Stability analysis in the R3BP under the effect of heterogeneous spheroid

Abstract

In this paper, we investigate motion of infinitesimal mass m in the restricted three-body problem using heterogeneous spheroid with three layers. We consider the less massive primary m2 as a heterogeneous spheroid with three layers having different densities, and more massive primary m1 is considered as a point mass. We also derived the potential of proposed model and equations of motion of infinitesimal mass m. It is found that there exist five libration points Li(i=1,2,3,4,5) in the proposed model, three are collinear and two are non-collinear. The locations of all libration points have been investigated for the mass parameter μ(0<μ<0.585688k1) analytically and numerically. Furthermore, the collinear libration points Li(i=1,2,3) are found unstable while non-collinear libration points L4,5 are conditionally stable for the mass parameter μ∈(0,μc),μc=0.585688k1.