Solar system tests of the equivalence principle and constraints on higher-dimensional gravity

In most studies of equivalence principle violation by solar system bodies it is assumed that the ratio of gravitational to inertial mass for a given body deviates from unity by a parameter $\Delta$ which is proportional to its gravitational self-energy. Here we inquire what experimental constraints can be set on $\Delta$ for various solar system objects when this assumption is relaxed. Extending an analysis originally due to Nordtvedt, we obtain upper limits on linearly independent combinations of $\Delta$ for two or more bodies from Kepler’s third law, the position of Lagrange libration points, and the phenomenon of orbital polarization. Combining our results, we extract numerical upper bounds on $\Delta$ for the Sun, Moon, Earth and Jupiter, using observational data on their orbits as well as those of the Trojan asteroids. These are applied as a test case to the theory of higher-dimensional (Kaluza-Klein) gravity. The results are three to six orders of magnitude stronger than previous constraints on the theory, confirming earlier suggestions that extra dimensions play a negligible role in solar system dynamics and reinforcing the value of equivalence principle tests as a probe of nonstandard gravitational theories.