Exploring the Perturbed Restricted Three-Body Problem under the Effect of Albedo and Straight Segment

Abstract

The research presented in this work focuses on investigating the characteristics of equilibrium points within the context of the photogravitational restricted three-body problem. Specifically, the study considers the influences of albedo effect, a straight segment, radiation pressure, as well as small perturbations in the Coriolis and centrifugal forces. The dynamical model proposed in this study reveals the presence of five equilibrium points. Among these, three are collinear with the centers of the massive bodies, while the remaining two are non-collinear. By examining various parameters involved in the system, the effect on the position of the equilibrium points is explored through numerical and graphical analysis. These investigations provide valuable insights into how the positions of these points are affected by changes in the parameters. Another significant aspect addressed in this research is the stability of the equilibrium points. The study finds that the collinear equilibrium points are unstable, irrespective of the parameters involved. On the other hand, the non-collinear points exhibit stability within a specific range of the mass parameter. The precise range of stability depends on the values of the other parameters present in the system. Additionally, the research delves into the study of the permissible and forbidden regions of motion for an infinitesimal body within the system. This analysis is conducted by considering different values of the Jacobian constant and it suggests that the Jacobian constant significantly influences the dynamics of the system and has a direct impact on the permissible regions of motion of the infinitesimal body.