Cosmic Perspective Fundamentals
3rd Edition
ISBN: 9780134988504
Author: Bennett, Jeffrey O., Donahue, M. (megan), SCHNEIDER, Nicholas, Voit, Mark
Publisher: Pearson,
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Textbook Question
Chapter 4, Problem 14SEQ
Explain all answers clearly, with complete sentences and proper essay structure, if needed. An asterisk (*) designates a quantitative problem, for which you should show all your work.
Patters of Motion. In one or two paragraphs, summarize the orderly patterns of motion in our system and explain why they suggest that the Sun and the planets all formed at one time from one cloud of gas, rather than as individual objects at different times.
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ROTATIONAL DYNAMICS
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A solid circular cylinder and a solid spherical ball of the same mass and radius are rolling
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rolling motion Question 02
A sphere and cylinder of the same mass and radius start from ret at the same point and more
down the same plane inclined at 30° to the horizontal
Which body gets the bottom first and what is its acceleration
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Question 03
i)
Define the angular velocity of a rotating body and give its SI unit
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Question 04
in 20
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 4 Solutions
Cosmic Perspective Fundamentals
Ch. 4 - Choose the best answer to each of the following....Ch. 4 - Choose the best answer to each of the following....Ch. 4 - Choose the best answer to each of the following....Ch. 4 - Choose the best answer to each of the following....Ch. 4 - Choose the best answer to each of the following....Ch. 4 - Choose the best answer to each of the following....Ch. 4 - Choose the best answer to each of the following....Ch. 4 - Choose the best answer to each of the following....Ch. 4 - Choose the best answer to each of the following....Ch. 4 - Choose the best answer to each of the following....
Ch. 4 - Choose the best answer to each of the following....Ch. 4 - Choose the best answer to each of the following....Ch. 4 - Explain all answers clearly, with complete...Ch. 4 - Explain all answers clearly, with complete...Ch. 4 - Explain all answers clearly, with complete...Ch. 4 - Explain all answers clearly, with complete...Ch. 4 - Explain all answers clearly, with complete...Ch. 4 - Explain all answers clearly, with complete...Ch. 4 - Explain all answers clearly, with complete...Ch. 4 - Explain all answers clearly, with complete...Ch. 4 - Explain all answers clearly, with complete...Ch. 4 - Explain all answers clearly, with complete...Ch. 4 - Explain all answers clearly, with complete...
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