Constraints on $R^n$ gravity from precession of orbits of S2-like stars:   a case of a bulk distribution of mass
  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. 
Alexander F. Zakharov, Dusko Borka, Vesna Borka Jovanovi\'c and   Predrag Jovanovi\'c
astro-ph.GA astro-ph.CO gr-qc