Testing Relativity with Laser Ranging to the Moon

Precise laser ranging to the moon is shown to be capable of measuring the ratio (mgmᵢ) of gravitational mass to inertial mass of the earth to accuracy sufficient to detect gravitational self-energy contributions. If mgmᵢ of the earth differs from 1 by an amount of order (earth gravitational self-energy)/(earth total energy), then the lunar orbit will acquire a range oscillation of amplitude about 12 m.