Periodic orbits of the Stark problem

The Stark problem is Kepler problem with an external constant acceleration. In this paper, we study the periodic orbits for Stark problem for both planar case and spatial case. We have conducted a detailed analysis of the invariant tori and periodic orbits appearing in the Stark problem, providing a more refined characterization of the properties of the orbits. Interestingly, there exists a family of circular orbits in the spatial case, some of which are quite stable with $L$ being fixed.