The Inverse Problem for Collinear Central Configurations

Details The Inverse Problem for Collinear Central Configurations The Inverse Problem for Collinear Central Configurations

Sep 2000

adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=2000cemda..77...77a&link_type=abstract

Celestial Mechanics and Dynamical Astronomy, v. 77, Issue 2, p. 77-91 (2000).

Astronomy and Astrophysics

Astronomy

6

Inverse Problem, N-Body Problem, Central Configuration

Scientific paper

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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