8 Measurement of the Gravitational Constant G

Measurement of the Gravitational Constant G 8 Measurement of the Gravitational Constant G F. Nolting, J. Schurr, E. Holzschuh, and W. K undig The most precise published results for the gravitational constant G have claimed uncertainties of about 100 ppm. Such measurements are usually done by some variant of the Cavendish torsion balance [1], but other methods have also been tried. During the last thirty years quite a few experiments have been performed, however without signi cant progress. What makes things worse, the results show large and unexplained discrepancies indicating that there are not well understood systematic e ects. To overcome these di culties, we have developed a new method for measuring G. The idea arose from our previous experiment at the Gigerwald storage lake [2,3]. The method has become feasible due to recent progress in the construction of beam balances with extremely high sensitivity. The principle of the experiment will be explained in the following section. The experiment is set up and running. A rst result for G with an uncertainty of 230 ppm was published recently [4] and will brie y be described in this report. Presently, preparations are made for measurements with higher accuracy. 8.1 The principle of the experiment A schematic view of the experiment is shown in Fig. 8.1. The essential components of the set-up are a single-pan beam balance, two test masses and two large eld masses. The test masses (1 kg each) are suspended with thin tungsten wires and alternately connected to the balance. The di erence of their weights is measured with high precision and taken as the signal. The balance and the test masses are inside a vacuum system. The eld masses are cylindrical in shape and have a central bore such that the test masses can pass through. By moving the eld masses between the two positions shown, their gravitational force on the test masses changes the signal. From the di erence of the signal for the two states and from