This review presents a groundbreaking approach for investigating low-satellite orbits through the derivation of comprehensive equations governing their motions. The present work also presents some of the forces affecting this motion at low satellite orbit levels. This paper also presents different numerical methods for solving the equations governing two-body problems. The goal is to develop a strong mathematical model for the satellite to find a suitable path for orbital movement. Due to the effects on the orbit, the orbit must be controlled. For this purpose, orbital control uses orbital maneuvers to move the satellite to the desired location. Some modern technology (intelligent modeling) was used to create a simulator to increase the mathematical accuracy of the model and control its orbit. The objective is to develop a comprehensive mathematical model of orbital motion. This includes the design of a control unit for satellite orbits and the application of optimization algorithms. Furthermore, it involves developing a neural network-based model for the orbital control system. This study aims to achieve the desired outcomes in satellite orbital motion control by integrating these components.