Measurement of G with Angular Acceleration Feedback Method

Abstract

The large spread in recent published $G$ values suggests that there may be some undiscovered systematic sources in these experiments. With the aim of identifying possible errors and obtaining a more reliable $G$ value, our group has performed two independent methods simultaneously. Besides the time-of-swing method which we have worked on for more than 20 years [1], [2], another determination of $G$ with the angular acceleration feedback method was carried out at the same laboratory. In the AAF method, two coaxial turntables are used to rotate the torsion pendulum and the source masses individually. With the help of a feedback control system [3], the torsion fiber does not twist by matching the rotating rate of the two turntables. As a result, this method is insensitive to the fiber's properties. In this work, several sources of uncertainty existed in our preliminary experiment [4] are reduced: (1) An ultra-low thermal expansion (ULE) glass shelfis used to support the source masses instead of the aluminium shelf to reduce the temperature influence on the distance between source masses; (2) The background gravity gradient of the rotating shelf is measured and compensated with small blocks so that its effect to the $G$ value is reduced to ~1 ppm; (3) Two different methods are used to check the source mass distance to improve the confidence level. With the improvements shown above and a lot of careful systematic error evaluation, a new $G$ value with a prospective uncertainty of less than 15 ppm will be obtained.