Astronomy
1st Edition
ISBN: 9781938168284
Author: Andrew Fraknoi; David Morrison; Sidney C. Wolff
Publisher: OpenStax
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Textbook Question
Chapter 28, Problem 13E
If we see a double image of a quasar produced by a gravitational lens and can obtain a spectrum of the galaxy that is acting as the gravitational lens, we can then put limits on the distance to the quasar. Explain how.
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Question B3
Consider the following FLRW spacetime:
t2
ds² = -dt² +
(dx²
+ dy²+ dz²),
t2
where t is a constant.
a)
State whether this universe is spatially open, closed or flat.
[2 marks]
b) Determine the Hubble factor H(t), and represent it in a (roughly drawn) plot as a function
of time t, starting at t = 0.
[3 marks]
c) Taking galaxy A to be located at (x, y, z) = (0,0,0), determine the proper distance to galaxy
B located at (x, y, z) = (L, 0, 0). Determine the recessional velocity of galaxy B with respect
to galaxy A.
d) The Friedmann equations are
2
k
8πG
а
4πG
+
a²
(p+3p).
3
a
3
[5 marks]
Use these equations to determine the energy density p(t) and the pressure p(t) for the
FLRW spacetime specified at the top of the page.
[5 marks]
e) Given the result of question B3.d, state whether the FLRW universe in question is (i)
radiation-dominated, (ii) matter-dominated, (iii) cosmological-constant-dominated, or (iv)
none of the previous. Justify your answer.
f)
[5 marks]
A conformally…
SECTION B
Answer ONLY TWO questions in Section B
[Expect to use one single-sided A4 page for each Section-B sub question.]
Question B1
Consider the line element
where w is a constant.
ds²=-dt²+e2wt dx²,
a) Determine the components of the metric and of the inverse metric.
[2 marks]
b) Determine the Christoffel symbols. [See the Appendix of this document.]
[10 marks]
c)
Write down the geodesic equations.
[5 marks]
d) Show that e2wt it is a constant of geodesic motion.
[4 marks]
e)
Solve the geodesic equations for null geodesics.
[4 marks]
Chapter 28 Solutions
Astronomy
Ch. 28 - How are distant (young) galaxies different from...Ch. 28 - What is the evidence that star formation began...Ch. 28 - Describe the evolution of an elliptical galaxy....Ch. 28 - Explain what we mean when we call the universe...Ch. 28 - Describe the organization of galaxies into...Ch. 28 - What is the evidence that a large fraction of the...Ch. 28 - When astronomers make maps of the structure of the...Ch. 28 - How does the presence of an active galactic...Ch. 28 - Describe how you might use the color of a galaxy...Ch. 28 - Suppose a galaxy formed stars for a few million...
Ch. 28 - Given the ideas presented here about how galaxies...Ch. 28 - Can an elliptical galaxy evolve into a spiral?...Ch. 28 - If we see a double image of a quasar produced by a...Ch. 28 - The left panel of Figure 27.1 shows a cluster of...Ch. 28 - Suppose you are standing in the center of a large,...Ch. 28 - Astronomers have been making maps by observing a...Ch. 28 - Human civilization is about 10,000 years old as...Ch. 28 - Given that only about 5% of the galaxies visible...Ch. 28 - Using the information from Example 28.1, how much...Ch. 28 - Using the information from Example 28.1, if...Ch. 28 - Using the information from Example 28.1, how much...Ch. 28 - Galaxies are found in the “walls” of huge voids;...Ch. 28 - Calculate the velocity, the distance, and the...Ch. 28 - Assume that dark matter is uniformly distributed...Ch. 28 - The simulated box of galaxy filaments and...Ch. 28 - The first objects to collapse gravitationally...
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