Periodic orbits as centers of stability in the secular 3D planetary three body problem View Full Text


Ontology type: schema:ScholarlyArticle     


Article Info

DATE

2008-09

AUTHORS

Jacques Henrard, Anne-Sophie Libert

ABSTRACT

In a previous paper, we have developed an analytical model of the secular 3D planetary problem by expanding the perturbation function up to the twelfth order in the eccentricities and the inclinations. Although the expansion is limited the model is able to describe with accuracy most of the observed systems of exoplanets. With the help of this model we were able to describe the geometry of the phase space of a typical system. The kernel of this description is a series of surfaces of section showing the chaotic and the regular domains of the phase space. We have observed in this previous paper that a family of unstable periodic orbits is responsible for the chaoticity, while we have hinted that the islands of stability are organized around stable periodic orbits. In this contribution we compute the main families of periodic orbits of the problem and show that indeed they are responsible for sculpting the phase space. More... »

PAGES

177-189

References to SciGraph publications

  • 2007-01. Continuation of normal doubly symmetric orbits in conservative reversible systems in CELESTIAL MECHANICS AND DYNAMICAL ASTRONOMY
  • 1983-10. On Brown's conjecture in CELESTIAL MECHANICS AND DYNAMICAL ASTRONOMY
  • 2006-05. Symmetric and asymmetric librations in extrasolar planetary systems: a global view in CELESTIAL MECHANICS AND DYNAMICAL ASTRONOMY
  • 2006-04. Dynamics of Two Planets in the 3/2 Mean-motion Resonance: Application to the Planetary System of the Pulsar PSR B1257+12 in CELESTIAL MECHANICS AND DYNAMICAL ASTRONOMY
  • 2006-05. Symmetric and asymmetric 3:1 resonant periodic orbits with an application to the 55Cnc extra-solar system in CELESTIAL MECHANICS AND DYNAMICAL ASTRONOMY
  • 1995-07. Stability of the planetary three-body problem in CELESTIAL MECHANICS AND DYNAMICAL ASTRONOMY
  • 2002-05. The Web of Periodic Orbits at L4 in CELESTIAL MECHANICS AND DYNAMICAL ASTRONOMY
  • 1973-06. Proof of a conjecture of E. Strömgren in CELESTIAL MECHANICS AND DYNAMICAL ASTRONOMY
  • 2007-05. General solution of the Kozai mechanism in CELESTIAL MECHANICS AND DYNAMICAL ASTRONOMY
  • 2005-09. Analytical Approach to the Secular Behaviour of Exoplanetary Systems in CELESTIAL MECHANICS AND DYNAMICAL ASTRONOMY
  • 2006-04. Stationary Orbits in Resonant Extrasolar Planetary Systems in CELESTIAL MECHANICS AND DYNAMICAL ASTRONOMY
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    http://scigraph.springernature.com/pub.10.1007/s10569-007-9111-8

    DOI

    http://dx.doi.org/10.1007/s10569-007-9111-8

    DIMENSIONS

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