With 10 years of high-resolution imaging data now available on the stellar cluster in the Galactic Center , we analyze the dynamics of the stars at projected distances \leq 1.2 ^ { \prime \prime } from the central black hole candidate Sagittarius A* ( Sgr A* ) . We find evidence for radial anisotropy of the cluster of stars surrounding Sgr A* . We confirm/find accelerated motion for 6 stars , with 4 stars having passed the pericenter of their orbits during the observed time span . We calculated/constrained the orbital parameters of these stars . All orbits have moderate to high eccentricities . The center of acceleration coincides with the radio position of Sgr A* . From the orbit of the star S2 , the currently most tightly constrained one , we determine the mass of Sgr A* to 3.3 \pm 0.7 \times 10 ^ { 6 } M _ { \odot } and its position to 2.0 \pm 2.4 Â mas East and 2.7 \pm 4.5 Â mas South of the nominal radio position . The data provide compelling evidence that Sgr A* is a single supermassive black hole .