MEASUREMENT OF THE GRAVITATIONAL CONSTANT USING THE ATTRACTION BETWEEN TWO FREELY FALLING DISCS: A PROPOSAL

The constant of gravitation, G, is the least well-known of the physical constants. A new, independent method of measurement, estimated as having a potential uncertainty at least as small as that achieved by existing methods, would be useful for an improvement in G determination. This experiment is based on the measurement of the relative motion of two freely falling test bodies (discs), caused by their gravitational attraction. The uncertainties are analyzed for two parallel tungsten discs with masses of about 30 kg. The use of test bodies with an incorporated optical system of multipass two-beam interferometers, as well as of multibeam interferometers, is proposed to measure their relative displacement. The estimations were made for laboratory experiment with free fall duration of 0.714 s. In this case, the relative displacement to be measured is about 0.1 μm. These estimates show that relative uncertainties lower than 5 × 10^-5 can be obtained in G measurement in a single drop of the test bodies. The proposed experiment can be made in outer space. In space a lower uncertainty can be achieved because the time interval of the measurement of relative motion of the test bodies can be increased.