Influence of bulk mass distribution on orbital precession of S2 star in Yukawa gravity

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.