Location of the collinear equilibrium points in the elliptic restricted three-body problem with various perturbation effects

Abstract

Abstract This study aims to examine the elliptic restricted three-body problem (ERTBP) by modifying the classical case and applying various perturbation sources to the three-body system. In this study, the locations of the Lagrange collinear equilibrium points of ERTBP were examined. We consider that the first primary body emits radiation and has an oblate shape. In contrast, the second primary body was considered to be elongated and approximated as a finite straight-segment. In addition, the perturbations from the disk-like structure around the three-body system were also included. The equations of motion of the infinitesimal body are presented in a dimensionless pulsating coordinate system. Three collinear equilibrium points were identified. The locations of the collinear equilibrium points were calculated numerically for several cases of perturbation values and also presented versus eccentricity over its range. We observed that the position of the collinear equilibrium points (L 1, L 2, and L 3) shifted when perturbing parameters were included, as opposed to where they were in the classical ERTBP.