Existence of Equilibrium Points in the R3BP with Variable Mass When the Smaller Primary is an Oblate Spheroid

Abstract

The paper deals with the existence of equilibrium points in the restricted three-body problem when the smaller primary is an oblate spheroid and the infinitesimal body is of variable mass. Following the method of small parameters; the co-ordinates of collinear equilibrium points have been calculated, whereas the co-ordinates of triangular equilibrium points are established by classical method. On studying the surface of zero-velocity curves, it is found that the mass reduction factor has very minor effect on the location of the equilibrium points; whereas the oblateness parameter of the smaller primary has a significant role on the existence of equilibrium points.

Libration Points in the R3BP with a Triaxial Rigid Body as the Smaller Primary and a Variable Mass Infinitesimal Bod

“…They have found that in non-linear sense, collinear points are unstable for all mass ratios and the triangular points are stable in the range of linear stability except for three mass ratios depending upon the mass variation parameter β governed by Jean's law. Hassan et al [9] studied the existence of libration points with variable mass in the R3BP when the smaller primary is an oblate spheroid. They found that Jacobi constant 1, 2 C C = = shows no effect in the position of libration points, but for 3 C = , slight shifting of libration points is found due to oblateness only not due to the mass reduction factor α .…”

“…In present work, we have established coordinates of five libration points ( ) 1, 2,3, 4,5 i L i = in the R3BP with variable mass when smaller primary is a triaxial rigid body by small parameter method [10] and the method used by Hassan et al [9].…”