We study eclipse charging events on the SCATHA spacecraft in a plasma environment which produced large vehicle potentials. We derive a simple relation which relates the spacecraft potential to spacecraft surface-averaged and angle-averaged fluxes and yields without assuming Maxwellian velocity distributions for the environment: e&PHgr;=Ei[1+Ies/(Iio(1+Y¿i))>. The potential varies with the ion mean energy Ei and with the net high-energy electron current Ies above a critical energy Ec. Below Ec the incoming electrons are balanced by their own secondaries. Above Ec the incoming electrons are balanced by incoming ions and both electron-produced and ion-produced secondaries. The potential also depends on the ion thermal current Iio and the average ion yield Y¿i. Data from five events show that the spacecraft potential correlates well with Ies when the ion properties stay relatively constant. Data from other events show that the potential varies with the ion mean energy. The magnitude of Ec is on the order of 20 to 30 keV. Quantitative prediction of the spacecraft potential depends sensitively on the secondary yield due to electrons. ¿ American Geophysical Union 1988