The Fresnel–Fizeau effect and the atmospheric time delay in geodetic VLBI

The Fresnel–Fizeau effect is a special relativistic effect that makes the speed of light dependent on the velocity of a transparent, moving medium. We present a theoretical formalism for discussing propagation of electromagnetic signals through the moving Earth atmosphere taking into account the Fresnel–Fizeau effect. It provides the rigorous relativistic derivation of the atmospheric time delay equation in the consensus model of geodetic VLBI observations which has never been published before. The paper confirms the atmospheric time delay of the consensus VLBI model used in IERS standards and provides a firm theoretical basis for calculation of even more subtle relativistic corrections.