Gravitational perturbations amongst closely separated galaxies impose velocities that are different to those expected simply from the general expansion of the universe. When we observe very distant galaxies however, the velocity due to the expansion of spacetime, is much greater than these locally induced motions.

The peculiar velocity of a galaxy is its velocity relative to the motion due to the isotropic expansion of the universe as described by the Hubble Flow. The total velocity of a galaxy is the sum of the velocity due to the Hubble flow and the local motion of the galaxy within its cluster or group environment due to local gravitational effects. The deviations from a pure Hubble flow is referred to as a peculiar velocity. In reality we only measure the radial component of each galaxy’s peculiar velocity.

Hence the total velocity of a galaxy is the sum of its velocity as described by Hubble’s Law and its peculiar velocity.

V_total = H_o x D + V_pec

where V_total is the total (radial) velocity, D is the distance, H_o is the Hubble constant, and V_pec is the peculiar velocity.