The analysis of basins of convergence in the regular polygon problem of [formula omitted] bodies system with spheroidal primaries

Abstract

In the present manuscript, we unveil the topology of the basins of convergence in the regular polygon problem of (N+1)-bodies in two different cases, i.e., in case-I, only the central primary creates the Manev-type quasi-homogeneous potential, and in case-II, the peripheral primaries create the Manev-type quasi-homogeneous potential. The regular polygon problem of (N+1)-bodies describes the motion of the test particle moving in the force field of N primaries, the ν=N−1 peripheral primaries of equal masses situated at the vertices of the imaginary regular ν-gon and the Nth primary with different mass i.e., the central primary situated at the centre of mass of the system. In this model, we assume that the primaries create quasi-homogeneous potentials instead of Newtonian potentials and forces. In order to approximate various phenomena due to the irregular shape of the primaries or due to emitting radiation, an inverse cube corrective term is inserted to the inverse square Newtonian law of gravitation. We, numerically, investigated the evolution of the positions of the libration points and their linear stability for different values of ν in both the cases. Further, the multivariate version of Newton-Raphson iterative scheme is applied to unveil the topology of the basins of convergence. Moreover, the “basin entropy” is also computed to analyse the basins of convergence quantitatively.