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Problem%20Set%206%20Solution - Problem Set 6 Solutions...

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- 1 - Problem Set 6 Solutions Astronomy 202 Assigned: 17 April 2006 Due: 01 May 2006 Chapter 26 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 universe. Hubble's law is a relationship between velocity of recession of objects in the universe and their distance, v = H o d. Since we know that velocity is distance divided by time, the Hubble constant, H o , 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 traveled. 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 th magnitude could detect a galaxy as bright as the Milky Way (absolute magnitude -20)?
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- 2 - Use the distance modulus: m – M = 5 log(d/10). 20 - (-20) = 5log(d/10), d = 10 9 pc. 6. According to the Big Bang theory described in this chapter,
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Problem%20Set%206%20Solution - Problem Set 6 Solutions...

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