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On the stability of circular ‘asteroid’ orbits in anN-planetary system

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Abstract

The restricted problem of the motion of a point of negligible mass (‘asteroid’) in anN-planetary system is considered. It is assumed that all the planets move about the central body (‘Sun’) along circular orbits in the same plane and the mean motions of the asteroid and the planets are incommensurable. The asteroid orbit evolution is described as a first approximation by secular equations with the perturbing function averaged by the mean longitudes of the asteroid and the planets. For small values of the asteroid orbit eccentricity an expression for the secular part of the perturbing function has been obtained. This expression holds for the arbitrary values of the asteroid orbit semiaxis which are different from those of the planet orbit radii. The stability of the asteroid circular orbits in a linear approximation with respect to the eccentricity is studied. The critical inclinations for a Solar system model are calculated.

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Authors and Affiliations

  1. Institute of Applied Mathematics, The U.S.S.R. Academy of Sciences, Moscow, U.S.S.R.

    M. A. Vashkovjak

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  1. M. A. Vashkovjak
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Vashkovjak, M.A. On the stability of circular ‘asteroid’ orbits in anN-planetary system. Celestial Mechanics 13, 313–324 (1976). https://doi.org/10.1007/BF01228649

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  • DOI: https://doi.org/10.1007/BF01228649

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