Low-thrust propulsion systems offer a fuel-efficient means to maneuver satellites to new orbits; however, they can only perform such maneuvers when they are continuously operated for a long time. Such long-term maneuvers occur over many orbital revolutions, often rendering short time scale trajectory optimization methods ineffective. An approach to multirevolution large time scale optimal control of an electrodynamic tether is investigated for a tethered satellite system in low Earth orbit with atmospheric drag. Control is assumed to be periodic over several orbits because, under the assumptions of a nearly circular orbit, periodic control yields the only solution that significantly contributes to secular changes in the orbital parameters. The optimal control problem is constructed in such a way as to maneuver the satellite to a new orbit while minimizing a cost function subject to the constraints of the time-averaged equations of motion by controlling current in the tether. Three optimal maneuvers were investigated for a 4 km tether in a 270 km initial orbit: maximum climb, maximum final inclination, and a minimum time orbit change. The resulting control solutions were propagated to verify their accuracy.