Determination of the Newtonian Gravitational Constant<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mi>G</mml:mi></mml:math>with Time-of-Swing Method

Abstract

We present a new value of the Newtonian gravitational constant G by using the time-of-swing method. Several improvements greatly reduce the uncertainties: (1) measuring the anelasticity of the fiber directly; (2) using spherical source masses minimizes the effects of density inhomogeneity and eccentricities; (3) using a quartz block pendulum simplifies its vibration modes and minimizes the uncertainty of inertial moment; (4) setting the pendulum and source masses both in a vacuum chamber reduces the error of measuring the relative positions. By two individual experiments, we obtain G = 6.673 49(18) x 10;{-11} m;{3} kg;{-1} s;{-2} with a standard uncertainty of about 2.6 parts in 10;{5}.