Performance of astrometric detection of a hotspot orbiting on the
  innermost stable circular orbit of the galactic centre black hole
  The galactic central black hole Sgr A* exhibits outbursts of radiation in the
near infrared (so-called IR flares). One model of these events consists in a
hotspot orbiting on the innermost stable circular orbit (ISCO) of the hole.
These outbursts can be used as a probe of the central gravitational potential.
One main scientific goal of the second generation VLTI instrument GRAVITY is to
observe these flares astrometrically. Here, the astrometric precision of
GRAVITY is investigated in imaging mode, which consists in analysing the image
computed from the interferometric data. The capability of the instrument to put
in light the motion of a hotspot orbiting on the ISCO of our central black hole
is then discussed.
  We find that GRAVITY's astrometric precision for a single star in imaging
mode is smaller than the Schwarzschild radius of Sgr A*. The instrument can
also demonstrate that a body orbiting on the last stable orbit of the black
hole is indeed moving. It yields a typical size of the orbit, if the source is
as bright as m_K=14.
  These results show that GRAVITY allows one to study the close environment of
Sgr A*. Having access to the ISCO of the central massive black hole probably
allows constraining general relativity in its strong regime. Moreover, if the
hotspot model is appropriate, the black hole spin can be constrained.
