Hubble's law
Hubble's law is the statement in astronomy that galaxies move away from each other, and that the velocity with which they recede is proportional to their distance. It leads to the picture of an expanding universe and, by extrapolating back in time, to the Big Bang theory.
The law was first formulated by Edwin Hubble in 1929. Hubble compared the distances to nearby galaxies to their redshift, found a linear relationship, and interpreted the redshift as caused by the receding velocity. His estimate of the proportionality constant, now known as Hubble's constant, was however off by a factor of about 10. Furthermore, if one takes Hubble's original observations and then use the most accurate distances and and velocities currently known, one ends up with a random scatter plot with no discernable relationship between redshift and velocity. Nevertheless the relationship appears to be confirm by observations after Hubble.
The law can be stated as follows:
- v = H0 D
where v is the receding velocity of a galaxy due to the expansion of the universe (typically measured in km/sec), H0 is Hubble's constant, and D is the distance to the galaxy (measured in mega parsec Mpc).
The current value of H0 is estimated to be between 50 and 90 km/sec/Mpc. The value of the Hubble constant was the topic of a long and rather bitter controversy between Gerard d'Vaculeours who claimed the value was 50 and Alan Sandage who claimed the value was 100.
One can derive Hubble's law mathematically if one assumes that the universe expands (or shrinks) and that the universe is homogeneous, meaning that all points within it are equal.
There are several notes to be made:
- Hubble's constant is "constant" in the sense that it is believed to work for all velocities and distances right now. The value of H decreases over time however. Gravitational effects tend to slow down the expansion, while other effects such as the cosmological constant tend to accelerate it. Based on recent observations, it is now believed that galaxies are accelerating away from us. Note that this is consistent with a decreasing value of H.
- The distance D to nearby galaxies can be estimated for example by comparing their apparent luminosity to their postulated absolute luminosity. If the galaxies are far away, one has to take as D the distance to the galaxy right now, not when the light from it was emitted. This distance is extremely hard to determine.
- The velocity v is defined to be the time rate of change of D. For relative nearby galaxies, the velocity v can be determined from the galaxy's redshift z using the formula v ≈ zc where c is the speed of light. However, only the velocity due to the expansion of the universe should be used: all galaxies move relative to each other independent of the expansion of the universe, and these relative velocities, called peculiar velocities are not accounted for by Hubble's law. For far away galaxies, v is larger than c.
- Systems that are gravitationally bound, such as galaxies or our planetary system, are not subject to Hubble's law and do not expand.