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

Abstract

We measured Newton's gravitational constant $G$ using a new torsion balance method. Our technique greatly reduces several sources of uncertainty compared to previous measurements: (1) It is insensitive to anelastic torsion fiber properties; (2) a flat plate pendulum minimizes the sensitivity due to the pendulum density distribution; (3) continuous attractor rotation reduces background noise. We obtain $G=(6.674215\pm 0.000092)\times {10}^{-11\mathrm{}}{\mathrm{m}}^3{\mathrm{kg}}^{-1\mathrm{}}{\mathrm{s}}^{-2\mathrm{}}$; the Earth's mass is, therefore, $M_{\oplus }=(5.972245\pm 0.000082)\times {10}^{24}\mathrm{kg}$ and the Sun's mass is $M_{\odot }=(1.988435\pm 0.000027)\times {10}^{30}\mathrm{kg}$.