Constraints on alternative theories of gravity with observations of the
  Galactic Center
  To evaluate a potential usually one analyzes trajectories of test particles.
For the Galactic Center case astronomers use bright stars or photons, so there
are two basic observational techniques to investigate a gravitational
potential, namely, (a) monitoring the orbits of bright stars near the Galactic
Center as it is going on with 10m Keck twin and four 8m VLT telescopes equipped
with adaptive optics facilities (in addition, recently the IR interferometer
GRAVITY started to operate with VLT); (b) measuring the size and shape of
shadows around black hole with VLBI-technique using telescopes operating in
mm-band. At the moment, one can use a small relativistic correction approach
for stellar orbit analysis, however, in the future the approximation will not
be precise enough due to enormous progress of observational facilities and
recently the GRAVITY team found that the first post-Newtonian correction has to
be taken into account for the gravitational redshift in the S2 star orbit case.
Meanwhile for smallest structure analysis in VLBI observations one really needs
a strong gravitational field approximation. We discuss results of observations
and their interpretations.
