Study of the Restricted Three Body Problem When One Primary Is a Uniform Circular Disk

In this paper we have studied the location and stability of the equilibrium points in the restricted three body problem by taking into consideration the bigger primary as an uniform circular disc. We have observed that there exist six collinear (L-i, i = 1..6) and two non-collinear (L-i, i = 7, 8) equilibrium points. We have found that the points L-1 and L-3 move towards the center of mass while L-2, L-4, L-5 and L-6 go away from the center of mass as parameter of mass mu increases. We have also observed that the points L-1, L-2 and L-3 move away from the primaries and L-4 moves toward the primaries as radius a of the circular disk increases. Also the points L-7 and L-8 shift towards the center of mass as mu increases. We have found that equilibrium point L-1, L-2, L-3, L-4 and L-6 are unstable where L-5, L-7 and L-8 are stable for the given values of mu and a. We have also derived the zero velocity curves (ZVC) and periodic orbits around the equilibrium points. We have noticed that in ZVC the outer oval expands and inner oval slightly shrinks as the value of Jacobian constant C increases; we have also discussed the motion around the collinear equilibrium points.