One axis gravity gradiometer for the measurement of Newton's gravitational constant G

This Letter presents preliminary works concerning a new technique to measure the gravitational constant G, using a single axis gravity gradiometer designed to detect an off-line component of the gravity gradient tensor and able to reject the linear acceleration due to the vibrational noise (common mode rejection: CMR). The main part of such an instrument is a torsional mechanical oscillator which is forced at the frequency fr, by means of a gravitational torque produced with a system of two masses rotating at a frequency fr/2. The low frequency of the mechanical oscillator, together with a high sensitivity capacitive bridge measurement system, enables the detection of the gravitational signal with high accuracy, also in presence of quite high seismic noise. A precision of one part in 103 in the determination of the gravitational torque was achieved in our laboratory with an integration time of about 5 h and a factor 10 can be easily gained performing the measurement in a place with a lower differential seismic noise. The detection accuracy can be translated into experimental accuracy in the determination of G if the physical parameters of the whole system are measured with the same relative error. The experiment proposed in this Letter has strong similarities with the classic torsion balance [Rev. Sci. Instrum. 64 (1993) 283], but it has some peculiarities that make it particularly interesting as follows: the oscillating system is in indifferent equilibrium under the action of the Earth gravity field, so that it can have any orientation with respect to the local vertical; the instrument can also be used in the absence of gravity (free fall experiment); the capacitive bridge pick-up system has a high transducer factor for converting mechanical signals into electrical signals which are much greater than the pre-amplifier noise, even for very small displacements of the oscillator