Effect of Perturbations in Coriolis and Centrifugal Forces on Libration Points in the Restricted Six-Body Problem

Abstract

This paper deals with the existence and stability of libration points in linear sense in central square configuration of restricted six-body problem when small perturbations υ and ρ are given to the coriolis and the centrifugal forces, respectively. This is observed that there exist twelve libration points out of which four libration points are collinear and eight are non-collinear and all libration points lie on the concentric circles C1, C2 and C3 centered at origin. This is also observed that the eight libration points are on the axes and four are off the axes, i.e., L1, L2, L3 and L4 are on x-axis, L5, L6, L7 and L8 are on y-axis and rest are off the axes. Also, the locations of all the libration points are only influenced by a small change in the centrifugal force. It is further observed that the stability of libration points lying on circles C1 and C3 is not influenced by the perturbations and they remain unstable for all values of mass parameter μ while the libration points lying on circle C2 are influenced by the perturbations and stable for the critical mass parameter μc.