On a Source of Systematic Error in Absolute Measurement of Galactocentric Distance from Solving for the Stellar Orbit Around Sgr A*

Eisenhauer et al. (2003, 2005) derived absolute (geometrical) estimates of the distanceto the center of the Galaxy, $R_0$, from the star S2 orbit around Sgr A* on the assumption that the intrinsic velocity of Sgr A* is negligible. This assumption produces the source of systematic error in $R_0$ value owing to a probable motion of Sgr A* relative to the accepted velocity reference system which is arbitrary to some extent. Eisenhauer et al. justify neglecting all three spatial velocity components of Sgr A* mainly by low limits of Sgr A*'s proper motion of 20--60 km/s. In this brief paper, a simple analysis in the context of the Keplerian dynamics was used to demonstrate that neglect of even low (perhaps, formal) radial velocity of Sgr A* leads to a substantial systematic error in $R_0$: the same limits of 20--60 km/s result in $R_0$ errors of 1.3--5.6%, i.e., (0.1--0.45)$\times (R_0/8)$ kpc, for current S2 velocities. Similar values for Sgr A*'s tangential motion can multiply this systematic error in the case of S2 orbit by factor ${\approx}1.5$--1.9 in the limiting cases.