Study of Stokes Drag and Radiation Pressure in the Restricted Four-Body Problem with Variable Mass

Abstract

This manuscript illustrates the existence, locations, and stability of equilibrium points under the effect of Stokes drag in the restricted four-body problem (R4BP) with variable mass when all the primaries are source of radiation. The motion of the fourth body of negligible mass (infinitesimal mass) is effected by the motion of the primaries, and its motion is perturbed by the radiation pressure and Stokes drag. All the primaries are established at the vertices of an equilateral triangle and known as Lagrangian configuration. The dynamics of an infinitesimal body has been studied under the influences of radiation pressure of all the primaries with Stokes drag and variable mass. Jeans’ law and space time transformations of Meshcherskii have been used to formulate the equations of motion of the infinitesimal body. We have numerically investigated the existence and locations of the equilibrium points in the theoretical ranges of the parameters. The numerical investigations delved that all the equilibrium points are non-collinear, the collinear equilibrium points do not exist due to the presence of Stokes drag. Further, we have observed that all the equilibrium points are unstable for all values of the parameters considered. Moreover, the regions of motion have been drawn for different values of the parameters, i.e., for the radiation parameters \({{q}_{i}} (0 < {{q}_{i}} < 1),\) \(i = 1,2,3\), the proportionality constant \(\alpha (0 < \alpha \leqslant 2.2)\) occurs due to Jeans’ law, the mass parameter \(\mu (0 < \mu \leqslant 1{\text{/}}3)\), and for the dissipative constant \(k (0 < k < 1)\). This model has novelty in the sense that we have studied this problem first time by combining the concept of Stokes drag in the restricted four-body problem, considering all primaries as the source of radiation and the fourth body having variable mass. This paper is applicable in various di-sciplines of celestial mechanics as space mission planning, satellite dynamics, and fundamental astrodynamics research. Finally, we have justified the importance of our model by applying it to an appropriate stellar system.