An estimate for the number of relative equilibria in the motion of a plane rigid body and a material point under mutual attraction

We study the problem of the planar motion of a rigid body with a discrete mass distribution and a material point under the action of mutual attraction. There are exist stationary configurations of the system when the mass of the point is negligible and the body rotates about its center of gravity with a non-zero angular velocity and when the body and the material point are in interaction. It is shown that in such systems there are always at least two different positions of relative equilibrium.