Theory of an experiment in an orbiting space laboratory to determine the gravitational constant

Abstract

The paper analyzes an experiment in an orbiting laboratory to determine the gravitational constantG. A massive sphere, according to a suggestion of L. S. Wilk, is to have three tunnels drilled through it along mutually perpendicular diameters. The sphere either floats in the orbiting laboratory, with its center held fixed by means of external jets issuing from the spacecraft, or is tethered to the spacecraft. In either case it is free to rotate; in the second case this freedom would be achieved by a system of gimbals.

Each tunnel contains a small test object, which is held on the tunnel's axis by means of a suspension system, perhaps electrostatic, and held at rest relative to the sphere by slowly rotating the latter by means of inertia reaction wheels, governed by a servomechanism. Fundamentally, one balances the gravitational forces on the test objects by centrifugal force, determines the latter by measuring the components of angular velocity, and calculatesG from the resulting balance. It is better to use three tunnels than one because their use minimizes the effects of the Earth's gravity-gradient.

Many other measurements and corrections are required. The latter arise from Earth gravity-gradient, aerodynamic drag (with the tethered sphere), gravitational forces produced by the spacecraft itself, and the force reductions produced by the empty space in all three tunnels. After the consideration of these effects there is a presentation and discussion of the equations required to reduce the observations to obtainG. There then follow the extra equations, not needed in the reduction, that are required for a computer simulation to investigate the possible extraction of a test object and to aid in designing the servomechanisms.

In Appendix B, I have devised another version of the experiment, in which the sphere is kept intact, but has short thin hollow ‘vestigial tunnels’ attached to the outside of the sphere, along perpendicular diameters. These external tunnels would contain the test objects and the suspension systems. The servomechanisms would then have to prevent collision of a test object with the sphere, as well as extraction. This second method could allow for some inhomogeneities in the sphere, would require no accurate drilling, and would make the suspension systems more accessible for construction and adjustment.