Rapid variations in spacecraft potential are observed on entry and exit from the earth's shadow. Generalized equations, based on elementary plasma probe theory, are developed which make quantitative estimates of the spacecraft potential as a function of satellite position in the earth's penumbra and are compared with data from the ATS-5 and ATS-6 geosynchronous satellites. The agreement between the observations and the predictions results from the approximate constancy of the ratio of the ambient ion to electron current during injection events. Due to the significant size and shape differences of the ATS-5 and ATS-6 satellites, the results are applicable in many space physics situations such as estimating the effects of electron beams on satellite potential and of spacecraft charging on very large space structures.