The second generation instrument of the VLTI, GRAVITY, is expected to reach an astrometric accuracy of about 10 μas. It will thus possible to probe the spacetime close to the compact source Sagittarius A* (Sgr A*) at the Galactic Center by using accurate astrometric observations of the second closest star to the Galactic Center, S2. In particular, we show that combining GRAVITY and spectrograph instruments will allow us to detect several relativistic effects such as pericenter advance or the Lense-Thirring effect.
