The inverse problem for collinear central configurations

We consider the problem: given a collinear configuration of n bodies, find the masses which make it central. We prove that for n less than or equal to 6, each configuration determines a one-parameter family of masses (after n ormalization 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 circul ar periodic orbit when n is odd. The result is expected to be true for any n.