With 10 years of high-resolution imaging data now available on the stellar cluster in the Galactic Center , we present proper motions for > 40 stars at projected distances \leq 1.2 ^ { \prime \prime } from Sagittarius A* ( Sgr A* ) .
We find evidence on a \geq 2 \sigma level for radial anisotropy of the cluster of stars within 1 ^ { \prime \prime } of Sgr A* .
For a brightness limit of \mathrm { K } \sim 15.5 we find no evidence for a stationary source at the position of Sgr A* or for a source at this position that would be variable on a time scale of at least several hours to days .
On time scales of seconds to tens of minutes , we find no variability at the Sgr A* position on brightness levels \mathrm { K } \leq 13.5 .
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 .
We discuss the possible bias in detecting preferentially orbits with high eccentricities and find that measured values of e > 0.9 might be detected by about a factor of 1.5 - 2 more frequently .
We find that the center of acceleration for all the orbits 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 be 3.3 \pm 0.7 \times 10 ^ { 6 } M _ { \odot } and its position to 2.0 \pm 2.4 mas East and 2.7 \pm 4.5 mas South of the nominal radio position .
The mass estimate for the central dark mass from the orbit of S2 is fully consistent with the mass estimate of 3.4 \pm 0.5 \times 10 ^ { 6 } M _ { \odot } obtained from stellar proper motions within 1.2 ^ { \prime \prime } of Sgr A* using a Leonard-Merritt mass estimator .
We find that radio astronomical observations of the proper motion of Sgr A* in combination with its intrinsic source size place at the moment the tightest constraints on the mass density of Sgr A* , which must exceed \rho _ { \mathrm { Sgr~ { } A* } } > 3 \times 10 ^ { 19 } \mathrm { M } _ { \odot } \mathrm { pc } ^ { -3 } .