Impacts of Poynting–Robertson Drag and Dynamical Flattening Parameters on Motion around the Triangular Equilibrium Points of the Photogravitational ER3BP

Abstract

Using an analytical and numerical study, this paper investigates the equilibrium state of the triangular equilibrium points L 4 , 5 of the Sun-Earth system in the frame of the elliptic restricted problem of three bodies subject to the radial component of Poynting–Robertson (P–R) drag and radiation pressure factor of the bigger primary as well as dynamical flattening parameters of both primary bodies (i.e., Sun and Earth). The equations of motion are presented in a dimensionless-pulsating coordinate system ξ − η , and the positions of the triangular equilibrium points are found to depend on the mass ratio μ and the perturbing forces involved in the equations of motion. A numerical analysis of the positions and stability of the triangular equilibrium points of the Sun-Earth system shows that the perturbing forces have no significant effect on the positions of the triangular equilibrium points and their stability. Hence, this research work concludes that the motion of an infinitesimal mass near the triangular equilibrium points of the Sun-Earth system remains linearly stable in the presence of the perturbing forces.

Perturbation due to a Circumbinary Disc around <i>L_4,5</i> in the Photogravitational Elliptic Restricted Three-Body Problem

“…Equation ( 18) determines the stability or otherwise of the system. If (18) is not satisfied, this means the roots of equation ( 15) will be either real or complex conjugate leading to the instability of the investigated points. Now, from (17)…”