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.
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March 2014
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March 01 2014
Isotropic photon drag: Analytic expressions for velocity (3D) and position (1D) with applications to blackbody friction
Joseph West
Joseph West
a)
Department of Chemistry and Physics, Indiana State University
, Terre Haute, Indiana 47809
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Electronic mail: [email protected]
Am. J. Phys. 82, 217–223 (2014)
Article history
Received:
November 08 2012
Accepted:
November 19 2013
Citation
Joseph West; Isotropic photon drag: Analytic expressions for velocity (3D) and position (1D) with applications to blackbody friction. Am. J. Phys. 1 March 2014; 82 (3): 217–223. https://doi.org/10.1119/1.4839075
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