Skip to main content
SpringerLink
Log in

Families of periodic orbits in the three-body problem

  • Published:
Celestial mechanics Aims and scope Submit manuscript

Abstract

We show by a general argument that periodic solutions of the planar problem of three bodies (with given masses) form one-parameter families. This result is confirmed by numerical investigations: two orbits found earlier by Standish and Szebehely are shown to belong to continuous one-parameter families of periodic orbits. In general these orbits have a non-zero angular momentum, and the configuration after one period is rotated with respect to the initial configuration. Similar general arguments whow that in the three-dimensional problem, periodic orbits form also one-parameter families; in the one-dimensional problem, periodic orbits are isolated.

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

  • Bray, T. A. and Goudas, C. L.: 1967,Adv. Astron. Astrophys. 5, 71.

    Google Scholar 

  • Broucke, R.: 1969, Technical Report 32-1360, Jet Propulsion Laboratory, Pasadena, California.

    Google Scholar 

  • Bulirsch, R. and Stoer, J.: 1966,Numerische Mathematik 8, 1.

    Google Scholar 

  • Hadjidemetriou, J. D. and Christides, Th.: 1974, submitted toCeles. Mech.

  • Jefferys, W.: 1966,Astron. J. 71, 566.

    Google Scholar 

  • Poincaré, H.: 1892,Les méthodes nouvelles de la mécanique céleste, vol. I, Gauthier-Villars, Paris.

    Google Scholar 

  • Schubart, J.: 1956,Astron. Nachr. 283, 17.

    Google Scholar 

  • Siegel, C. L. and Moser, J. K.: 1971,Lectures on Celestial Mechanics, Springer-Verlag, Berlin, p. 138.

    Google Scholar 

  • Standish, E. M.: 1970, in G. E. O. Giacaglia (ed.),Periodic Orbits, Stability and Resonances, D. Reidel Publ. Co., Dordrecht, Holland, p. 375.

    Google Scholar 

  • Szebehely, V.: 1970, in G. E. O. Giacaglia (ed.),Periodic Orbits, Stability and Resonances, D. Reidel Publ. Co., Dordrecht, Holland, p. 382.

    Google Scholar 

  • Szebehely, V.: 1973, in B. D. Tapley and V. Szebehely (eds.),Recent Advances in Dynamical Astronomy, D. Reidel Publ. Co., Dordrecht, Holland, p. 75.

    Google Scholar 

  • Szebehely, V. and Feagin, T.: 1973,Celes. Mech. 8, 11.

    Google Scholar 

  • Szebehely, V. and Peters, C. F.: 1967,Astron. J. 72, 1187.

    Google Scholar 

  • Waldvogel, J.: 1972,Celes. Mech. 6, 221.

    Google Scholar 

  • Whittaker, E. T.: 1937,Analytical Dynamics of Particles and Rigid Bodies, fourth edition, Cambridge University Press, p. 386, § 167.

Download references

Author information

Authors and Affiliations

  1. Observatoire de Nice, France

    M. Hénon

Authors
  1. M. Hénon
    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

Hénon, M. Families of periodic orbits in the three-body problem. Celestial Mechanics 10, 375–388 (1974). https://doi.org/10.1007/BF01586865

Download citation

  • Received:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF01586865

Keywords

Search

Navigation