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 $\sim 1$ m.

8 pages, 5 figures

References in corpus (13)

• Advanced Virgo: a 2nd generation interferometric gravitational wave detector
• Precision Measurement of the Newtonian Gravitational Constant Using Cold Atoms
• Millikelvin cooling of an optically trapped microsphere in vacuum
• GHz Rotation of an Optically Trapped Nanoparticle in Vacuum
• Search for Millicharged Particles Using Optically Levitated Microspheres
• Review of short-range gravity experiments in the LHC era
• Optical levitation of 10 nanogram spheres with nano-$g$ acceleration sensitivity
• A Measurement of Newton's Gravitational Constant
• Optical Rotation of Levitated Spheres in High Vacuum
• Three-dimensional force-field microscopy with optically levitated microspheres
• Single-beam dielectric-microsphere trapping with optical heterodyne detection
• First Tests of a Newtonian Calibrator on an Interferometric Gravitational Wave Detector
• Electrically Driven, Optically Levitated Microscopic Rotors

Cited by in corpus (2)

• High sensitivity, levitated microsphere apparatus for short-distance force measurements
• A Pseudo Plane-wave Gravitational Calibrator for Gravitational Wave Observatories