The center of the Milky Way hosts a massive black hole. The observational
evidence for its existence is overwhelming. The compact radio source Sgr A* has
been associated with a black hole since its discovery. In the last decade,
high-resolution, near-infrared measurements of individual stellar orbits in the
innermost region of the Galactic Center have shown that at the position of Sgr
A* a highly concentrated mass of 4 x 10^6 M_sun is located. Assuming that
general relativity is correct, the conclusion that Sgr A* is a massive black
hole is inevitable. Without doubt this is the most important application of
stellar orbits in the Galactic Center. Here, we discuss the possibilities going
beyond the mass measurement offered by monitoring these orbits. They are an
extremely useful tool for many scientific questions, such as a geometric
distance estimate to the Galactic Center or the puzzle, how these stars reached
their current orbits. Future improvements in the instrumentation will open up
the route to testing relativistic effects in the gravitational potential of the
black hole, allowing to take full advantage of this unique laboratory for
celestial mechanics.Comment: Proceedings of the Galactic Center Workshop 2009, Shangha
