Celestial Mechanics and Dynamical Astronomy

, Volume 78, Issue 1–4, pp 47–74 | Cite as

Invariant Tori in the Secular Motions of the Three-body Planetary Systems

  • Ugo Locatelli
  • Antonio Giorgilli


We consider the problem of the applicability of KAM theorem to a realistic problem of three bodies. In the framework of the averaged dynamics over the fast angles for the Sun–Jupiter–Saturn system we can prove the perpetual stability of the orbit. The proof is based on semi-numerical algorithms requiring both explicit algebraic manipulations of series and analytical estimates. The proof is made rigorous by using interval arithmetics in order to control the numerical errors.

KAM theory stability in planetary motion three-body problem computer-assisted proofs 


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Copyright information

© Kluwer Academic Publishers 2000

Authors and Affiliations

  • Ugo Locatelli
    • 1
  • Antonio Giorgilli
    • 2
  1. 1.Dipartimento di MatematicaMilanoItaly
  2. 2.Dipartimento di Matematica e ApplicazioniMilanoItaly

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