The belief that celestial bodies as perfect spheres results in certain idealistic conditions because most often they are in irregular shapes. With this in mind, we conduct an analysis to study the restricted three-body problem by taking the primaries as oblate spheroids. The modified mean motion expression [1] is used by incorporating the secular perturbation effect due to oblateness of the primaries on mean anomaly, argument of perigee and right ascension of ascending node. The model possesses five equilibrium points, which are subsequently affected by the oblateness parameters. Furthermore, we have studied the stability of the equilibrium points and it is observed that the collinear equilibrium points are always unstable. However, the non-collinear equilibrium points are stable for some combinations of the involved parameters. We have also plotted the zero velocity curves of the infinitesimal body for different values of the Jacobian constant and oblateness parameter. It has been observed that the value of the Jacobian constant has been playing a vital role in obtaining the permissible regions of motion of the infinitesimal body. Further, the results obtained of the study are applied to study the motion of a satellite in the Saturn–Titan system.

Locations of Lagrangian points and periodic orbits around triangular points in the photo gravitational elliptic restricted three-body problem with oblateness

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.

The triangular Lagrangian points of the elliptic restricted three-body problem (ERTBP) with oblate and radiating more massive primary are studied. The mean motion equation used here is different from the ones employed in many studies on the perturbed ERTBP. The effect of oblateness on the mean motion equation varies. This change influences the location and stability of the triangular Lagrangian points. The points tend to shift in the y-direction. The influence of the oblateness on the critical mass ratio is also altered. But the eccentricity limit for stability remains the same. The triangular Lagrangian points of the elliptic restricted three-body problem (ERTBP) with oblate and radiating more massive primary are studied. The mean motion equation used here is different from the ones employed in many studies on the perturbed ERTBP. The effect of oblateness on the mean motion equation varies. This change influences the location and stability of the triangular Lagrangian points. The points tend to shift in the y-direction. The influence of the oblateness on the critical mass ratio is also altered. But the eccentricity limit for stability remains the same.