Testing General Relativity with stellar orbits around the supermassive
  black hole in our Galactic center
  In this Letter, we demonstrate that short-period stars orbiting around the
supermassive black hole in our Galactic Center can successfully be used to
probe the gravitational theory in a strong regime. We use 19 years of
observations of the two best measured short-period stars orbiting our Galactic
Center to constrain a hypothetical fifth force that arises in various scenarios
motivated by the development of a unification theory or in some models of dark
matter and dark energy. No deviation from General Relativity is reported and
the fifth force strength is restricted to an upper 95% confidence limit of
$\left|\alpha\right| < 0.016$ at a length scale of $\lambda=$ 150 astronomical
units. We also derive a 95% confidence upper limit on a linear drift of the
argument of periastron of the short-period star S0-2 of $\left|\dot
\omega_\textrm{S0-2} \right|< 1.6 \times 10^{-3}$ rad/yr, which can be used to
constrain various gravitational and astrophysical theories. This analysis
provides the first fully self-consistent test of the gravitational theory using
orbital dynamic in a strong gravitational regime, that of a supermassive black
hole. A sensitivity analysis for future measurements is also presented.
