On the Periodic Solutions for the Perturbed Spatial Quantized Hill Problem
Elbaz I. Abouelmagd,
Sawsan Alhowaity,
Zouhair Diab,
Juan L. G. Guirao,
Mahmoud H. Shehata
Affiliations
Elbaz I. Abouelmagd
Celestial Mechanics and Space Dynamics Research Group (CMSDRG), Astronomy Department, National Research Institute of Astronomy and Geophysics (NRIAG), Helwan 11421, Cairo, Egypt
Sawsan Alhowaity
Department of Mathematics, College of Science & Humanities, Shaqra University, Shaqra 15551, Saudi Arabia
Zouhair Diab
Department of Mathematics and Computer Science, Larbi Tebessi University, Tebessa 12002, Algeria
Juan L. G. Guirao
Departamento de Matemáca Aplicada y Estadística, Universidad Politécnica de Cartagena, 30202 Cartagena, Spain
Mahmoud H. Shehata
Celestial Mechanics and Space Dynamics Research Group (CMSDRG), Astronomy Department, National Research Institute of Astronomy and Geophysics (NRIAG), Helwan 11421, Cairo, Egypt
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.
