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On the expansion of the secular part of the perturbing function of mutual attraction in the satellite systems of planets

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Abstract

We propose a special representation for the secular part of the perturbing function describing the mutual attraction of satellites. In contrast to the known representations, it has a single analytical form for any ratio between the semimajor axes of the perturbed and perturbing satellites. The resulting expression is a partial sum of a power series with respect to the small eccentricities and planet-equatorial inclinations of the satellites’ orbits. This sum includes terms up to and including the fourth degree with respect to these small parameters. The proposed expansion is compared with one of the known expansions for the secular part of the perturbing function.

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Authors and Affiliations

  1. Keldysh Institute of Applied Mathematics, Russian Academy of Sciences, Moscow, Russia

    M. A. Vashkov’yak

  2. Sternberg Astronomical Institute, Moscow State University, Moscow, Russia

    S. N. Vashkov’yak & N. V. Emel’yanov

  3. Institute of Celestial Mechanics and Ephemerides Calculation, Paris Observatory, Paris, France

    N. V. Emel’yanov

Authors
  1. M. A. Vashkov’yak
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  2. S. N. Vashkov’yak
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  3. N. V. Emel’yanov
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Original Russian Text © M.A. Vashkov’yak, S.N. Vashkov’yak, N.V. Emel’yanov, 2013, published in Astronomicheskii Vestnik, 2013, Vol. 47, No. 1, pp. 32–39.

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Vashkov’yak, M.A., Vashkov’yak, S.N. & Emel’yanov, N.V. On the expansion of the secular part of the perturbing function of mutual attraction in the satellite systems of planets. Sol Syst Res 47, 31–37 (2013). https://doi.org/10.1134/S0038094613010097

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  • DOI: https://doi.org/10.1134/S0038094613010097

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