<p>The total cross section for electron–proton radiative recombination is calculated. Unlike previous studies that primarily employed the stationary-proton approximation, the present work considers the case in which both interacting particles are in motion. This condition is characteristic of the solar wind and various astrophysical plasma environments. The analysis is carried out within the framework of nonrelativistic quantum electrodynamics, which is appropriate for particle energies typical of the solar atmosphere and the solar wind. An analytical expression for the recombination cross section is derived as a function of the relevant kinematic parameters. The results demonstrate that accounting for proton motion significantly modifies the recombination cross section.</p>