A Method to Measure Newton's Gravitational Constant

Abstract

This paper describes the design and testing of a method to measure the Newtonian gravitational constant G. The method uses a torsion balance in which a small cylindrical mass is suspended from a slender fibre. Two large cylindrical masses produce a gravitationally induced torque on the small mass. This induced torque is balanced by the electrostatic torque produced by an electrometer. A servo-control system adjusts the electrostatically induced torque so that the fibre does not twist during the measurement. The torque produced by the electrometer is calibrated by an acceleration method that uses torques much larger than those produced by the gravitational attraction of the large masses. Other features of the method include a reduction in sensitivity of the measurement to density variations in the suspended mass, a measurement strategy which reduces the effect of drift in the measurement and computer control of the measurement. Preliminary measurements of the terms used to calculate G showing an uncertainty of 2,5 parts in 104 can currently be achieved. The limiting factor at present is the variation in the gravitational potential seen as the apparatus accelerates. Indications are that further modifications and measurements will provide a value of G with an uncertainty of about 1 part in 104.