Recessional velocity

Hubble's law is the relationship between a galaxy's distance and its recessional velocity, which is approximately linear for galaxies at distances of up to a few hundred megaparsecs. It can be expressed as

${\displaystyle v_{r}=H_{0}D\ +v_{pec}}$

where ${\displaystyle H_{0}}$ is the Hubble constant, ${\displaystyle D}$ is the proper distance, ${\displaystyle v_{r}}$ is the object's recessional velocity, and ${\displaystyle v_{pec}}$ is the object's peculiar velocity.

The recessional velocity of a galaxy can be calculated from the redshift observed in its emitted spectrum. One application of Hubble's law is to estimate distances to galaxies based on measurements of their recessional velocities. However, for relatively nearby galaxies the peculiar velocity can be comparable to or larger than the recessional velocity, in which case Hubble's Law does not give a good estimate of an object's distance based on its redshift. In some cases (such as the Andromeda Galaxy, 2.5 million light-years away and approaching us at 300 km/s, or even Messier 81 at 12 million light-years away and approaching at 34 km/s) ${\displaystyle v_{r}}$ is negative (i.e., the galaxy's spectrum is observed to be blueshifted) as a result of the peculiar velocity.