Isotropic photon drag: Analytic expressions for velocity (3D) and position (1D) with applications to blackbody friction

The motion of objects traveling at relativistic speeds and subject only to isotropic photon drag (blackbody friction as a special case) is modeled. The objects are assumed to be perfectly absorbing. Analytic expressions for velocity and position as a function of time for objects subject to photon drag are obtained for the case in which the photons are constrained to one-dimensional motion. If the object is also assumed to be a perfect emitter of energy, analytic expressions are found for time as a function of velocity of the body for photons constrained to one-dimensional motion, and for a full three-dimensional isotropic photon background. The derivations are carried out entirely from the point of view of a reference frame at rest relative to the isotropic photon field, so that no changes of reference frame are involved. The results for the three-dimensional model do not agree with work by previous authors, and this discrepancy is discussed. The derivations are suitable for use in the undergraduate classroom. Example cases for a light sail and a micron-sized sand grain are examined for interactions with the cosmic background radiation, assuming a temperature of 3000 K, the temperature at the time the universe became transparent, and it is found that relativistic speeds would decay on a time scale of years.