We analytically work out the cumulative , i.e . averaged over one orbital revolution , time variations \left \langle \dot { v } _ { \rho } \right \rangle of the radial velocity v _ { \rho } of a typical S star orbiting the Supermassive ( M _ { \bullet } \approx 10 ^ { 6 } M _ { \odot } ) Black Hole ( SBH ) hosted by the Galactic Center ( GC ) in Sgr A ^ { \ast } caused by several dynamical effects . They are the general relativistic gravitoelectromagnetic ( GEM ) fields of the SBH , its quadrupole mass moment Q _ { 2 } , and a diffuse dark matter distribution around the SBH . All of them induce non-zero long-term radial accelerations proportional to the eccentricity e of the orbit . By taking the S2 star , orbiting the SBH along a highly eccentric ( e = 0.8831 ) ellipse with a period P _ { b } = 15.9 yr and semi-major axis a = 1031.69 au , we numerically compute the magnitudes of its radial accelerations . The largest effects are due to the general relativistic Schwarzschild-like gravitoelectric ( GE ) field , with \left \langle \dot { v } _ { \rho } ^ { ( GE ) } \right \rangle = 8.2 \times 10 ^ { -5 } { m s% } ^ { -2 } , and the diffuse material distribution , modeled with a Plummer-type mass density profile , with \left \langle \dot { v } _ { \rho } ^ { ( dm ) } \right \rangle = 3.8 \times 10 ^ { -6 } { m s% } ^ { -2 } . The effects caused by the general relativistic Kerr-type gravitomagnetic ( GM ) field and by Q _ { 2 } are smaller by orders of magnitude . By assuming an uncertainty in measuring the radial velocities of about 15 km s ^ { -1 } , the future accuracy in measuring \left \langle \dot { v } _ { \rho } \right \rangle can be evaluated to be of the order of 2.4 \times 10 ^ { -5 } m s ^ { -2 } over an observational time span \Delta t = 20 yr . Currently , the available radial velocity measurements cover just 7 yr .