Restricted Three-Body Problem Considering Perturbations of Oblate Primaries

In this paper, the effect of perturbations of oblate primaries in the Circular Restricted Three-Body Problem is studied, and the equations of satellite orbital motion in the Circular Restricted Three-Body Problem are developed by employing Lagrangian mechanics. Since the equations have no closed-form solution and numerical methods must be applied, the problem can have different periodic or quasi-periodic solutions depending on the equation's initial conditions of orbital state parameters. For this purpose, an algorithm named “orbital correction algorithm” is proposed to correct the initial conditions of orbital state parameters. The limited number of periodic orbits in the study environment indicates the algorithm’s need for suitable initial guesses as input. In the present paper, suitable initial guesses for orbital state parameters are selected from the third-order approximation of the Unperturbed Circular Restricted Three-Body Problem’s periodic solutions, increasing the chance of obtaining desired periodic solutions. The obtained perturbed and unperturbed periodic orbits are compared in order to understand the effect of perturbations. Adding the perturbations brings the study environment closer to the real environment and helps understand satellites' natural motion.