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The Sitnikov problem for several primary bodies configurations

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Abstract

In this paper we address an \(n+1\)-body gravitational problem governed by the Newton’s laws, where n primary bodies orbit on a plane \(\varPi \) and an additional massless particle moves on the perpendicular line to \(\varPi \) passing through the center of mass of the primary bodies. We find a condition for the described configuration to be possible. In the case when the primaries are in a rigid motion, we classify all the motions of the massless particle. We study the situation when the massless particle has a periodic motion with the same minimal period as the primary bodies. We show that this fact is related to the existence of a certain pyramidal central configuration.

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Authors and Affiliations

  1. CONICET - Dpto. de Matemática, Facultad de Ciencias Exactas Fsico-Qumicas y Naturales, Universidad Nacional de Río Cuarto, 5800, Río Cuarto, Córdoba, Argentina

    Gastón Beltritti & Fernando Mazzone

  2. CONICET - Instituto de Investigaciones Matemáticas “Luis A. Santaló”, Facultad de Ciencias Exactas y Naturales-UBA, C1428EGA, Buenos Aires, Argentina

    Martina Oviedo

Authors
  1. Gastón Beltritti
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  2. Fernando Mazzone
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  3. Martina Oviedo
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Correspondence to Gastón Beltritti.

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Beltritti, G., Mazzone, F. & Oviedo, M. The Sitnikov problem for several primary bodies configurations. Celest Mech Dyn Astr 130, 45 (2018). https://doi.org/10.1007/s10569-018-9838-4

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  • DOI: https://doi.org/10.1007/s10569-018-9838-4

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