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Dynamics of a particle in a gravitational field of a homogeneous annulus disk

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Abstract

We formulate the problem of an infinitesimal particle moving in the space under the influence of the gravitational force induced by a homogeneous annulus disk fixed on a plane. We compute using different coordinates and in terms of an elliptic integral the potential associated to this problem. Also we study the symmetries of the associated potential. After that, we look at the dynamics in some particular cases, namely: in the line perpendicular to the plane that contains the annulus disk and passes through the center of the ring and on the plane that contains the massive annulus.

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Authors and Affiliations

  1. Departamento de Matemática, Universidade Federal de Pernambuco, Av. Prof. Luiz Freire, s/n, Cidade Universitária, Recife-Pe, Brasil

    Angelo Alberti

  2. Departamento de Matemática, Facultad de Ciencias, Universidad del Bio Bio, Casilla 5-C, Concepción, VIII-Región, Chile

    Claudio Vidal

Authors
  1. Angelo Alberti
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  2. Claudio Vidal
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Correspondence to Claudio Vidal.

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Alberti, A., Vidal, C. Dynamics of a particle in a gravitational field of a homogeneous annulus disk. Celestial Mech Dyn Astr 98, 75–93 (2007). https://doi.org/10.1007/s10569-007-9071-z

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  • DOI: https://doi.org/10.1007/s10569-007-9071-z

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