Electrodynamic tethers are wires deployed across the earth's geomagnetic field through which a current is flowing. The radiation impedance of a tether with end connectors carrying an AC current is computed from classical antenna theory. This simulates the use of a tether on a space structure. It is shown that the current flow pattern at the tether connector is critical to determining the overall radiation impedance. If the tether makes direct electrical contact with the ionosphere then radiation impedances of the order of several thousand Ohms can be expected. If the only electrical contact is through the end connectors then the impedance is only a few Ohms for a DC current rising to several tens of Ohms for an AC current with frequencies in the whistler range. ¿American Geophysical Union 1987