The concentric Sitnikov problem: Circular case

A new configuration in the sense of concentric Sitnikov problem is introduced in this paper. This configuration consists of four primariesP(t)(i = 1, 2, 3, 4) of masses mi, respectively. Here, all the primaries are placed on a straight line and moving in concentric circular orbits around their common center of mass under the restrictions of masses as m(1) = m(2) =m, m(3) = m(4) = m ' and m > m '. The objective of the present manuscript is to study the existence of equilibrium points and their linear stability, first return map, periodic orbits, and N-R BoA in the proposed model. Under the restriction of mass parameter 0 < mu ' < 1/4, it is found that there exist three equilibrium points and all the equilibrium points are linearly unstable for all values of mass parameter 0 < mu ' < 1/4. Graphically, the nature of orbits have been examined with the help of first return map. The families of periodic orbits of infinitesimal mass.. 5 around the primaries and equilibrium points have been obtained for different values of mass parameter mu '. Finally, we explore the Newton-Raphson Basins of Attraction (N-R BoA), related to the equilibrium points in the concentric problem of Sitnikov.