Cosmology and the Universe: The Big Bang, Dark Matter and Dark Energy 261
with time. The observation of a number of Cepheid variables in the
Large Magellanic Cloud, a nearby galaxy, revealed a relation between
the absolute luminosity of this type of star and the period of the variation
of its luminosity. The observed luminosity of a star is equal to its
absolute luminosity divided by the square of the distance from the
observer. By calibrating the Cepheid variables in our own galaxy whose
distance could be determined, the distance to galaxies containing
Cepheid variables could be determined using the relation between
absolute and observed luminosities.
For those galaxies without a Cepheid variable another technique for
determining distances was developed. By observing many galaxies
whose distances are known one is able to determine the absolute
magnitude of the brightest star of each of these galaxies. The brightness
of these stars, the brightest of their galaxies, is more or less the same.
One can, therefore, estimate the distance to a galaxy with no Cepheid
variable by determining the observed brightness of the galaxy’s brightest
stars and assuming its absolute brightness is the same as that of the other
brightest stars. This same type of comparison is also used to estimate the
distance to a cluster of galaxies. In this case one measures the luminosity
of the brightest galaxy of the cluster and assumes the absolute luminosity
is the same as that of the brightest galaxies of other clusters whose
distances are known.
Hubble discovered that for distances greater than 30 million light
years that the recessional velocity of a cluster of galaxies is proportional
to its distance from us. He found that the velocity of the cluster increases
30 kilometers per second for every million light years away the cluster is
found. A cluster 100 million light years away, for example, will have a
velocity equal to 30 kilometers per second times 100 which is 3000
kilometers per second or 1/100 the velocity of light. Most clusters are
observable up to distances of 3 billion light years after which they
become too faint to be observed. Their velocities at these distances is
approximately 90,000 kilometers per second or 3/10 the velocity of light.
There is a special class of galaxies known as exploding galaxies which
are much brighter than normal galaxies and hence, can be seen further
away. These galaxies have been observed as far away as 6 billion light
years with receding velocities as high as 6/10 the velocity of light. At
first the universe was thought to be expanding at a constant rate but
recent observations seem to indicate that the rate of expansion is
increasing or accelerating.