Skip to main content
SpringerLink
Log in

Resonances in Multiple Planetary Systems

  • Published:
Celestial Mechanics and Dynamical Astronomy Aims and scope Submit manuscript

Abstract

Since the first extrasolar planet was discovered about 10 years ago, a major point of dynamical investigations was the determination of stable regions in extrasolar planetary systems where additional planets may exist. Using numerical methods, we investigate the dynamical stability in known multiple planetary systems (HD74156, HD38529, HD168443, HD169830) with special interest on the region between the two known planets and on the mean motion resonances inside this region. As a dynamical model we take the restricted 4-body problem containing the host star, the two planets and massless test-planets. For our numerical integrations, we used the Lie-integrator and additionally the Fast Lyapunov Indicators as a tool for detecting chaotic motion. We also investigated the inner resonances with the outer planet and the outer resonances with the inner planet with test-planets located inside the resonances.

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

  • C. Beauge T. A. Michtchenko (2003) ArticleTitle‘Modelling the high-eccentricity planetary three-body problem. Application to the GJ876 planetary system’ Monthly Notices Roy. Astr. Soc 341 760–770 Occurrence Handle10.1046/j.1365-8711.2003.06345.x

    Article  Google Scholar 

  • R. Dvorak E. Pilat-Lohinger B. Funk F. Freistetter (2003a) ArticleTitle‘Planets in habitable zones: A study of the binary γ Cephei’ Astr. Astrophys. 398 L1–L4 Occurrence Handle10.1051/0004-6361:20021805

    Article  Google Scholar 

  • R. Dvorak E. Pilat-Lohinger B. Funk F. Freistetter (2003b) ArticleTitle‘A study of the stability regions in the planetary system HD 74156: Can it host earthlike planets in habitable zones?’ Astr. Astrophys. 410 LI3–LI6

    Google Scholar 

  • S. Ferraz-Mello C. Beaugé T. A. Michtchenko (2003) ArticleTitle‘Evolution of migrating planet pairs in resonance’ Celestial Mech. Dyn. Astr 87 99–112 Occurrence Handle10.1023/A:1026126716612

    Article  Google Scholar 

  • C. Froeschlé E. Lega R. Gonzi (1997) ArticleTitle‘Fast lyapunov indicators. Application to asteroidal motion’ Celestial Mech. Dyn. Astr 67 41–62 Occurrence Handle10.1023/A:1008276418601

    Article  Google Scholar 

  • K. Gozdziewski E. Bois A. J. Maciejewski (2001) ArticleTitle‘Global dynamics of planetary systems with the MEGNO criterion’ Astr. Astrophys 378 569–586 Occurrence Handle10.1051/0004-6361:20011189

    Article  Google Scholar 

  • A. Hanslmeier R. Dvorak (1984) ArticleTitle‘Numerical integrations with Lie-series’ Astr. Astrophys 132 203–211

    Google Scholar 

  • L. Kiseleva-Eggleton E. Bois N. Rambaux R. Dvorak (2002a) ArticleTitle‘Global dynamics and stability limits for planetary systems around HD 12661 HD 38529 HD 37124 and HD 160691’ Astrophys. J. 578 L145–L148 Occurrence Handle10.1086/344706

    Article  Google Scholar 

  • L. Kiseleva-Eggleton,E.Bois,N.Rambaux, R. Dvorak, E.J. Rivera 2002b.‘On the dynamical state of new multi-planet systems’ Am. Astr. Soc. Meeting201♯ 24.04.

  • M. H. Lee S. J. Peale (2003) ArticleTitle‘Extrasolar planets and mean-motion resonances’ Sci. Frontiers Res. Extrasolar Planets, ASP Conf. Ser 294 197–200

    Google Scholar 

  • H. Lichtenegger (1984) ArticleTitle‘The dynamics of bodies with variable masses’ Celestial Mech. Dyn. Astr 34 357–368

    Google Scholar 

  • M. Mayor D. Queloz (1995) ‘A jupiter-mass companion to a solar-type star’, Nature 378 355

    Google Scholar 

  • K. Menou S. Tabachnik (2003) ArticleTitle‘Dynamical habitability of known extrasolar planetary systems’ The Astrophys. J 583 473–488 Occurrence Handle10.1086/345359

    Article  Google Scholar 

  • T. A. Michtchenko R. Malhotra (2004) ArticleTitle‘Secular dynamics of the three-body problem: application to the \upsilon Andromedae planetary system’ Icarus 168 237–248 Occurrence Handle10.1016/j.icarus.2003.12.010

    Article  Google Scholar 

  • Z. Sándor B. Érdi C. Efthymiopoulos (2000) ArticleTitle‘The phase space structure around L4 in the restricted three-body problem’ Celestial Mech. Dyn. Astr 78 113–123 Occurrence Handle10.1023/A:1011112228708

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Institute for Astronomy , University of Vienna, Austria

    B. Funk, E. Pilat-Lohinger, R. Dvorak & F. Freistetter

  2. Department of Astronomy, Eötvös University, Hungary

    B. Èrdi

Authors
  1. B. Funk
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. E. Pilat-Lohinger
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. R. Dvorak
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. F. Freistetter
    View author publications

    You can also search for this author in PubMed Google Scholar

  5. B. Èrdi
    View author publications

    You can also search for this author in PubMed Google Scholar

Rights and permissions

Reprints and permissions

About this article

Cite this article

Funk, B., Pilat-Lohinger, E., Dvorak, R. et al. Resonances in Multiple Planetary Systems. Celestial Mech Dyn Astr 90, 43–50 (2004). https://doi.org/10.1007/s10569-004-0516-3

Download citation

  • Received:

  • Revised:

  • Accepted:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10569-004-0516-3

Keywords

Search

Navigation