Measurement of the Newtonian constant of gravitation G by precision displacement sensors

Abstract

The Newtonian constant of gravitation G historically has the largest relative uncertainty over all other fundamental constants with some discrepancies in values between different measurements. We propose a new scheme to measure G by detecting the position of a test mass in a precision displacement sensor induced by a force modulation from periodically rotating source masses. To seek different kinds of experimental setups, laser interferometers for the gravitational wave detection and optically-levitated microspheres are analyzed. The high sensitivity of the gravitational wave detectors to the displacement is advantageous to have a high signal-to-noise ratio of 10 −6 with a few hours of the measurement time, whereas the tunability of parameters in optically-levitated microspheres can enable competitive measurements with a smaller scale setup dedicated to the G measurement. To achieve an accuracy of G better than currently available measurements, developments in force calibration is essential. These measurements can provide an alternative method to measure G precisely, potentially leading to the improvement in the accuracy of G, as well as a better search for non-Newtonian gravity at a length scale of ∼ 1 m.

Initial Results from the LIGO Newtonian Calibrator

“…Additionally, future iterations of this instrument may allow novel gravitational experiments such as searches for non-Newtonian gravity [54], terrestrial measurements of Shapiro delay [55,56], and measurements of the gravitational constant [57].…”

Dynamic gravitational excitation of structural resonances in the hertz regime using two rotating bars

“…It will help to reveal new insights in dynamic gravitation, such as frequency dependency or amplitude/phase effects due to objects between transmitter and detector (gravitational shielding). The results and findings of this and future related works can also help to advance the research and application of Newtonian calibrators that are used in gravitational-wave detectors [5,6,[20][21][22][23]. A power-law behavior can be identified, the exponents are given in Table 3.…”

Initial results from the LIGO Newtonian calibrator

“…Additionally, future iterations of this instrument may allow novel gravitational experiments such as searches for non-Newtonian gravity [54], terrestrial measurements of Shapiro delay [55,56], and measurements of the gravitational constant [57]. The authors would like to thank Peter Fritschel, Zsuzsanna Marka, Szabolcs Marka, and Dimitri Estevez for their helpful comments.…”

“…In addition to the calibration results discussed here, the NCal system allows a unique measurement of the gravitational constant, G [57]. The pre-existing calibration system [15] allows the force acting on the test mass to be measured precisely while the simulations described in Section IV B can account for the mass distributions.…”