The use of electrodynamic tethers for propulsion and power generation is attractive for missions to the outer planets, which are traditionally handicapped by large propellant requirements, large times of flight, and a scarcity of power available. The proposed electrodynamic tether propulsion scheme is shown to be capable at reducing or eliminating these mission constraints. In this work, the orbital dynamics of a spacecraft using electrodynamic tether propulsion during the mission phases of capture, apojove pump-down and perijove pump-up in the Jovian system are investigated. The main result is the mapped design space involving mission duration, tether length and minimum perijove radius. Phase-free flyby sequences and bang-bang control laws are also included, which provide performance upper bounds for a given mission architecture. It is found to be advantageous to utilize in-bound only flybys of the Galilean moons during capture, and few, if any, out-bound only flybys during apojove pump-down. The electrodynamic tether system is also shown to be capable of lowering the spacecraft’s orbit to a Europa-Ganymede Hohmann orbit with a total flight time after entering Jupiter’s sphere of influence of just under two years. The benefits of leveraging solar third body perturbations, ballistic flyby tours, and adding a secondary propulsion system are also considered. / text