A new approach to the analysis of absolute gravimeter operation proposes that the measured value of gravity should be found as a mean-weighted value of the acceleration of a free-moving body averaged within every measurement. The weighting functions of absolute gravimeters are determined. They depend on the gravimeter model used and the allocation of chosen data points within a single measurement. The effective measurement heights of absolute gravimeters can thus be found and the corrections due to linear gravity gradient and finite speed of light established. The results presented cover both direct free-fall and symmetric rise-and-fall types of apparatus.
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 µGal 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 2 3 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.
Although the equation of motion developed in the paper (Ashby 2018 Metrologia 55 1) depends on the parameters of the falling cube, such as depth and refraction index, the parameters are only associated with powers of time no greater than one, and so do not affect the acceleration. The paper's correction due to the light propagation within the cube is therefore not supported by the equation of motion, and probably caused by omissions in data analysis. The 'speed of light' component of the acceleration that follows from the equation, agrees with the results obtained by other authors. ‡ 1 µGal= 10 −8 ms −2 § formula (47), third line, of [1] arXiv:1802.05540v1 [physics.ins-det]
In the article (Rothleitner and Francis 2011 Metrologia 48 187-195) the correction due to the finite speed of light in absolute gravimeters is analyzed from the viewpoint of special relativity. The relativistic concepts eventually lead to the two classical approaches to the problem: analysis of the beat frequency, and introduction of the retarded times. In the first approach, an additional time delay has to be assumed, because the frequency of the beam bounced from the accelerated reflector differs at the point of reflection from that at the point of interference. The retarded times formalism is equivalent to a single Doppler shift, but results in the same correction as the beat frequency approach, even though the latter is explicitly combines two Doppler shifts. In our comments we discuss these and other problems we found with the suggested treatment of the correction.
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 µGal 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 2 3 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.
scite is a Brooklyn-based organization that helps researchers better discover and understand research articles through Smart Citations–citations that display the context of the citation and describe whether the article provides supporting or contrasting evidence. scite is used by students and researchers from around the world and is funded in part by the National Science Foundation and the National Institute on Drug Abuse of the National Institutes of Health.