Measuring Newton's Gravitational Constant With a Gravitational   Oscillator
  Newton's gravitational constant G, which determines the strength of gravitational interactions both in Newton's theory and in Einstein's General Relativity, is the least well known of all the fundamental constants. Given its importance, and with recent disparities between experimental measurements, a new approach is suggested. It is based on a purely gravitational oscillator without any non-gravitational restoring forces. The suggested technique is based on the oscillation period of a test mass oscillating through a hole bored in a solid sphere in free space, or, equivalently, in orbit. The period of oscillation depends only on the density of the solid sphere, providing a method with systematic errors different from terrestrial approaches to the determination of G. Deviations from standard Newtonian gravity and the equality of gravitational and inertial mass can also be searched for. 
John Swain
gr-qc