A self-consistent field theory involving the Vlasov equation and the Poisson equation is applied to the study of the potential field around a spherical satellite, the Coulomb drag, and its wake trails in an ionized atmosphere. It is considered that undisturbed particles have a Maxwellian distribution of speeds with large mean free paths in comparison with the Debye length. In the vicinity of the sphere, both the incident and the reflected distribution functions are considered. It is found that the electrical potential around a rapidly moving satellite is not in the form of spherical symmetry, which is a new and essential contribution to the existing state of knowledge on this subject. From this nonspherical potential field, the Coulomb drag is easily formulated, and the characteristics of the wakes behind the satellite are readily predicted. The theoretical value as computed for Explorer VIII satellite leads to a potential of —0.156 v, which is in close agreement with the actual observed measurement of — 0.15 v. This analysis also presents a method of obtaining results from the nonlinear self-consistent set of Vlasov-Poisson equations.