Astronomy
1st Edition
ISBN: 9781938168284
Author: Andrew Fraknoi; David Morrison; Sidney C. Wolff
Publisher: OpenStax
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Textbook Question
Chapter 4, Problem 29E
The secret recipe to the ever-popular veggie burgers in the college cafeteria is hidden in a drawer in the director’s office. Two students decide to break in to get their hands on it, but they want to do it a few hours before dawn on a night when there is no Moon, so they are less likely to be caught. What phases of the Moon would suit their plans?
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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
Astronomy
Ch. 4 - Discuss how latitude and longitude on Earth are...Ch. 4 - What is the latitude of the North Pole? The South...Ch. 4 - Make a list of each main phase of the Moon,...Ch. 4 - What are advantages and disadvantages of apparent...Ch. 4 - What are the two ways that the tilt of Earth’s...Ch. 4 - Why is it difficult to construct a practical...Ch. 4 - Explain why there are two high tides and two low...Ch. 4 - What is the phase of the Moon during a total solar...Ch. 4 - On a globe or world map, find the nearest marked...Ch. 4 - Explain three lines of evidence that indicate that...
Ch. 4 - What is the origin of the terms “a.m.” and “p.m.”...Ch. 4 - Explain the origin of the leap year. Why is it...Ch. 4 - Explain why the year 1800 was not a leap year,...Ch. 4 - What fraction of the Moon’s visible face is...Ch. 4 - Why don’t lunar eclipses happen during every full...Ch. 4 - Why does the Moon create tidal bulges on both...Ch. 4 - Why do the heights of the tides change over the...Ch. 4 - Explain how tidal forces are causing Earth to slow...Ch. 4 - Explain how tidal forces are causing the Moon to...Ch. 4 - Explain why the Gregorian calendar modified the...Ch. 4 - The term equinox translates as “equal night.”...Ch. 4 - The term solstice translates as “Sun stop.”...Ch. 4 - Why is the warmest day of the year in the United...Ch. 4 - When Earth’s Northern Hemisphere is tilted toward...Ch. 4 - Where are you on Earth if you experience each of...Ch. 4 - In countries at far northern latitudes, the winter...Ch. 4 - What is the phase of the Moon if it . . . A. rises...Ch. 4 - A car accident occurs around midnight on the night...Ch. 4 - The secret recipe to the ever-popular veggie...Ch. 4 - Your great-great-grandfather, who often...Ch. 4 - One year in the future, when money is no object,...Ch. 4 - Suppose you lived in the crater Copernicus on the...Ch. 4 - In a lunar eclipse, does the Moon enter the shadow...Ch. 4 - Describe what an observer at the crater Copernicus...Ch. 4 - The day on Mars is 1.026 Earth-days long. The...Ch. 4 - What is the right ascension and declination of the...Ch. 4 - What is the right ascension and declination of the...Ch. 4 - What is the right ascension and declination of the...Ch. 4 - During summer in the Northern Hemisphere, the...Ch. 4 - On the day of the vernal equinox, the day length...Ch. 4 - Regions north of the Arctic Circle are known as...Ch. 4 - In a part of Earth’s orbit where Earth is moving...Ch. 4 - In a part of Earth’s orbit where Earth is moving...Ch. 4 - If Sirius rises at 8:00 p.m. tonight, at what time...Ch. 4 - What are three lines of evidence you could use to...Ch. 4 - If the Moon rises at a given location at 6:00 p.m....Ch. 4 - Explain why some solar eclipses are total and some...Ch. 4 - Why do lunar eclipses typically last much longer...Ch. 4 - Suppose Earth took exactly 300.0 days to go around...Ch. 4 - Consider a calendar based entirely on the day and...Ch. 4 - If a star rises at 8:30 p.m. tonight,...Ch. 4 - What is the altitude of the Sun at noon on...Ch. 4 - Show that the Gregorian calendar will be in error...
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