  Here we investigate possible applications of observed stellar orbits around
Galactic Center for constraining the R$^n$ gravity at Galactic scales. For that
purpose, we simulated orbits of S2-like stars around the massive black hole at
Galactic Center, and study the constraints on the R$^n$ gravity which could be
obtained by the present and next generations of large telescopes. Our results
show that R$^n$ gravity affects the simulated orbits in the qualitatively
similar way as a bulk distribution of matter (including a stellar cluster and
dark matter distributions) in Newton's gravity. In the cases where the density
of extended mass is higher, the maximum allowed value of parameter $\beta$ in
R$^n$ gravity is noticeably smaller, due to the fact that the both extended
mass and $R^n$ gravity cause the retrograde orbital precession.
