We study the dynamics of an infinitesimal mass under the gravitational attraction of N-1 primaries arranged in a planar ring configuration plus the influence of the central mass with a Manev potential (-1/r + e/r2), e \not= 0, where e is a parameter related to the oblaticity or radiation source (according to the sign of the parameter e). Specifically, we investigate the relative equilibria of the infinitesimal mass and their linear stability as functions of the parameter e and the mass parameter \beta, the ratio of mass of the central body to the mass of one of the N - 1 remaining bodies. We also prove the nonexistence of binary collisions between the central body and the infinitesimal mass.