Investigating Motion around Equilibrium Points in the Restricted Three-body Problem Under Effects of Radiation Forces and Circumbinary Disc

This paper investigates motion around equilibrium points in the restricted three-body problem (R3BP) when a disc encloses two radiating primaries together with effective Poynting-Robertson (P-R) drag. The equations of motion are derived and coordinates of equilibrium points are analyzed. Six collinear equilibrium points are found, one depends on the mass parameter and the P-R drag of the primaries, three are the classical collinear equilibrium points while the remaining two are characterized by the mass parameter and disc. Further, two triangular equilibrium points exist and are defined by the disc, mass parameter, radiation pressure and P-R drag. The stability analysis of the equilibrium points are discussed analytically. It is seen that the collinear equilibrium points are unstable in the presence and absence of radiation force due to at least a positive root of the characteristic equation, while the triangular points can be stable in the absence of radiation force but in general unstable when they are present due to appearance of a complex root. The radiation pressure and P-R drag of the primaries has a strong destabilizing tendency. In particular, we explored the study of the triangular points numerically. It is seen that in the absence of radiation and the presence of the disc, when the mass parameter is less than the critical mass, all the roots are pure imaginary and the triangular point is stable. However, when miu greater miu c, the four roots are complex, but become pure imaginary quantities when the disc is present. This proves that the disc is a stabilizing force. Next, on introducing the radiation force, all earlier purely imaginary roots turned complex roots in the entire range of the mass parameter. Hence, the component of the radiation force is strongly a destabilizing force and induces instability of the equilibrium points.