The inverse problem for collinear central configurations

Alain Albouy, Richard Moeckel

Research output: Contribution to journalArticlepeer-review

32 Scopus citations


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.

Original languageEnglish (US)
Pages (from-to)77-91
Number of pages15
JournalCelestial Mechanics and Dynamical Astronomy
Issue number2
StatePublished - 2000


  • Central configuration
  • Inverse problem
  • n-body problem


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