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 P 1 , P 2 , …, P 6 , 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 P i ( i = 1, 2, …, 6) are revolve in a way such that P 1 , P 3 , P 5 and P 2 , P 4 , P 6 always form equilateral triangles of side l and have a common circumcenter where the seventh more massive primary P 0 of mass m 0 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 C 1 , C 2 and C 3 centered at origin and there exists exactly six equilibrium points on each circle. The equilibrium points on circle C 2 are stable for the critical mass parameter β 0 while the equilibrium points on circles C 1 and C 3 are unstable for all values of mass parameter β . The regions of motion for infinitesimal mass are also analyzed in this paper.