The fourth test of general relativity

Publisher Website
Google Scholar
Abstract
In the 'fourth test of general relativity' the gravitational acceleration of celestial bodies-the Earth and the Moon-were experimentally compared in the gravitational field of the Sun. Because such bodies obtain an appreciable fraction of their total mass-energy from their internal gravitational self-energy (5*10-10 for the Earth), this comparison of free-fall rates measures, among other things, how gravity pulls on gravitational energy and how gravitational energy contributes to the inertial mass of celestial bodies. Using high-precision laser ranging between Earth and reflectors on the Moon's surface, it was found that the Earth and Moon's acceleration in the Sun's gravitational field are the same to one part in 1011. Hypothesising that the gravitational to inertial mass ratio of a celestial body may differ from one by the order of the gravitational self-energy content of the body divided by the total mass-energy: MG/MI=1+ eta (UG/Mc2) eta being a dimensionless constant determined by gravitational theory, the lunar laser ranging experiment limits mod eta mod to less than 1.4*10-2. This experiment is consistent with general relativity which predicts eta =0, but scalar-metric tensor theories, such as the Brans-Dicke theory, vector-metric tensor theories and two-tensor theories of gravity are inconsistent with this experiment unless sufficient adjustable parameters are used.