Abstract: The paper presents the optimal retrieval control for a three-dimensional tethered satellite system subject to different level of impacts from space debris. Tether elasticity and complex constraints are taken into consideration in the controller design firstly, which features full exploitation of the second-order differential inclusion concept and the Legendre pseudo-spectral algorithm. The optimal tension and state profiles are solved with respect to the initial impact velocities. The various effects of impacts from space debris on the tethered satellite system are analyzed.