Celestial Mechanics and Dynamical Astronomy

, Volume 77, Issue 2, pp 77–91

The Inverse Problem for Collinear Central Configurations

  • Alain Albouy
  • Richard Moeckel


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.

inverse problem n-body problem central configuration 


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Copyright information

© Kluwer Academic Publishers 2000

Authors and Affiliations

  • Alain Albouy
    • 1
  • Richard Moeckel
    • 2
  1. 1.Astronomie et Systèmes DynamiquesInstitut de MécaniqueParisFrance
  2. 2.School of MathematicsUniversity of MinnesotaMinneapolisU.S.A.

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