Skip to main content
SpringerLink
Log in

Trojan orbits in secular resonances

  • Periodic Orbits, Resonances, and Asteroid Motions
  • Published:
Celestial mechanics Aims and scope Submit manuscript

Abstract

A near equality between the nodal rates of suitably defined Trojan orbits and Jupiter represents an important type of a secular resonance. This case is realized by the model Sun-Jupiter-Saturn-Trojan, referred to the invariable plane. A second theoretical example is based on the elliptic three-body problem Sun-Jupiter-Trojan, where the vanishing nodal rate of a special Trojan orbit and the vanishing rate of Jupiter's longitude of perihelion define a secular resonance.

We investigate the perturbations in the asteroidal inclinations and the nodes and consider the possibility of a libration.

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

References

  • Bien,R. and Schubart,J.: 1983,Dynamical Trapping and Evolution in the Solar System, Ed.: V.V. Markellos and Y. Kozai, IAU Coll. No. 74, pp.153–161.

  • Cohen,C.J., Hubbard,E.C., and Oesterwinter,C.: 1973,Astron. Papers American Ephemeris Washington, Vol. 22, part 1.

  • Schubart,J.: 1966,The Theory of Orbits in the Solar System and in Stellar Systems, Ed.: G. Contopoulos, IAU Symp. No. 25, pp.187–193.

  • Schubart,J. and Stumpff,P.: 1966,Veröffentl.Astron. Rechen-Inst. Heidelberg No. 18.

  • Williams,J.G.: 1975,J. Geophys.Res. 80, pp.2914–2916.

    Google Scholar 

  • Yoder,C.F.: 1979,Icarus 40, pp.341–344.

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Astronomisches Rechen-Institut, Mönchhofstrasse 12-14, D-6900, Heidelberg 1, Federal Republic of Germany

    R. Bien & J. Schubart

Authors
  1. R. Bien
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. J. Schubart
    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

Bien, R., Schubart, J. Trojan orbits in secular resonances. Celestial Mechanics 34, 425–434 (1984). https://doi.org/10.1007/BF01235819

Download citation

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF01235819

Keywords

Search

Navigation