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.
Highlights
Restricted problem of three bodies with variable mass is of great importance in celestial mechanics
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
Summary
Restricted problem of three bodies with variable mass is of great importance in celestial mechanics. Lukyanov [7] discussed the stability of equilibrium points in the restricted problem of three bodies with variable mass. He found that for any set of parameters, all the equilibriums points in the problem (Collinear, Triangular and Coplanar) are stable with respect to the conditions considered in the Meshcherskii space-time transformation. El Shaboury [8] discussed the equation of motion of Elliptic Restricted Three-body Problem (ER3BP) with variable mass and two triaxial rigid bodies He applied the Jeans law, Nechvili’s transformation and space-time transformation given by Meshcherskii in a special case. Singh et al [12] has discussed the non-linear stability of equilibrium points in the restricted problem of three bodies with variable mass.
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