Scholar 

  22. J.-B. Delisle, J. Laskar, A.C.M. Correia, G. Boué, A&A 546, A71 (2012)

    Article  ADS  Google Scholar 

  23. K.I. Antoniadou, G. Voyatzis, CeMDA 115, 161 (2013)

    Article  ADS  MathSciNet  Google Scholar 

  24. K.I. Antoniadou, G. Voyatzis, ApSS 349, 657 (2014)

    ADS  Google Scholar 

  25. J.-B. Delisle, J. Laskar, A.C.M. Correia, A&A 566, A137 (2014)

    Article  ADS  Google Scholar 

  26. K.I. Antoniadou, G. Voyatzis, H. Varvoglis, in Proceedings of the 6th International Conference on Numerical Analysis (NumAn2014) (AMCL/TUC, Greece, 2014), p. 7, ISBN: 978-960-8475-22-9

  27. K.I. Antoniadou, Ph.D. thesis, Aristotle University of Thessaloniki, 2014

  28. G. Voyatzis, ApJ 675, 802 (2008)

    Article  ADS  Google Scholar 

  29. K.I. Antoniadou, G. Voyatzis, T. Kotoulas, IJBC 21, 2211 (2011)

    ADS  MathSciNet  Google Scholar 

  30. C. Beaugé, S. Ferraz-Mello, T.A. Michtchenko, ApJ 593, 1124 (2003)

    Article  ADS  Google Scholar 

  31. S. Ferraz-Mello, T.A. Michtchenko, C. Beaugé, in Chaotic Worlds: from Order to Disorder in Gravitational N-Body Dynamical Systems, edited by B.A. Steves, A.J. Maciejewski, M. Hendry (Springer, The Netherlands, 2006), p. 255

  32. C. Marchal, The three-body problem (Elsevier, Amsterdam, 1990)

  33. J.D. Hadjidemetriou, in Chaotic Worlds: from Order to Disorder in Gravitational N-Body Dynamical Systems, edited by B.A. Steves, A.J. Maciejewski, M. Hendry (Springer, The Netherlands, 2006), p. 43

  34. J.D. Hadjidemetriou, D. Psychoyos, G. Voyatzis, CeMDA 104, 23 (2009)

    Article  ADS  MathSciNet  Google Scholar 

  35. J.D. Hadjidemetriou, G. Voyatzis, CeMDA 111, 179 (2011)

    Article  ADS  MathSciNet  Google Scholar 

  36. P. Robutel, A. Pousse, CeMDA 117, 17 (2013)

    Article  ADS  MathSciNet  Google Scholar 

  37. C. Froeschlé, E. Lega, R. Gonczi, CeMDA 67, 41 (1997)

    Article  ADS  Google Scholar 

  38. X. Tan, M.J. Payne, M.H. Lee, E.B. Ford, A.W. Howard, J.A. Johnson, G.W. Marcy, J.T. Wright, ApJ 777, 101 (2013)

    Article  ADS  Google Scholar 

  39. R.A. Wittenmyer, X. Tan, M.H. Lee, J. Horner, C.G. Tinney, R.P. Butler, G.S. Salter, B.D. Carter, H.R.A. Jones, S.J. O’Toole, J. Bailey, D. Wright, J.D. Crane, S.A. Schectman, P. Arriagada, I. Thompson, D. Minniti, M. Diaz, ApJ 780, 140 (2014)

    Article  ADS  Google Scholar 

  40. R. Barnes, R. Deitrick, R. Greenberg, T.R. Quinn, S.N. Raymond, ApJ 801, 101 (2015)

    Article  ADS  Google Scholar 

  41. S.S. Vogt, R.P. Butler, G.W. Marcy, D.A. Fischer, G.W. Henry, G. Laughlin, J.T. Wright, J.A. Johnson, ApJ 632, 638 (2005)

    Article  ADS  Google Scholar 

  42. A.C.M. Correia, S. Udry, M. Mayor, W. Benz, J.-L. Bertaux, F. Bouchy, J. Laskar, C. Lovis, C. Mordasini, F. Pepe, D. Queloz, A&A 496, 521 (2009)

    Article  ADS  Google Scholar 

  43. K.I. Antoniadou, G. Voyatzis, MNRAS 461, 3822 (2016)

    Article  ADS  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Physics, Aristotle University of Thessaloniki, 54124, Thessaloniki, Greece

    K.I. Antoniadou

Authors
  1. K.I. Antoniadou
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to K.I. Antoniadou.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Antoniadou, K. Regular and chaotic orbits in the dynamics of exoplanets. Eur. Phys. J. Spec. Top. 225, 1001–1016 (2016). https://doi.org/10.1140/epjst/e2016-02651-6

Download citation

  • Received:

  • Revised:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1140/epjst/e2016-02651-6

Search

Navigation