Lagrangian points in a collinear R4BP under multiple perturbations: Variable mass, radiation, oblateness, and Stokes drag

This study examines the restricted four-body problem (R4BP) in a collinear configuration, incorporating various physical perturbation factors relevant to real-world scenarios, including radiation pressure, oblateness, Stokes drag, and the variable mass of the fourth body. The objective is to explore the Lagrangian points and the associated Newton–Raphson attraction basin of this enhanced model. Under the influence of these perturbations, the problem exhibits two, four, six, ten, and fourteen Lagrangian points; however, no stationary collinear equilibria exist under Stokes drag. The linear instability of these points is confirmed using the Routh–Hurwitz stability criterion. Additionally, a novel finding regarding the attraction basin is presented: the dissipation force constant k related to Stokes drag significantly influences the structure of the Newton–Raphson attraction basin. Specifically, for a given set of parameters, an increase in the constant k leads to the convergence of the six Lagrangian points into two points in groups of three, while variations in the radiation parameter and oblateness coefficient result in only minor changes.