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Problem Set 6 Solutions
17 April 2006
01 May 2006
Review and Discussion:
2, 3, 4, 8, 13
2. What is the cosmological principle?
The cosmological principle is made up of two assumptions fundamental to cosmology. They are
homogeneity and isotropy. At a large enough scale, the universe is homogeneous; one part is pretty much
like any other part. Isotropy means that it looks the same in all directions. The cosmological principle tells
us there can be no edge to the universe and there is no center to it either.
3. What is Olbers’s paradox? How is it resolved?
According to the cosmological principle, the universe is homogeneous and isotropic. If it is also infinite
in extent and unchanging in time, then the universe is uniformly populated with galaxies filled with stars.
In that case, when you look at the night sky, your line of sight must eventually encounter a star; the sky
should appear as bright as the surface of the Sun. This was first proposed by Olber and is known as
Olber's paradox. Since this is not what is observed, however, something must be different than what was
assumed. The universe is, in fact, not infinite and it is also expanding.
The best current explanation is the
finite age of the universe
light from objects lying beyond 15 billion ly have not had time to reach us yet.
4. Explain how an accurate measure of Hubble’s constant can lead to an estimate of the age of the
Hubble's law is a relationship between velocity of recession of objects in the universe and their distance, v
d. Since we know that velocity is distance divided by time, the Hubble constant, H
, is a measure of
one divided by time, the time of the expansion of the universe to its present size. It turns out that this time
gives a maximum age for the universe.
8. How does the cosmological redshift relate to the expansion of the universe?
A wave of electromagnetic radiation, as it moves through the universe, will experience the same
expansion of the space experienced by the universe. As the wave travels farther and farther, it expands
more and more. By the time it is observed, it appears redshifted in proportion to the distance it has
13. What do observations of distant supernovae tell us about the expansion of the universe?
The observations of distant supernovae indicate motions that are slower than expected. This suggests that
the universe is actually accelerating.
Problems: 1, 6, 7, 8, 9, 13
1. What is the greatest distance at which a galaxy survey sensitive to objects as faint as 20
could detect a galaxy as bright as the Milky Way (absolute magnitude -20)?