Archive for Rational Mechanics and Analysis

, Volume 170, Issue 2, pp 91–135

Elliptic Two-Dimensional Invariant Tori for the Planetary Three-Body Problem

  • Luca Biasco
  • Luigi Chierchia
  • Enrico Valdinoci
Article

DOI: 10.1007/s00205-003-0269-2

Cite this article as:
Biasco, L., Chierchia, L. & Valdinoci, E. Arch. Rational Mech. Anal. (2003) 170: 91. doi:10.1007/s00205-003-0269-2

Abstract.

The spatial planetary three-body problem (i.e., one ‘‘star’’ and two ‘‘planets’’, modelled by three massive points, interacting through gravity in a three dimensional space) is considered. It is proved that, near the limiting stable solutions given by the two planets revolving around the star on Keplerian ellipses with small eccentricity and small non-zero mutual inclination, the system affords two-dimensional, elliptic, quasi-periodic solutions, provided the masses of the planets are small enough compared to the mass of the star and provided the osculating Keplerian major semi-axes belong to a two-dimensional set of density close to one.

Copyright information

© Springer-Verlag Berlin Heidelberg 2003

Authors and Affiliations

  • Luca Biasco
    • 1
  • Luigi Chierchia
    • 2
  • Enrico Valdinoci
    • 2
  1. 1.Dipartimento di MatematicaUniversità ‘‘Roma Tre’’, LargoRoma (Italy)
  2. 2.Dipartimento di MatematicaUniversità di Roma ‘‘Tor Vergata’‘Scientifica 1Roma, Italy

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