On the Periodic Solutions for the Perturbed Spatial Quantized Hill Problem

In this work, we investigated the differences and similarities among some perturbation approaches, such as the classical perturbation theory, Poincaré–Lindstedt technique, multiple scales method, the KB averaging method, and averaging theory. The necessary conditions to construct the periodic solutions for the spatial quantized Hill problem—in this context, the periodic solutions emerging from the equilibrium points for the spatial Hill problem—were evaluated by using the averaging theory, under the perturbation effect of quantum corrections. This model can be used to develop a Lunar theory and the families of periodic orbits in the frame work for the spatial quantized Hill problem. Thereby, these applications serve to reinforce the obtained results on these periodic solutions and gain its own significance