Celestial Mechanics and Dynamical Astronomy

, Volume 77, Issue 2, pp 77-91

The Inverse Problem for Collinear Central Configurations

  • Alain AlbouyAffiliated withAstronomie et Systèmes Dynamiques, Institut de Mécanique
  • , Richard MoeckelAffiliated withSchool of Mathematics, University of Minnesota

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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