  During the next closest approach of the orbiting star S2/S0-2 to the Galactic
supermassive black hole (SMBH), it is estimated that RV uncertainties of ~ 10
km/s allow us to detect post-Newtonian effects throughout 2018. To evaluate an
achievable uncertainty in RV and its stability, we have carried out
near-infrared, high resolution (R ~ 20,000) spectroscopic monitoring
observations of S2 using the Subaru telescope and the near-infrared
spectrograph IRCS from 2014 to 2016. The Br-gamma absorption lines are used to
determine the RVs of S2. The RVs we obtained are 497 km/s, 877 km/s, and 1108
km/s in 2014, 2015, and 2016, respectively. The statistical uncertainties are
derived using the jackknife analysis. The wavelength calibrations in our
three-year monitoring are stable: short-term (hours to days) uncertainties in
RVs are < 0.5 km/s, and a long-term (three years) uncertainty is 1.2 km/s. The
uncertainties from different smoothing parameter, and from the partial
exclusion of the spectra, are found to be a few km/s. The final results using
the Br-gamma line are 497 +- 17 (stat.) +- 3 (sys.) km/s in 2014, 877 +- 15
(stat.) +- 4 (sys.) km/s in 2015, and 1108 +- 12 (stat.) +- 4 (sys.) km/s in
2016. When we use two He I lines at 2.113\mum in addition to Br-gamma, the mean
RVs are 513 km/s and 1114 km/s for 2014 and 2016, respectively. The standard
errors of the mean are 16.2 km/s (2014) and 5.4 km/s (2016), confirming the
reliability of our measurements. The difference between the RVs estimated by
Newtonian mechanics and general relativity will reach about 200 km/s near the
next pericenter passage in 2018. Therefore our RV uncertainties of 13 - 17 km/s
with Subaru enable us to detect the general relativistic effects in the RV
measurements with more than 10 sigma in 2018.
