  In this study we investigate possible applications of observed S2 orbit
around Galactic Center for constraining the Yukawa gravity at scales in the
range between several tens and several thousands astronomical units (AU) to
obtain graviton mass constraints. In our model we suppose that bulk
distribution of matter (includes stellar cluster, interstellar gas distribution
and dark matter) exists near Supermassive Black Hole (SMBH) in our Galactic
Center. We obtain the values of orbital precession angle for different values
of mass density of matter and we require that the value of orbital precession
is the same like in General Relativity (GR). From that request we determine
gravity parameter $\lambda$ and the upper value for graviton mass. We found
that in the cases where the density of extended mass is higher, the maximum
allowed value for parameter $\lambda$ is smaller and the upper limit for
graviton mass is higher. It is due to the fact that the extended mass causes
the retrograde orbital precession. We believe that this study is a very
efficient tool to evaluate a gravitational potential at the Galactic Center,
parameter $\lambda$ of the Yukawa gravity model, and to constrain the graviton
mass.
