Nonlinear optimal state feedback control is designed for the deployment and retrieval of a tethered satellite in the orbital plane. The mass and flexibility of the tether are neglected, and the controlled system is expressed by a bilinear state equation. To stabilize the system asymptotically, the receding horizon control is applied with the terminal state constrained to be zero. As a practical approach to the problem, the time-dependent penalty function method is employed to achieve the terminal constraint asymptotically, and an algorithm is derived so that an increase of the terminal penalty will cause no numerical difficulty. The effectiveness and robustness of the present approach are confirmed in numerical simulations.