The Role of Oblateness in Shaping Stability and Zero Velocity Curves in the Perturbed Restricted Three-Body Problem

The objective of this research is to investigate the findings in the perturbed restricted three-body problem involving oblate spheroids as the primary bodies. The analysis focuses on examining the influence of small perturbations in Coriolis and centrifugal forces, as well as the implementation of a new mean motion. The dynamical system is formulated, and the equations of motion for the infinitesimal body are derived accordingly. Five equilibrium points are identified within the current configuration, and their positions are subsequently affected by variations in mass, oblateness, and perturbed centrifugal force parameters. Furthermore, we have performed a comprehensive numerical and graphical analysis to observe and understand the impact of the various parameters on the position of the equilibrium points. We have also conducted a detailed stability analysis to examine the behavior of the equilibrium points. It is observed that the collinear equilibrium points are unstable, indicating that even slight disturbances can cause the system to deviate from these points. However, the non-collinear equilibrium points exhibited stability under certain combinations of the involved parameters. By plotting the zero velocity curves for different values of the Jacobian constant, we have gained insights into the regions where the infinitesimal body can freely move. Remarkably, our observations showed that as the Jacobian constant decreased within the considered range of parameters, the permissible regions of motion for the infinitesimal body expanded, providing it with more freedom in it.