Solar System Tests of the Equivalence Principle and Constraints on Higher-Dimensional Gravity

Abstract

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 systemdynamics and reinforcing the value of equivalence principle tests as a probe of nonstandard gravitational theories.