We report measurements with the Very Long Baseline Array of the proper motion of Sgr A* relative to two extragalactic radio sources spanning 18 years .
The apparent motion of Sgr A* is -6.411 \pm 0.008 mas y ^ { -1 } along the Galactic plane and -0.219 \pm 0.007 mas y ^ { -1 } toward the North Galactic Pole .
This apparent motion can almost entirely be attributed to the effects of the Sun ’ s orbit about the Galactic center .
Removing these effects yields residuals of -0.58 \pm 2.23 km s ^ { -1 } in the direction of Galactic rotation and -0.85 \pm 0.75 km s ^ { -1 } toward the North Galactic Pole .
A maximum-likelihood analysis of the motion , both in the Galactic plane and perpendicular to it , expected for a massive object within the Galactic center stellar cluster indicates that the radiative source , Sgr A* , contains more than about 25 % of the gravitational mass of 4 \times 10 ^ { 6 } ~ { } { { M } _ { \odot } } deduced from stellar orbits .
The intrinsic size of Sgr A* is comparable to its Schwarzschild radius , and the implied mass density of \mathrel { \hbox { \raise 2.15 pt \hbox { $ > $ } \hbox to 0.0 pt { \lower 2.15 pt \hbox { $ \sim$% } } } } 4 \times 10 ^ { 23 } { M } _ { \odot } pc ^ { -3 } is very close to that expected for a black hole , providing overwhelming evidence that it is indeed a super-massive black hole .
Finally , the existence of “ intermediate mass ” black holes more massive than \approx 3 \times 10 ^ { 4 } { M } _ { \odot } between approximately 0.003 and 0.1 pc from Sgr A* are excluded .