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The aim of our investigation is to derive a particular theory among the class of scalar-tensor(ST) theories of gravity, and then to test it by studying kinematics and dynamics of S-stars around supermassive black hole (BH) at Galactic Center (GC). We also discuss the Newtonian limit of this class of ST theories of gravity, as well as its parameters. We compare the observed orbit of S2 star with our simulated orbit which we obtained theoretically with the derived ST potential and constrained the parameters. Using the obtained best fit parameters we calculated orbital precession of S2 star in ST gravity,and found that it has the same direction as in General Relativity (GR), but causes much larger pericenter shift.

Constraining scalar-tensor gravity models by S2 star orbits around the galactic center