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*.

中文翻译：

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Sgr A* 周围 S 星的 PPN 运动

考虑了最靠近银河中心致密相对论天体 SgrA* 的几个 S 星的参数化后牛顿 (PPN) 运动方程。考虑了牛顿和后牛顿情况之间的轨道周期差异的影响。S2 的最佳拟合 PN 轨道的周期比牛顿轨道长 16 天。测量了 PPN 参数 $\beta_\text{PPN}$ 和 $\gamma_\text{PPN}$。贝叶斯采样用于拟合 PPN 运动定律的轨迹。$\beta_\text{PPN}$ 和 $\gamma_\text{PPN}$ 的后验估计分别为 $0.97^{+0.42}_{-0.65}$ 和 $0.81^{+0.46}_{-0.60}$。结果证实了在 SgrA* 附近轨道运动条件下后牛顿运动方程的广义相对论预测。