Abstract
The paper deals with the existence of the coplanar libration points in the restricted three-body problem when the smaller primary is a triaxial rigid body and the infinitesimal body is of variable mass. Following small parameter method, the coordinates of collinear libration points are established whereas the coordinates of triangular libration points are established by classical method. It is found that the mass reduction factor has small effect but triaxiality parameters of the smaller primary have great effects on the coordinates of the libration points.
Highlights
Restricted three-body problem with variable mass has an important role in celestial mechanics
The paper deals with the existence of the coplanar libration points in the restricted three-body problem when the smaller primary is a triaxial rigid body and the infinitesimal body is of variable mass
It is found that the mass reduction factor has small effect but triaxiality parameters of the smaller primary have great effects on the coordinates of the libration points
Summary
Restricted three-body problem with variable mass has an important role in celestial mechanics. Lukyanov [6] discussed the stability of libration points in the restricted three-body problem with variable mass. El Shaboury [7] had established the equations of motion of elliptic restricted three-body problem (ER3BP) with variable mass with two triaxial rigid primaries. He has applied the Jeans law, Nechvili’s transformation and space-time transformation given by Meshcherskii in a special case. Singh et al [8] have discussed the non-linear stability of libration points in the restricted three-body problem with variable mass.
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