Astronomy
1st Edition
ISBN: 9781938168284
Author: Andrew Fraknoi; David Morrison; Sidney C. Wolff
Publisher: OpenStax
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Textbook Question
Chapter 4, Problem 44E
If Sirius rises at 8:00 p.m. tonight, at what time will it rise tomorrow night, to the nearest minute? Explain.
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ROTATIONAL DYNAMICS
Question 01
A solid circular cylinder and a solid spherical ball of the same mass and radius are rolling
together down the same inclined. Calculate the ratio of their kinetic energy. Assume pure
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
acceleration
Question 03
i)
Define the angular velocity of a rotating body and give its SI unit
A car wheel has its angular velocity changing from 2rads to 30 rads
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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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