The measurement of the gravitational constant in an orbiting laboratory |
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| Authors: | Paolo Farinella Andrea Milani Anna M Nobili |
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| Institution: | (1) Osservatorio Astronomico di Brera, Merate, Italy;(2) Istituto di Matematica  L. Tonelli , Università di Pisa, Italy;(3) Istituto di Scienze dell'Informazione, Università di Pisa, Italy |
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| 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. |
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