Motion around equilibrium points of an oblate body in the PR3BP with disc

Abstract

This paper examines motion around equilibrium points (EPs) of an oblate body having a third body in the PR3BP with the disc. The problem is photogravitational, such that the third body gravitates under the influence of two primaries, which emit radiation pressure and the Poynting–Robertson (P–R) drag. Further, the primaries are enclosed by a disc. The mathematical analysis (equations of motion) and the locations of EPs have been studied. There exist six collinear EPs in the line joining the primaries. The first is an additional EP, which depends on parameters, $\mu$ and $W_{i} \,(i = 1,2)$ of the primaries, while the three are analogous to the collinear EPs of the classical R3BP. The last two are the Jiang–Yeh EPs, which exist due to the mass parameter and the disc. Further, two triangular EPs are found and are characterized by the disc, oblateness of the third body, radiation pressure, P–R drag and mass parameters of the primaries. The stability of the EPs is examined, and it is that they are unbounded due to either a positive root or a positive real part of the complex root. In particular, the numerical exploration is being performed using the binary Achird to compute numerically the locations/or positions of the EPs and the roots of their corresponding characteristic equations. In the case of the collinear point, the roots contain a positive real root and a complex root with positive real part. In view of the triangular points, the roots contain positive real parts of the complex roots. Hence, we conclude that for the R3BP when the primaries emit radiation pressure and P–R drag with disc and the third body is in shape of a sphere, eight EPs exist and are unstable due to radiational forces which reveal positive real part of the complex root.