# Hubble's Law

• The dominant motion in the universe is the smooth expansion known as Hubble's Law.

Recessional Velocity = Hubble's constant times distance

V = Ho D

where

V is the observed velocity of the galaxy away from us, usually in km/sec

H is Hubble's "constant", in km/sec/Mpc

D is the distance to the galaxy in Mpc

In 1929, Hubble estimated the value of the expansion factor, now called the Hubble constant, to be about 500 km/sec/Mpc. Today the value is still rather uncertain, but is generally believed to be in the range of 45-90 km/sec/Mpc.

While in general galaxies follow the smooth expansion, the more distant ones moving faster away from us, other motions cause slight deviations from the line predicted by Hubble's Law. This diagram shows a typical plot of distance versus recessional velocity, with each point showing the relationship for an individual galaxy. In the example shown here, two things should be apparent:

 Few of the points fall exactly on the line. This is because all galaxies have some additional residual motion in addition to the pure expansion. This is referred to as the "cosmic velocity dispersion" or "cosmic scatter" and is probably due to the fact that the gas clouds that formed the galaxies all had some small additional motion of their own. The recessional velocity of a galaxy at a particular distance inferred from Hubble's law is called the "Hubble velocity".
• About in the middle of the diagram, there are a bunch of galaxies that appear to be at about the same distance but are spread out a lot in the velocity direction. This feature suggests the presence of a large cluster of galaxies, like the Virgo cluster. In addition to their "Hubble velocities", these galaxies have an extra velocity caused by their orbital motion around the center of the cluster. Because clusters of galaxies are very massive, this orbital velocity can be very large, more than 1000 km/s. Therefore in the vicinity of nearby clusters of galaxies, we cannot use Hubble's law to determine accurately the distance to the galaxy.