Velocity Definition

There are two velocity definitions in use in radio astronomy. The ``radio'' definition, used in Galactic radio astronomy:

$$V^{r} = \frac{\nu_{0} - \nu}{\nu_{0}} \; c$$ (3.1)

and the ``optical'' definition, used throughout extragalactic astronomy:

$$V^{o} = \frac{\nu_{0} - \nu}{\nu} \; c \; = \frac{\lambda - \lambda_{0}}{\lambda_{0}} \; c \; = zc$$ (3.2)

where $z$ is the redshift. Neither optical, nor radio velocities represent physical quantities; they are merely approximations of the full relativistic expressions for velocities $\leq$ 1000 km s$^{-1}$.