The origin of chaotic behaviour in the Miranda-Umbriel 3 : 1 resonances View Full Text


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Article Info

DATE

1989-12

AUTHORS

Jacques Henrard, Massae Sato

ABSTRACT

We have investigated the pericentric resonances through which Miranda and Umbriel are believed to have passed when, due to tidal evolution, their orbital mean motions reached a 3 : 1 commensurability. Our investigation is based upon a perturbative treatment. The predictions of this theory are in good agreement with the results of numerical integrations concerning both the extend of the chaotic layers generated by the separatrices of the primary resonances and the location of the secondary resonances. The effect of tidal evolution is discussed on the bases of the adiatatic invariant theory and its extension to separatrix crossing. We recover qualitatively the mean features of the numerical experiments of Tittermore and Wisdom (1988–1989), Dermott et al (1988) and Malhotra and Dermott (1989). More... »

PAGES

391-417

References to SciGraph publications

  • 1986-09. A perturbation method for problems with two critical arguments in CELESTIAL MECHANICS AND DYNAMICAL ASTRONOMY
  • 1989-06. Motion near the 3/1 resonance of the planar elliptic restricted three body problem in CELESTIAL MECHANICS AND DYNAMICAL ASTRONOMY
  • 1984-02. A simple derivation of capture probabilities for the J+1:J and J+2:J orbit-orbit resonance problems in CELESTIAL MECHANICS AND DYNAMICAL ASTRONOMY
  • 1979-01. Diagrammatic theory of transition of pendulum like systems in CELESTIAL MECHANICS AND DYNAMICAL ASTRONOMY
  • 1988. Sweeping through a second order resonance in LONG TERM EVOLUTION OF PLANETARY SYSTEMS
  • 1979-06. How tidal heating in Io drives the galilean orbital resonance locks in NATURE
  • 1982-05. Capture into resonance: An extension of the use of adiabatic invariants in CELESTIAL MECHANICS AND DYNAMICAL ASTRONOMY
  • 1984-02. High-order resonances in the restricted three-body problem in CELESTIAL MECHANICS AND DYNAMICAL ASTRONOMY
  • 1987-03. Sweeping through a second order resonance in CELESTIAL MECHANICS AND DYNAMICAL ASTRONOMY
  • 1983-06. A second fundamental model for resonance in CELESTIAL MECHANICS AND DYNAMICAL ASTRONOMY
  • Identifiers

    URI

    http://scigraph.springernature.com/pub.10.1007/bf00051013

    DOI

    http://dx.doi.org/10.1007/bf00051013

    DIMENSIONS

    https://app.dimensions.ai/details/publication/pub.1053186131


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