A determination of the local acceleration of gravity for the NIST-4 watt balance

A new watt balance is being constructed at the National Institute of Standards and Technology (NIST) in preparation for the redefinition of the International System of Units and the realization of mass through an exact value of the Planck constant. The total relative uncertainty goal for this instrument of a few parts in $10^{8}$ requires that the local acceleration due to gravity be known at the location of a test mass with a relative uncertainty on the order of only a few parts in $10^{9}$. To make this determination, both the horizontal and vertical gradients of gravity must be known such that gravity may be tied from an absolute reference in the laboratory to the precise mass location. We describe the procedures used to model and measure gravity variations throughout the laboratory and give our results.