What inherent advantage in precision does the measurement technique for radial velocity ($V_r$) offer over tangential velocity ($V_t$) determination?

Radial velocity is derived from stable atomic transitions, often yielding accuracy to meters per second

The measurement of radial velocity ($V_r$) relies on analyzing the Doppler shift of specific absorption lines created by known elements like hydrogen or calcium. Because the laboratory wavelengths of these atomic transitions are extremely stable and well-known, the resulting velocity calculation is highly precise, often measured to within a few meters per second accuracy. Tangential velocity determination, conversely, depends on measuring proper motion ($ ext{μ}$), which is a tiny angular shift observed over many years or decades. Furthermore, converting this angle to a physical speed requires distance ($d$), which is frequently the dominant source of uncertainty unless the star is very near to Earth, making $V_r$ inherently more precise under ideal conditions.