Stars very close to the massive black hole (MBH) in the center of the Galaxy allow us to probe post-Newtonian (PN) physics in a yet unexplored regime of celestial mechanics. Recent advances in infrared spectroscopy enable us to take precise measurements of stellar redshift curves and thereby detect O(β~2) PN effects (gravitational redshift in the MBH's potential and the transverse Doppler shift). We use simulations to show that these effects can be decisively detected with existing instruments after ～10 years of observations. We find that neglecting these effects leads to statistically significant systematic errors in the derived MBH mass and distance.
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