The locations of triangular equilibrium points in elliptic restricted three-body problem under the oblateness and radiation Effects

The Restricted Three-Body Problem (R3BP) considers motion of a third infinitesimal object under the gravitational influences of the primaries (bigger and smaller massive bodies) whose orbits are around the center of mass. If the orbits are elliptical, this belongs to Elliptic R3BP (ER3BP). In planar case it possesses five equilibrium points consisting of three collinear (L₁, L₂, and L₃) and two triangular (L₄ and L₅). To mimic a better astrophysical R3BP, such as motion of a satellite in star-planet system, the classical problem can be generalized by considering the effects of radiation pressure and oblate spheroid shape on the primaries. We study analytically the locations and the stability of L₄ and L₅ equilibrium points in the frame of ER3BP with incorporating the effects of radiation for bigger primary and oblateness for smaller primary. Our study suggests that the oblateness factor (A₂) and the radiation factor (q₁) shift the positions of L₄ and L₅ points compared with the classical ones. We also find that there is a stability limit for motion of the third body around these points.