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On the Principle of Least Interaction Action and the Laplacean satellites of Jupiter and Uranus

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Abstract

The Principle of Least Interaction Action, which explains the observed preference in the Solar System for two-satellite resonant configurations, is shown to apply also to the Laplacean satellites of Jupiter and Uranus, in the sense that these triplet resonant structures lie close to configurations for which the time-mean of the action associated with the mutual interaction of the satellites is an overall minimum. Far from the minimum configuration, significant changes take place in the major semi-axes on time-scales ∼106-107y. Both systems require times ∼108 y to come close to the minimum configuration; to approach resonance to the observed precision of the Laplace relationship (3×10−4 for the Uranian case, 2×10−7 for the Jovian case) requires, for both systems, a time closely comparable with the age of the solar system.

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Authors and Affiliations

  1. Dept. of Geophysics and Astronomy, and Institute of Astronomy and Space Science, The University of British Columbia, Vancouver, Canada

    Michael W. Ovenden

  2. Dept. of Aerospace Engineering and Engineering Mechanics, The University of Texas at Austin, U.S.A.

    Terry Feagin & Otis Graf

Authors
  1. Michael W. Ovenden
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  2. Terry Feagin
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  3. Otis Graf
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Additional information

A more detailed summary of these arguments, including their relationship to Bode's Law, is given by Ovenden (1973).

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Ovenden, M.W., Feagin, T. & Graf, O. On the Principle of Least Interaction Action and the Laplacean satellites of Jupiter and Uranus. Celestial Mechanics 8, 455–471 (1974). https://doi.org/10.1007/BF01227798

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  • DOI: https://doi.org/10.1007/BF01227798

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