Effect of perturbed potential of heterogeneous triaxial rigid bodies of N layers on the stability of libration points in the R3BP

Abstract

In this paper, we investigate the motion of an infinitesimal mass $m_3$ in the restricted three-body problem by taking both the primaries as heterogeneous triaxial rigid bodies with N layers. The potential of the proposed model and the equations of motion for the infinitesimal mass $m_3$ are derived. Our findings reveal the existence of five libration points denoted as $L_i$ $(i=1,2,3,4,5)$ in the proposed model, with three being collinear and two being non-collinear. We observed that the collinear libration points $L_i(i=1,2,3)$ are unstable, whereas the non-collinear libration points $L_{4,5}$ are conditionally stable for the mass parameter $\mu \in (0,{\mu }_c)$, where ${\mu }_c=0.25681k_1-1.31619k_2-2.24318k_3-6.10258k_4$.