Periodic solutions of photo-gravitational R4BP with variable mass and Stokes drag

The present paper describes the motion of an infinitesimal body in the framework of restricted four-body problem, incorporating perturbations from photo-gravitational, variable mass, and Stokes drag effects. Dynamic equations governing a fourth body with changing mass are obtained using Jeans’ law and Meshcherskii space-time transformations. The locations of the Lagrangian points and their evolution under variations of the aforementioned perturbations have been numerically studied, revealing the sensitivity of the locations and quantities of Lagrangian points to these varying parameters. Furthermore, the stability of Lagrangian points in the linear sense has been investigated, and it has been found that all Lagrangian points considered in this study are unstable. The zero-velocity curves have also been studied as a function of the Jacobian integral constant. As this constant decreases, the Hill region becomes larger. The Lindstedt–Poincaré method is applied to calculate the perturbation solutions near non-collinear Lagrangian points, yielding second- and third-order periodic solutions. A numerical work is conducted to track the evolution of periodic solutions near non-collinear Lagrangian points with variable mass parameter \(\gamma \) $\gamma$ . It demonstrates that a substantial increase in \(\gamma \) $\gamma$ results in a larger area surrounding the periodic solutions of the triangular Lagrangian points, exhibiting a visually regular elliptical shape. Conversely, a decrease in \(\gamma \) $\gamma$ leads to a reduction in the region of periodic solutions, accompanied by notable alterations in shape, particularly concerning third-order periodic solutions.