Transverse velocity

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 vr and transverse vT components.

Aa star’s transverse velocity vT 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):

vT = 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:

vT = 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).

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