Precision Test of the Equivalence Principle

We used a torsion balance instrument installed on a continuously rotating turntable to measure the acceleration difference of beryllium and titanium test bodies towards sources at a variety of distances. Our result $\Delta $a$_{N,Be-Ti}$ = (0.6$\pm $3.1)$\times $10$^{-15}$ m/s$^{2}$ improves previous limits on equivalence-principle violations with ranges from 1 m to $\infty $ by nearly an order of magnitude. The E\"{o}tv\"{o}s parameter is $\eta _{Earth,Be-Ti }$= (0.3$\pm $1.8)$\times $10$^{-13}$. By analyzing our data for accelerations towards the center of the Milky Way we find equal attractions of Be and Ti towards galactic dark matter, yielding $\eta _{DM,Be-Ti}$ = (-4$\pm $7)$\times $10$^{-5}$. Space-fixed differential accelerations in any direction are limited to less than 8.8 $\times $ 10$^{-15}$ m/s$^{2}$ with 95{\%} confidence.