Measurement of Newton's Constant Using a Torsion Balance with Angular Acceleration Feedback

The pendulum is one of the oldest gravimeters, featuring frequency-based readout limited by geometric nonlinearity. While modern gravimeters focus on displacement-based spring-mass or free-fall designs, the advent of nanofabrication techniques invites a revisiting of the pendulum, motivated by the prospect of low-loss, compact, isochronous operation, leveraging precise dimensional control. Here we exploit advances in strain-engineered nanomechanics -- specifically, strained S...

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 p...

A Kibble balance measures the $gravitational$ mass (weight) of a test mass with extreme precision by balancing the gravitational pull on the test mass against the electromagnetic lift force. The uncertainty in such mass measurement is currently ~$1\times 10^{-8} $. We show how the same Kibble balance can be used to measure the $inertial$ mass of a test mass, that too with potentially 50% better measurement uncertainty, i.e., ~$5\times 10^{-9} $. For measuring the inertial mas...

We describe a torsion pendulum with a large mass-quadrupole moment and a resonant frequency of 2.8 mHz, whose angle is measured using a modified Michelson interferometer. The system achieved noise levels of $\sim200\ \text{prad}/\sqrt{\text{Hz}}$ between 0.2-30 Hz and $\sim10\ \text{prad}/\sqrt{\text{Hz}}$ above 100 Hz. Such a system can be applied to a broad range of fields from the study of rotational seismic motion and elastogravity signals to gravitational wave observatio...

We demonstrate gravitational coupling between two gold spheres of approximately 1mm radius and 90mg mass. By periodically modulating the source mass position at a frequency f=12.7mHz we generate a time-dependent gravitational acceleration at the location of the test mass, which is measured off resonance in a miniature torsional balance configuration. Over an integration time of 350 hours the test mass oscillator enables measurements with a systematic accuracy of 4E-11m/s^2 an...

We report progress on a program of gravitational physics experiments using cryogenic torsion pendula undergoing large-amplitude torsion oscillation. This program includes tests of the gravitational inverse square law and of the weak equivalence principle. Here we describe our ongoing search for inverse-square-law violation at a strength down to $10^{-5}$ of standard gravity. The low-vibration environment provided by the Battelle Gravitation Physics Laboratory (BGPL) is unique...

It is well-entrenched folklore that torsion gravity theories predict observationally negligible torsion in the solar system, since torsion (if it exists) couples only to the intrinsic spin of elementary particles, not to rotational angular momentum. We argue that this assumption has a logical loophole which can and should be tested experimentally. In the spirit of action=reaction, if a rotating mass like a planet can generate torsion, then a gyroscope should also feel torsion...

Measuring gravitational interactions on sub-100-$\mu$m length scales offers a window into physics beyond the Standard Model. However, short-range gravity experiments are limited by the ability to position sufficiently massive objects to within small separation distances. Here we propose mass-loaded silicon nitride ribbons as a platform for testing the gravitational inverse square law at separations currently inaccessible with traditional torsion balances. These microscale tor...

We present a new test for a possible Mach-Sciama dependence of the Gravitational constant G. According to Ernst Mach (1838-1916), the gravitational interaction depends on the distribution of masses in the universe. A corresponding hypothesis of Sciama (1953) on the gravitational constant, $c^2/G = \sum m_i/r_i$, can be tested since the elliptic earth orbit should then cause minute annual variations in G. The test is performed by analyzing the gravity signals of a network of s...

Motivated by higher-dimensional theories that predict new effects, we tested the gravitational 1/r^2 law at separations ranging down to 218 micrometers using a 10-fold symmetric torsion pendulum and a rotating 10-fold symmetric attractor. We improved previous short-range constraints by up to a factor of 1000 and find no deviations from Newtonian physics.