At present, measurements of Newton's constant of gravitation G ("big G") are discrepent at about 500 parts per million, while some experiments have stated uncertainties less than 30 parts per million. This level of variability, if not because of dark uncertainty, has inspired searches for a fifth force, and theories of the constant changing as a function of time. In 2016, the International Union of Pure and Applied Physics estabilished a working group (WG13) with the primary purpose of supporting experimental efforts to measure the Newtonian constant of gravitation.
We propose to measure G using the two-pendulum technique of Parks and Faller. A pair of field masses translate adjacent to a pendulum bob, thereby displacing the bob in accord with the change in the gravitational field. The displacement is read-out using Fabry-Perot interferometery. This bob displacement can be related to force, if the spring constant of the pendulum is accurately known. By careful measurement of mass and coordinates, the changes in the gravitational field can be calculated, and G determined through the observed force on the bobs.
Measuring the gravitational constant has been called the Mount Everest of precision measurement. The gravitational force acting on a pendulum bob is less than one micronewton, and we wish to measure that force to a few ppm (i.e., sub-piconewton). This force gives rise to a change in position of a pendulum bob of 50 nanometers, and we wish to measure that displacement to a few ppm (i.e., 50 femtometer). Determining the change in the gravitational field requires knowledge of position and movement of large cylindrical field masses to within 1 micrometer, which may in fact be the largest challenge.
Interferometry; Fabry-Perot; Length metrology; Precision measurement; Gravitation
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