The present invention comprises apparatus and methods for using and controlling electrodynamic tethers. The apparatus taught by the present invention uses an interconnected multiwire (compared to the long, narrow single wires of the prior art) conductive tether whose area maximizes electrodynamic drag while simultaneously minimizing the Area-Time-Product swept by the tether during its operating life. The preferred tether length is two kilometers to five kilometers. The preferred tether mass is one percent to five percent of the spacecraft mass. The methods of control taught by the present invention comprise orienting the tether structure at a preferred angle to the local vertical to maximize electrodynamic drag and minimize tether instabilities. The angle of 35.26 degrees to the local vertical line is preferred. The invention also includes useful methods of controlling current flow in an electrodynamic tether to limit tether dynamic instabilities including in plane libration, out of plane libration, transverse instability and skip-rope instability.