  Recent measurements, of the velocities of stars near the center of the Milky
Way have provided the strongest evidence for the presence of a supermassive
black hole in a galaxy, but the observational uncertainties poorly constrain
many of the properties of the black hole. Determining the accelerations of
stars in their orbits around the center provides much more precise information
about the position and mass of the black hole. Here we report measurements of
the accelerations for three stars located ~0.005 pc from the central radio
source Sgr A*; these accelerations are comparable to those experienced by the
Earth as it orbits the Sun. These data increase the inferred minimum mass
density in the central region of the Galaxy by an order of magnitude relative
to previous results and localized the dark mass to within 0.05 +- 0.04 arcsec
of the nominal position of Sgr A*. In addition, the orbital period of one of
the observed stars could be as short as 15 years, allowing us the opportunity
in the near future to observe an entire period.
