The measurement of the gravitational constant in an orbiting laboratory

Abstract

We propose to measure the gravitational constantG by putting in an orbiting laboratory a known mass of very high density and by tracking the motion of a small test mass under the gravitational influence of the primary mass. We analyse the different sources of perturbation; the consideration of the Earth's gravity gradient leads us to conclude that, if the laboratory is in a low Earth orbit, we cannot get stable satellite-like orbits of the test mass, but we must study only a process of ‘gravitational scattering’. In order to maximize the time of interaction it is proposed to use the ‘practical stability’ of a collinear equilibrium point of the system Earth-primary mass, by putting the test mass as close as possible to the stable manifold of an equilibrium point. This method will allow the determination of the value ofG within a few parts over 10⁵, as shown by some computer simulations of the experiment taking into account also some unknown perturbation and random noise.

Two main problems are involved in this experiment: (a) refined numerical methods are needed to take into account all significant perturbations and to extract the result aboutG from the experimental data; (b) during the motion of the test mass, the primary mass must always be free-falling inside the laboratory, so that this experiment needs a drag-free satellite technique of the same type which is necessary for high-precision gravimetric measurements.