Equidistant Central Configuration for the Restricted 1+N -Body Problem

We investigate the central configurations of the restricted 1+N -body problem, in which N bodies are infinitesimal and the remaining one is dominant. Assuming that the distances between the i-th and (i+1) -th infinitesimal bodies are identical for all i=1,2,… ,N-1 , we establish the following results: (1) For N = 4 , there exist two distinct equidistant central configurations: a square and a special isosceles trapezoid; (2) For N≥ 4 with all infinitesimal bodies of equal mass, the only possible equidistant central configuration is a regular polygon.