Effect of three-body interaction on the topology of basins of convergence linked to the libration points in the R3BP

Abstract

The modified circular restricted three-body problem is numerically investigated by exploring the effect of three-body interaction on the basins of convergence connected to the in-plane as well as out-of-plane equilibrium points. The evolution of the positions of the libration points and their stability are illustrated as a function of parameter k due to three-body interaction. It is observed that the number of equilibrium points strongly depends on the sign and the magnitude of the three-body interaction parameter and there exist at most seven libration points where four are non-collinear and three are collinear with the primaries. Moreover, in the Copenhagen case we have found seven collinear libration points. Moreover, the non-collinear as well as collinear libration points are stable for various combinations of mass parameter μ and k. The collinear as well as non-collinear libration points are stable for even those values of μ which are higher than the μcrit of the classical restricted three-body problem. The study of the regions of possible motion shows that as the value of the Jacobian constant decreases, the forbidden region decreases significantly. The attracting domains of the basins of convergence, on several types of two-dimensional planes, are unveiled by applying the multivariate Newton-Raphson iterative scheme. In an attempt to analyse the effect of parameter k on the topology of basins of convergence, a systematic and thorough investigations are presented. The degree of fractality is also unveiled by determining the basin entropy of the convergence plane.