On the first mission of the Tethered Satellite System (TSS-1), a 1.8 m diameter spherical satellite will be deployed a distance of 20 km above the space shuttle Orbiter on an insulated conducting tether. The satellite will be held at electric potentials up to 5000 volts positive with respect to the ambient plasma. Due to the passage of the conducting tether through the Earth's magnetic field, an emf will be created, driving electrons down the tether to the orbiter, out through an electron gun into the ionosphere and back into the positive biased satellite. Instrumentation on the satellite will measure electron flow to the surface at several locations, but these detectors have a limited range of acceptance angle. The problem addressed herein is the determination of the electron current distribution over the satellite surface and the angle of incidence of the incoming electrons relative to the surface normal.