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 (Li, i = 1::6) and two non-collinear (Li, i = 7; 8) equilibrium points.We have found that the points L1 and L3 move towards the center of mass while L2, L4, L5 and L6 go away from the center of mass as parameter of mass μ increases.We have also observed that the points L1, L2 and L3 move away from the primaries and L4 moves toward the primaries as radius a of the circular disk increases. Also the points L7 and L8 shift towards the center of mass as μ increases. We have found that equilibrium point L1, L2, L3, L4 and L6 are unstable where L5, L7 and L8 are stable for the given values of μ 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.
Arif, Mohd. and Sagar, Ravi K.
Study of the Restricted Three Body Problem When One Primary Is a Uniform Circular Disk,
Applications and Applied Mathematics: An International Journal (AAM), Vol. 13,
1, Article 11.
Available at: https://digitalcommons.pvamu.edu/aam/vol13/iss1/11