Testing Relativity with Laser Ranging to the Moon

Precise laser ranging to the moon is shown to be capable of measuring the ratio ($\frac{m_g}{m_i}$) of gravitational mass to inertial mass of the earth to accuracy sufficient to detect gravitational self-energy contributions. If $\frac{m_g}{m_i}$ 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.