Correction due to finite speed of light in absolute gravimeters

TL;DR

This paper revises the correction formulas for finite speed of light in absolute gravimeters, introducing new models and rules that clarify discrepancies and improve accuracy in measurements.

Contribution

It develops a rigorous physical model incorporating time scales and signal delays, resolving inconsistencies in existing correction formulas for absolute gravimetry.

Findings

Correction formulas vary up to 8 μGal in literature

Doppler effect accounts for two-thirds of the total correction

Simplified trajectory models cause significant inconsistencies

Abstract

Correction due to finite speed of light is among the most inconsistent ones in absolute gravimetry. Formulas reported by different authors yield corrections scattered up to 8 $\mu$Gal with 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 resting 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 formulas 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 $\frac23$ of the total correction due to 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.