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 Ro of 8.0+-0.6 kpc, M_bh of 4.1+-0.6x10^6 Mo, 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, we can further
constrain the fit and obtain Ro = 8.4+-0.4 kpc and M_bh = 4.5+-0.4x10^6 Mo.
More complex models constrain the extended dark mass distribution to be less
than 3-4x10^5 Mo 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 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 Ro and the Galaxy's local rotation
speed, which it is derived from combining Ro with the apparent proper motion of
Sgr A*, (theta0 = 229+-18 km/s), 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.Comment: ApJ, accepted (26 pages, 16 figures, 7 tables
