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The Inverse Problem for Collinear Central Configurations

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Abstract

We consider the problem: given a collinear configuration of n bodies, find the masses which make it central. We prove that for n ≤ 6, each configuration determines a one-parameter family of masses (after normalization of the total mass). The parameter is the center of mass when n is even and the square of the angular velocity of the corresponding circular periodic orbit when n is odd. The result is expected to be true for any n.

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Authors and Affiliations

  1. Astronomie et Systèmes Dynamiques, Institut de Mécanique, Céleste, 77, av. Denfert-Rochereau, 75014, Paris, France

    Alain Albouy

  2. School of Mathematics, University of Minnesota, Minneapolis, MN, 55455, U.S.A.

    Richard Moeckel

Authors
  1. Alain Albouy
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  2. Richard Moeckel
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Albouy, A., Moeckel, R. The Inverse Problem for Collinear Central Configurations. Celestial Mechanics and Dynamical Astronomy 77, 77–91 (2000). https://doi.org/10.1023/A:1008345830461

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  • DOI: https://doi.org/10.1023/A:1008345830461

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