The component of a object’s velocity that is perpendicular to our line of sight.

The breakdown of a star’s velocity v into the radial v_r and transverse v_T components.

Aa star’s transverse velocity v_T can be determined if the distance D and proper motion μ are known. These are related by the following formula where the proper motion is in natural units (radians per unit time):

v_T = μD

A common problem when calculating the transverse velocity of a star occurs when people mix the units of proper motion, velocity and distance. When the distance D, to a star is in kiloparsecs and the proper motion μ, in milliarcseconds per year, the formula becomes:

v_T = 4.74 (μD) km/s

The constant of 4.74 arises from the combination of the conversions of distance (kpc to km), angle (from milliarcseconds to radians), and time (from years to seconds).