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, ${Δ}{a}CD/{a}ₛ{{0ex}{0ex}}={{0ex}{0ex}}(+0.1±{}2.7±{}1.7)×{}{10}^{{-}13}$, and lunar-ranging data provide an unambiguous test at the $1.3×{}{10}^{{-}3}$ level.