  We present a horizontal gravity gradiometer atom interferometer for precision
gravitational tests. The horizontal configuration is superior for maximizing
the inertial signal in the atom interferometer from a nearby proof mass. In our
device, we have suppressed spurious noise associated with the horizonal
configuration to achieve a differential acceleration sensitivity of
4.2$\times10^{-9}g/\sqrt{Hz}$ over a 70 cm baseline or
3.0$\times10^{-9}g/\sqrt{Hz}$ inferred per accelerometer. Using the performance
of this instrument, we characterize the results of possible future
gravitational tests. We complete a proof-of-concept measurement of the
gravitational constant with a precision of 3$\times10^{-4}$ that is competitive
with the present limit of 1.2$\times10^{-4}$ using other techniques. From this
measurement, we provide a statistical constraint on a Yukawa-type fifth force
at 8$\times$10$^{-3}$ near the poorly known length scale of 10 cm. Limits
approaching 10$^{-5}$ appear feasible. We discuss improvements that can enable
uncertainties falling well below 10$^{-5}$ for both experiments.
