Comment on New apparatus design for high-precision measurement of G with atom interferometry

TL;DR

This paper analyzes systematic errors in high-precision G measurements using atom interferometry, showing the impact of gravitational gradient dependencies and proposing a source mass geometry to eliminate such errors.

Contribution

It identifies a previously overlooked systematic error due to radial gravitational gradients and proposes a source mass geometry to mitigate this error.

Findings

Radial gradient dependence causes significant systematic error

Calculated error exceeds previous predictions

Proposed source mass geometry eliminates the systematic error

Abstract

It is shown that even in the case of a negligibly small change in the gradient of the gravitational field of the mass source in the axial direction, the dependence of this gradient in the radial direction leads to a systematic error in Newton gravitational constant value. The magnitude of this error is calculated for two configurations of the field. For both configurations it was found that this error is larger than the inaccuracy predicted in the article by M. Jain et al [Eur. Phys. J. D 75, 197 (2021)]. In addition, we found the geometry of the source mass, for which this systematic error disappears.