Gravitational configuration effect upon precision mass measurements

Abstract

Modern weighing practice consists of making comparisons between the gravitational attractive forces exerted on standard and unknown weights. An effect coupling the gravitational force exerted on a weight to the height of the weight’s center of gravity above its base has been found to be significant when weighings of the highest precision are attempted. This effect will cause systematic errors in mass measurements if not properly accounted for. The effect, called the ’’gravitational configuration effect,’’ arises because the centers of gravity of nominally equal weights above their bases, and hence the weights’ effective distances from the center of the Earth, are affected by the weights’ size and shape. Variations of 1 cm in the separation between the centers of gravity of weights and the center of the Earth produce differences in gravitational attractions of 3.14 parts in 109. Currently, mass comparisons at the 1-kg level can be carried out with standard deviations as small as 1.5 parts in 109. Thus, the gravitational configuration effect must be considered if weighing accuracies approaching weighing precisions are to be obtained when kilogram weights of significantly different sizes and/or shapes are compared. Corrections for the gravitational configuration effect can readily be combined with corrections for better-known effects, such as air buoyancy, to generate an overall equation to express the results of mass comparisons.

Centre of mass of standard weights: another experiment with Lego and Tracker

“…Now, during mass comparisons of two weights, a and b, with the same nominal mass value (m a = m b ), and whose centres of gravity are separated for a distance, d, measured above their bottoms, assume that the gravitational forces on both weights are equal. It is easy to show [14] that applying equation ( 2) to both weights leads to…”

The electronic balance and some gravimetric applications (the density of solids and liquids, pycnometry and mass)

“…The differences in elevation between the calibration weight, the air weighing pan and the lower immersed pan require corrections for the gradient in the earths gravitational field [2,10]. This correction is approximately 200 micrograms per meter per kilogram.…”

Practical uncertainty limits to the mass determination of a piston-gage weight

“…Cancellation will not be perfect, however, if the centers of mass of the standard and unknown are placed on the balance at different elevations with respect to the earth. The lack of cancellation is due to the gravitational gradient at the earth’s surface (about −0.003 ppm/cm [ 8 ]). If left uncorrected, the gravitational gradient would produce only a small systematic error.…”

“…The balance was another H315-MC located in the NBS mass calibration laboratory (Bal-3). For this balance, the method described by Schoonover and Taylor for minimizing thermal problems is used [ 8 ]. In this scheme, there is no box around the balance.…”