Periodic orbit in the frame work of restricted three bodies under the asteroids belt effect

In this paper, we present a comprehensive analytical study on the perturbed restricted three bodies problem. We formulate the equations of motion of this problem, in the event of the asteroids belt perturbation. We find the locations of equilibrium points (collinear and triangular points) and analysis their linear stability. Furthermore the periodic orbits around both collinear and triangular points are found.