2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/74202We 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.Classical Analysis and ODEstext