The circular restricted eight-body problem

We study the motion of infinitesimal mass in the vicinity of the dominant primaries under the Newtonian law of gravitation in the restricted eight-body problem. The proposed problem is a particular case of n + 1-body problem studied by Kalvouridis (Astrophys. Space Sci 260: 309 325, 1999). We consider six peripheral primaries P1, P2, …, P6, each of mass m, revolve in a circular orbit of radius a with an angular velocity ω about their common center of mass. The primaries Pi (i = 1, 2, …, 6) are revolve in a way such that P1, P3, P5 and P2, P4, P6 always form equilateral triangles of side l and have a common circumcenter where the seventh more massive primary P0 of mass m0 rests. The primaries form a symmetric configuration with respect to the origin at any instant of time. This is observed that there exist 18 equilibrium points out of which four equilibrium points are on x-axis, two on y-axis and rest are in orbital plane of the primaries. All the equilibrium points lie on the concentric circles C1, C2 and C3 centered at origin and there exists exactly six equilibrium points on each circle. The equilibrium points on circle C2 are stable for the critical mass parameter β0 while the equilibrium points on circles C1 and C3 are unstable for all values of mass parameter β. The regions of motion for infinitesimal mass are also analyzed in this paper.