This paper investigates the dynamics and control problems of the long-term deorbiting of an electrodynamic tethered sat ellite system. The dynamics modeling of the system is carried out based on a dumbbell model assumption. To improve the accuracy of the system model， the orbital dynamics is described using a set of modified equinoctial elements， involving the effects of Lorentz force， atmospheric drag and J2 perturbation force. Three current control strategies are proposed to regulate the electrodynamic forc es for achieving a stable long-term deorbiting process， namely， the constant current input， the directionally variable current input， and the optimal control strategies. In the design of the optimal control strategy， the long-term deorbiting problem is formulated as an inverse problem of dynamics with nonlinear constraints， which is further solved via a nonlinear programming method to obtain the optimal reference trajectories. The deorbiting of the system is then achieved using the modified current control input obtained from a tracking feedback control law. Additionally， an energy-based current switch control strategy is adopted to ensure the stabili ty of system and the efficient utilization of Lorentz force. Case studies of the system with designed physical parameters are conduct ed to analyze the deorbiting efficiency and to validate the effectiveness of the proposed control strategies.