  We present new, more precise measurements of the mass and distance of our
Galaxy's central supermassive black hole, Sgr A*. These results stem from a new
analysis that more than doubles the time baseline for astrometry of faint stars
orbiting Sgr A*, combining two decades of speckle imaging and adaptive optics
data. Specifically, we improve our analysis of the speckle images by using
information about a star's orbit from the deep adaptive optics data (2005 -
2013) to inform the search for the star in the speckle years (1995 - 2005).
When this new analysis technique is combined with the first complete
re-reduction of Keck Galactic Center speckle images using speckle holography,
we are able to track the short-period star S0-38 (K-band magnitude = 17,
orbital period = 19 years) through the speckle years. We use the kinematic
measurements from speckle holography and adaptive optics to estimate the orbits
of S0-38 and S0-2 and thereby improve our constraints of the mass ($M_{bh}$)
and distance ($R_o$) of Sgr A*: $M_{bh} =
4.02\pm0.16\pm0.04\times10^6~M_{\odot}$ and $7.86\pm0.14\pm0.04$ kpc. The
uncertainties in $M_{bh}$ and $R_o$ as determined by the combined orbital fit
of S0-2 and S0-38 are improved by a factor of 2 and 2.5, respectively, compared
to an orbital fit of S0-2 alone and a factor of $\sim$2.5 compared to previous
results from stellar orbits. This analysis also limits the extended dark mass
within 0.01 pc to less than $0.13\times10^{6}~M_{\odot}$ at 99.7% confidence, a
factor of 3 lower compared to prior work.
