Solution of Sitnikov Restricted Four Body Problem When the Primaries are Point Masses or Spherical in Shape: Circular Case

In the present paper we have studied the Sitnikov problem when extended to four body problems. Here all the three primaries are moving in the circular orbit in the x-y plane and fourth particle is moving along the z-axis. First we have determined the equation of motion and then using the Lindstedt-Poincare methods and Green's function we have determined the motion of the fourth particles. Here we have find the analytical solution up to the second order. Then we have determined the time period of the motion.