Correction due to the finite speed of light in absolute gravimeters

Abstract

The correction due to the finite speed of light is among the most inconsistent in absolute gravimetry. Formulae reported by different authors yield corrections scattered up to 8 µGal for no obvious reasons. The problem, though noted before, has never been studied, and nowadays the correction is rather postulated than rigorously proven. In this paper we make an attempt to revise the subject. Like other authors, we use physical models based on signal delays and the Doppler effect; however, in implementing the models we additionally introduce two scales of time associated with moving and stationary reflectors, derive a set of rules to switch between the scales and establish the equivalence of trajectory distortions as obtained from either time delay or distance progression. The obtained results enabled us to produce accurate correction formulae for different types of instruments, and to explain the differences in the results obtained by other authors. We found that the correction derived from the Doppler effect is accountable only for two-thirds of the total correction due to the finite speed of light, if no signal delays are considered. Another major source of inconsistency was found in the tacit use of simplified trajectory models.