Astronomy
1st Edition
ISBN: 9781938168284
Author: Andrew Fraknoi; David Morrison; Sidney C. Wolff
Publisher: OpenStax
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Textbook Question
Chapter 9, Problem 15E
What is the main consequence of Mercury’s orbit being so highly eccentric?
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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)
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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 9 Solutions
Astronomy
Ch. 9 - What is the composition of the Moon, and how does...Ch. 9 - Why does the Moon not have an atmosphere?Ch. 9 - What are the principal features of the Moon...Ch. 9 - Frozen water exists on the lunar surface primarily...Ch. 9 - Outline the main events in the Moon’s geological...Ch. 9 - What are the maria composed of? Is this material...Ch. 9 - The mountains on the Moon were formed by what...Ch. 9 - With no wind or water erosion of rocks, what is...Ch. 9 - What differences did Grove K. Gilbert note between...Ch. 9 - Explain how high-speed impacts form circular...
Ch. 9 - Explain the evidence for a period of heavy...Ch. 9 - How did our exploration of the Moon differ from...Ch. 9 - Summarize the four main hypotheses for the origin...Ch. 9 - What are the difficulties with the capture...Ch. 9 - What is the main consequence of Mercury’s orbit...Ch. 9 - Describe the basic internal structure of Mercury.Ch. 9 - How was the rotation rate of Mercury determined?Ch. 9 - What is the relationship between Mercury’s...Ch. 9 - The features of Mercury are named in honor of...Ch. 9 - What do our current ideas about the origins of the...Ch. 9 - One of the primary scientific objectives of the...Ch. 9 - Apollo astronaut David Scott dropped a hammer and...Ch. 9 - Galileo thought the lunar maria might be seas of...Ch. 9 - Why did it take so long for geologists to...Ch. 9 - How might a crater made by the impact of a comet...Ch. 9 - Why are the lunar mountains smoothly rounded...Ch. 9 - The lunar highlands have about ten times more...Ch. 9 - At the end of the section on the lunar surface,...Ch. 9 - Give several reasons Mercury would be a...Ch. 9 - If, in the remote future, we establish a base on...Ch. 9 - The Moon has too little iron, Mercury too much....Ch. 9 - In the future, astronomers discover a solid moon...Ch. 9 - The Moon was once closer to Earth than it is now....Ch. 9 - Astronomers believe that the deposit of lava in...Ch. 9 - The Moon requires about 1 month (0.08 year) to...
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