We report new precision measurements of the properties of our Galaxy's supermassive black hole. Based on astrometric (1995-2007) and radial velocity (2000-2007) measurements from the W. M. Keck 10-meter telescopes, a fully unconstrained Keplerian orbit for the short period star S0-2 provides values for the distance (R0) of 8.0 +/- 0.6 kpc, the enclosed mass (M_bh) of 4.1 +/- 0.6 * 106 M_o, and the black hole's radial velocity, which is consistent with zero with 30 km/s uncertainty. If the black hole is assumed to be at rest with respect to the Galaxy (e.g., has no massive companion to induce motion), we can further constrain the fit and obtain R0 = 8.4 +/- 0.4 kpc and M_bh = 4.5 +/- 0.4 * 106 M_o. More complex models constrain the extended dark mass distribution to be less than 3-4 * 105 M_o within 0.01 pc, 100x higher than predictions from stellar and stellar remnant models. For all models, we identify transient astrometric shifts from source confusion (up to 5x the astrometric error) and the assumptions regarding the black hole's radial motion as previously unrecognized limitations on orbital accuracy and the usefulness of fainter stars. Future astrometric and RV observations will remedy these effects. Our estimates of R0 and the Galaxy's local rotation speed, which it is derived from combining R0 with the apparent proper motion of Sgr A*, ( theta 0 = 229 +/- 18 km s-1), are compatible with measurements made using other methods. The increased black hole mass found in this study, compared to that determined using projected mass estimators, implies a longer period for the innermost stable orbit, longer resonant relaxation timescales for stars in the vicinity of the black hole and a better agreement with the M_bh- sigma relation.
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