On the Existence of Periodic Orbits for the Fixed Homogeneous Circle   Problem
  We prove the existence of some types of periodic orbits for a particle moving in Euclidean three-space under the influence of the gravitational force induced by a fixed homogeneous circle. These types include periodic orbits very far and very near the homogeneous circle, as well as eight and spiral periodic orbits. 
C. Azevedo and P. Ontaneda