Existence and Stability of Libration Points of the Restricted Three Body Problem, when Both the Primaries are Heterogeneous Axes-Symmetric Bodies with N Layers

We have investigated the Existence and Stability of the libration points in the Restricted Three Body Problem when both the primaries are heterogeneous axes -symmetric bodies with N layers having different densities ρ_i, ρ_i axes (a_i, b_i, c_i) and (a_i, b_i, c_i), (i =1, 2, 3, …, N) respectively. It is observed that there exists five libration points L_i (i =1, 2, 3, 4, 5) three collinear along the line of sisgies and two non-collinear. The collinear, libration points are unstable for all values of μ (mass parameter) and non-collinear libration points are stable for μ < μ_c, a critical value.