PPN Motion of S-Stars Around Sgr A*

The equations of motion for the parametrized post-Newtonian (PPN) formalism for several S-stars close to the relativistic compact object Sgr A* at the center of the galaxy are examined. The effect of the difference in the periods of Newtonian and post-Newtonian orbits is taken into account. The period of the best approximation to the PN-orbit of the star S2 exceeds the period of the Newtonian orbit by 16 days. The PPN parameters βPPN and γPPN are measured. Bayesian methods are used for fitting the trajectories of the PPN motion. Posterior estimates of βPPN and γPPN $$ {0.97}_{-0.65}^{+0.42} $$ and $$ {0.81}_{-0.60}^{+0.46} $$ are obtained, respectively. This result confirms the prediction of the general theory of relativity for the post-Newtonian equations of motion under conditions close to Sgr A*.