Abstract: The motion of tether satellite system inner the orbital plane is described by the relative position vector between the subsatellite and base-satellite. As soon as the range rate control algorithm is established, the motion of the system is determined by the direction angle of the position vector, which has a stationary state. The stationary state is a limit point if the orbit is circular, and a limit cycle if the orbit is elliptical. An iterative algorithm is introduced to compute the limit cycle, and a method for stability analysis of the stationary state is also discussed. Computer simulations are carried out for both the limit point and limit cycle.