Skip to main content
SpringerLink
Log in

Formulation of the restricted three-body problem with two-center problem orbits as intermediate orbits

  • Published:
Astrophysics and Space Science Aims and scope Submit manuscript

Abstract

The restricted three-body Hamiltonian is partitioned into a two-center type principal part and its accompanying perturbational part. The mathematical analysis, involving the Jacobian elliptic functions, is adapted for the case of figure-eight orbits winding around the two given mass points. For many such orbits the elliptic function modulusk is small and can serve as a small parameter.

Fourier expansions in terms of a parameter related tot are obtained for the intermediate orbit functions which provide representations in terms of elementary functions.

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

  • Byrd, P. F. and Friedman, M. D.: 1954,Handbook of Elliptic Integrals for Engineers and Physicists, Springer, Berlin.

    Google Scholar 

  • Charlier, C. V.: 1902,Die Mechanik des Himmels” Veit and Co., Leipzig.

    Google Scholar 

  • Langebartel, R. G.: 1965, NASA Tech. Note, Washington, D.C., TN D-2939, p. 1.

  • Langebartel, R. G.: 1980,SIAM J. Math. Anal. 11, 506.

    Google Scholar 

  • Samter, H.: 1922,Astron. Nachr. 217, 129.

    Google Scholar 

  • Wintner, A.: 1947,The Analytical Foundations of Celestial Mechanics, Princeton University Press, Princeton, New Jersey.

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Mathematics Dept., University of Illinois, Urbana, Illinois, USA

    R. G. Langebartel

Authors
  1. R. G. Langebartel
    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

Langebartel, R.G. Formulation of the restricted three-body problem with two-center problem orbits as intermediate orbits. Astrophys Space Sci 75, 437–454 (1981). https://doi.org/10.1007/BF00648654

Download citation

  • Received:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF00648654

Keywords

Search

Navigation