What essential measurement, expressed in angular units like arcseconds per year ($ ext{arcsec}/ ext{year}$), is required to define tangential velocity ($V_t$)?

Proper motion ($ ext{μ}$)

Tangential velocity ($V_t$) describes the component of a star's motion that is perpendicular to our line of sight, causing its position to appear to drift across the celestial sphere over time. The measurement that quantifies this apparent angular drift is called proper motion ($ ext{μ}$). This quantity is typically recorded in angular units, such as arcseconds per year ($ ext{arcsec}/ ext{year}$). However, proper motion alone only provides an angle, not a physical speed. To convert this angular rate into a true physical speed in units like kilometers per second, the star's precise distance ($d$) from Earth must also be accurately known, as a distant object drifting by the same angle must be physically moving much faster than a closer object.