Stability analysis in the R3BP under the effect of heterogeneous spheroid
Kumari Shalini, M. Javed Idrisi, J. K. Singh, M. Shahbaz Ullah
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 m 2 as a heterogeneous spheroid with three layers having different densities, and more massive primary m 1 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 L i ( 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 . 585688 k 1 ) analytically and numerically. Furthermore, the collinear libration points L i ( i = 1 , 2 , 3 ) are found unstable while non-collinear libration points L 4 , 5 are conditionally stable for the mass parameter μ ∈ ( 0 , μ c ) , μ c = 0 . 585688 k 1 .