Secular dynamics of a planar model of the Sun-Jupiter-Saturn-Uranus system; effective stability in the light of Kolmogorov and Nekhoroshev theories View Full Text


Ontology type: schema:ScholarlyArticle      Open Access: True


Article Info

DATE

2017-01

AUTHORS

Antonio Giorgilli, Ugo Locatelli, Marco Sansottera

ABSTRACT

We investigate the long-time stability of the Sun-Jupiter-Saturn-Uranus system by considering a planar secular model, which can be regarded as a major refinement of the approach first introduced by Lagrange. Indeed, concerning the planetary orbital revolutions, we improve the classical circular approximation by replacing it with a solution that is invariant up to order two in the masses; therefore, we investigate the stability of the secular system for rather small values of the eccentricities. First, we explicitly construct a Kolmogorov normal form to find an invariant KAM torus which approximates very well the secular orbits. Finally, we adapt the approach that underlies the analytic part of Nekhoroshev’s theorem to show that there is a neighborhood of that torus for which the estimated stability time is larger than the lifetime of the Solar System. The size of such a neighborhood, compared with the uncertainties of the astronomical observations, is about ten times smaller. More... »

PAGES

54-77

References to SciGraph publications

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  • 2011-11. A semi-analytic algorithm for constructing lower dimensional elliptic tori in planetary systems in CELESTIAL MECHANICS AND DYNAMICAL ASTRONOMY
  • 2009-06. Existence of collisional trajectories of Mercury, Mars and Venus with the Earth in NATURE
  • 2014-08. On the convergence of an algorithm constructing the normal form for elliptic lower dimensional tori in planetary systems in CELESTIAL MECHANICS AND DYNAMICAL ASTRONOMY
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  • 1997-01. Invariant KAM tori and global stability for Hamiltonian systems in ZEITSCHRIFT FÜR ANGEWANDTE MATHEMATIK UND PHYSIK
  • 1979. Preservation of conditionally periodic movements with small change in the Hamilton function in STOCHASTIC BEHAVIOR IN CLASSICAL AND QUANTUM HAMILTONIAN SYSTEMS
  • Identifiers

    URI

    http://scigraph.springernature.com/pub.10.1134/s156035471701004x

    DOI

    http://dx.doi.org/10.1134/s156035471701004x

    DIMENSIONS

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