Improved Test of the Equivalence Principle for Gravitational Self-Energy

The lunar-ranging test of the equivalence principle for gravitational self-energy is ambiguous. Although the Earth has more gravitational self-energy than the Moon, its sizable Fe/Ni core also gives it a different composition than the Moon. We removed this ambiguity by comparing, in effect, the accelerations of “miniature” earths and moons toward the Sun. Our composition-dependent Earth-Moon acceleration, $\Delta a_{\mathrm{CD}}/a_{\mathrm{s}}=(+0.1\mathrm{}\pm 2.7\pm 1.7)\times {10}^{-13\mathrm{}}$, and lunar-ranging data provide an unambiguous test at the $1.3\times {10}^{-3\mathrm{}}$ level.