  We observed Sgr A* and two extragalactic radio sources nearby in angle with
the VLBA over a period of two years and measured relative positions with an
accuracy approaching 0.1 mas. The apparent proper motion of Sgr A* relative to
J1745-283 is 5.90 +/- 0.4 mas/yr, almost entirely in the plane of the Galaxy.
The effects of the orbit of the Sun around the Galactic Center can account for
this motion, and any residual proper motion of Sgr A*, with respect to
extragalactic sources, is less than about 20 km/s. Assuming that Sgr A* is at
rest at the center of the Galaxy, we estimate that the circular rotation speed
in the Galaxy at the position of the Sun is 219 +/- 20 km/s, scaled by Ro/8.0
kpc.
  Current observations are consistent with Sgr A* containing all of the nearly
2.6 x 10^6 solar masses, deduced from stellar proper motions, in the form of a
massive black hole. While the low luminosity of Sgr A*, for example, might
possibly have come from a contact binary containing of order 10 solar masses,
the lack of substantial motion rules out a "stellar" origin for Sgr A*. The
very slow speed of Sgr A* yields a lower limit to the mass of Sgr A* of about
1,000 solar masses. Even for this mass, Sgr A* appears to be radiating at less
than 0.1 percent of its Eddington limit.
