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

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 10⁹. 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 a relative uncertainty of 5.4 μGal ($k=2$), is achieved for the Tsinghua tabletop Kibble balance experiment.