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.
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