A Determination of the Local Gravitational Acceleration for the Tsinghua Tabletop Kibble Balance

TL;DR

This paper accurately measures the local gravitational acceleration for the Tsinghua tabletop Kibble balance, achieving an uncertainty of 5.4 μGal by modeling systematic effects and using polynomial fitting for transfer.

Contribution

It introduces a polynomial fitting method for absolute gravity transfer and models systematic effects to determine $g$ with high precision.

Findings

Achieved $g$ measurement with 5.4 μGal uncertainty.

Validated polynomial transfer method against tide correction.

Mapped gravity gradients at different heights.

Abstract

The Kibble balance requires a measurement of the local gravitational acceleration, $g$, with a typical relative measurement uncertainty of $10^{-9}$. In this paper, the determination of $g$ for the Tsinghua tabletop Kibble balance is presented. A polynomial fitting method is proposed for blind transfers of the absolute gravitational acceleration using relative gravimeters, showing agreement with the value obtained by the tide correction within a few parts in $10^{9}$. Horizontal and vertical gravity gradients are extracted by mapping the gravity distribution at different heights. The self-attraction effect of major components in the experiment, as well as some time-varying systematic effects, are modeled. The final determination of the gravitational acceleration at the mass position, with an uncertainty of 5.4 $\mu$Gal ($k=2$), is achieved for the Tsinghua tabletop Kibble balance experiment.