An impedance control framework is presented to detumble and stabilize the space robot after capturing a tumbling satellite. Firstly, the dynamics equation of the space robotic system in operational space is derived by employing inverse and forward chain approaches. Subsequently, a fast detumbling strategy using normalized time is designed, where the optimal detumbling time is determined with the imposed end-effector constraints. Finally, with the derived dynamics equation in operational space, an impedance control scheme is presented both for detumbling the target motion and stabilizing the base synchronously. Simulation results are presented for damping out a tumbling satellite and stabilizing the base using a 7 degree-of-freedom kinematically redundant space manipulator, which verifies the performance and effectiveness of the proposed method.