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One of the directly measured quantities which are used in monitoring theorbital motions of many of the S stars revolving around the Supermassive BlackHole (SMBH) in the Galactic Center (GC) is their radial velocity (RV) $V$obtained with near-infrared spectroscopy. Here, we devise a general approach tocalculate both the instantaneous variations $\Delta V\left(t\right)$ and thenet shifts per revolution $\left\langle\Delta V\right\rangle$ induced on suchan observable by some post-Keplerian (pK) accelerations. In particular, we lookat the general relativistic Schwarzschild (gravitoelectric) and Lense-Thirring(gravitomagnetic frame-dragging) effects, and the mass quadrupole. It turns outthat we may be on the verge of measuring the Schwarzschild-type 1pN staticcomponent of the SMBH's field with the S2 star for which RV measurementsaccurate to about $\simeq 30-50~\textrm{km s}^{-1}$ dating back to $t_0 =2003.271$ are currently available, and whose orbital period amounts to$P_\textrm{b} = 16$ yr. Indeed, while its expected general relativistic RV netshift per orbit amounts to just $\left\langle\Delta V^\textrm{GE}\right\rangle= -11.6~\textrm{km s}^{-1}$, it should reach a peak value as large as $\DeltaV_\textrm{max}^\textrm{GE}\left(t_\textrm{max}\right) = 551~\textrm{km s}^{-1}$at $t_\textrm{max} = 2018.35$. The periastron shift $\Delta\omega^\textrm{GE}$of S2 over the same time span will not be larger than $0.2$ deg, while thecurrent accuracy in estimating such an orbital element for this star is of theorder of $0.6$ deg. The frame-dragging and quadrupole-induced RV shifts are farsmaller for S2, amounting to, at most, $0.19~\textrm{kms}^{-1},0.0039~\textrm{km s}^{-1}$, respectively. Further studies should bededicated to the impact on the RV of possible diffused mass distribution in theGC and of other individual stars inside and outside the orbit of S2.

Post-Keplerian effects on radial velocity in binary systems and the possibility of measuring General Relativity with the S2 star in 2018