Astronomy
1st Edition
ISBN: 9781938168284
Author: Andrew Fraknoi; David Morrison; Sidney C. Wolff
Publisher: OpenStax
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Textbook Question
Chapter 29, Problem 4E
Which formed first: hydrogen nuclei or hydrogen atoms? Explain the sequence of events that led to each.
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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
b) What angle of inclination of the plane is needed to give the slower body the same
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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 29 Solutions
Astronomy
Ch. 29 - What are the basic observations about the universe...Ch. 29 - Describe some possible futures for the universe...Ch. 29 - What does the term Hubble time mean in cosmology,...Ch. 29 - Which formed first: hydrogen nuclei or hydrogen...Ch. 29 - Describe at least two characteristics of the...Ch. 29 - Describe two properties of the universe that are...Ch. 29 - Why do astronomers believe there must be dark...Ch. 29 - What is dark energy and what evidence do...Ch. 29 - Thinking about the ideas of space and time in...Ch. 29 - Astronomers have found that there is more helium...
Ch. 29 - Describe the anthropic principle. What are some...Ch. 29 - Describe the evidence that the expansion of the...Ch. 29 - What is the most useful probe of the early...Ch. 29 - What are the advantages and disadvantages of using...Ch. 29 - Would acceleration of the universe occur if it...Ch. 29 - Suppose the universe expands forever. Describe...Ch. 29 - Some theorists expected that observations would...Ch. 29 - There are a variety of ways of estimating the ages...Ch. 29 - Since the time of Copernicus, each revolution in...Ch. 29 - The anthropic principle suggests that in some...Ch. 29 - Penzias and Wilson’s discovery of the Cosmic...Ch. 29 - Construct a timeline for the universe and indicate...Ch. 29 - Suppose the Hubble constant were not 22 but 33...Ch. 29 - Assume that the average galaxy contains...Ch. 29 - The CMB contains roughly 400 million photons per...Ch. 29 - Following up on Exercise 29.27 calculate the...Ch. 29 - Continuing the thinking in Exercise 29.27 and...Ch. 29 - Continuing the thinking in the last three...Ch. 29 - There is still some uncertainty in the Hubble...Ch. 29 - It is possible to derive the age of the universe...
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