PPN motion of the S-stars around Sgr A*

Abstract

Parametrized Post-Newtonian (PPN) equations of motion for several S-stars nearest to the Galactic Center compact relativistic object SgrA* are considered. The effect of the orbital periods difference between Newtonian and Post-Newtonian cases is taken into account. The best fit PN orbit of S2 has a period which is 16 days longer than Newtonian one. The PPN parameters $\beta_\text{PPN}$ and $\gamma_\text{PPN}$ are measured. Bayesian sampling is used to fit the trajectories of the PPN laws of motion. Posterior estimates of $\beta_\text{PPN}$ and $\gamma_\text{PPN}$ are $0.97^{+0.42}_{-0.65}$ and $0.81^{+0.46}_{-0.60}$ respectively. The result confirms General Relativity prediction for the Post-Newtonian equations of motion in the conditions of orbital motions in vicinity of the SgrA*.