Basins of Attraction in the Photogravitational Magnetic-Binary Problem with Oblateness and Dissipations

This study explores the effects of dissipation forces on the photogravitational magnetic-binary problem (PMBP). These forces include the Poynting-Robertson drag, and the nebular gas (Stokes) drag. In PMBP, the larger primary body emits radiation, whereas the smaller primary body is oblate in shape. We have developed the equations of motion for a charged particle (secondary body) in PMBP. The linear stability of equilibrium points and their existence and location have been demonstrated, along with the parametric evolution of these points. We have plotted the Newton-Raphson basins of attraction while accounting for Poynting-Robertson drag and nebular gas (Stokes) drag. Our numerical findings reveal that the magnetic moment ratio \(\lambda \) influences the position and stability of the equilibrium points and Newton-Raphson basins of attraction. There exist nine or eleven equilibrium points depending on the mass parameter \(\mu \) values and the ratio of magnetic moments \(\lambda \) values. All these equilibrium points are unstable, according to the Lyapunov criterion. Moreover, the basins of convergence associated with the collinear equilibrium points \(L_{1}\) and \(L_{3}\) have infinite extents in all cases. Our numerical analysis demonstrates that the evolution of the attractive regions in this dynamical system is quite intricate. The spacecraft deviates from equilibrium points over time owing to the instability of these locations, and the drift is most at the \(L_{7}\) point.