The photo-gravitational concentric Sitnikov problem

The current framework involves a configuration of two pairs of primary celestial bodies engaged in synchronized circular orbits around a central point of mass. Additionally, an infinitesimal mass is positioned along the $z$-axis, traversing through the system’s center of mass. This distinctive celestial scenario is designated as the Concentric Sitnikov Problem. Notably, it is postulated that the initial pair of primary bodies emit radiation, while the latter pair remains radiation-free. Within the scope of this study, we delve into an exploration of equilibrium points, periodic orbits, and the intriguing Newton–Raphson basins of convergence (N-R BoC) within the concentric Sitnikov model, all subject to the influence of radiation pressure. Remarkably, our investigation uncovers the presence of three equilibrium points, each exhibiting linear instability across the entire spectrum of mass parameter values ${\mu }^{\ast }\in (0,0.25)$. To visually comprehend the character of these celestial paths, we employ a graphical analysis technique known as the first return map. Varied values of the mass parameter ${\mu }^{\ast }$ lead to the generation of diverse families of periodic orbits encircling both the primary celestial bodies and their equilibrium positions. Lastly, we embark on an exploration of the intricacies of the N-R BoC, intimately connected with the equilibrium points within this proposed celestial model.