Central configurations of the planar coorbital satellite problem

We study the planar central configurations of the 1 + n body problem where one mass is large and the other n masses are infinitesimal and equal. We find analytically all these central configurations when 2 ≤ n ≤ 4. Numerically, first we provide evidence that when n ≥ 9 the only central configuration is the regular n–gon with the large mass in its barycenter, and second we provide also evidence of the existence of an axis of symmetry for every central configuration