Measurement of the speed-of-light perturbation of free-fall absolute gravimeters

peer reviewedWe report on a direct measurement of the relativistic Doppler shift with a commercial free-fall absolute gravimeter of the type FG5X. The observed Doppler shift, which is commonly called speed-of-light perturbation, can be well described by the relativistic Doppler formula, where the constant object velocity is replaced by a time-dependent velocity with constant acceleration. The observed speed-of-light perturbation stands in contrast to other publications, which predict a higher frequency shift. It has been measured with a relative uncertainty of 1.1 × 10 −3