A methodology of the physical modeling of radiation electrification of the leeward surfaces of the materials used to construct space vehicles by auroral electrons, when the vehicles are flown supersonically around by the ionospheric plasma at low and middle heights, is developed. Based on laboratory modeling, numerical experiments, and in situ observations, the dependencies of charging levels and equilibrium potentials on the ratio of the auroral electron density to the positive ions in the near wake behind the body and in the undisturbed plasma are determined.