WebAssign for Seeds' The Solar System
10th Edition
ISBN: 9780357724729
Author: Seeds
Publisher: Cengage Learning US
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Textbook Question
Chapter 1, Problem 6P
Venus orbits 0.72 AU from the Sun. What is that distance in kilometers? (Hint: See Problem 3.)
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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
seconds. If the radius of the wheel is 400mm. calculate
ii)
The angular acceleration
iii)
The tangential linear acceleration of a point on the rim of the wheel
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 1 Solutions
WebAssign for Seeds' The Solar System
Ch. 1 - Prob. 1RQCh. 1 - What is the largest dimension of which you have...Ch. 1 - What is the difference between the Solar System,...Ch. 1 - What is the difference between the Moon and a...Ch. 1 - Prob. 5RQCh. 1 - Why are light-years more convenient than miles,...Ch. 1 - Why is it difficult to detect planets orbiting...Ch. 1 - Prob. 8RQCh. 1 - What is the difference between the Milky Way and...Ch. 1 - What are the Milky Way Galaxys spiral arms?
Ch. 1 - Prob. 11RQCh. 1 - Where are you in the Universe? If you had to give...Ch. 1 - Prob. 13RQCh. 1 - Prob. 14RQCh. 1 - Prob. 15RQCh. 1 - How do we know? How does the scientific method...Ch. 1 - The equatorial diameter of Earth is 7928 miles. If...Ch. 1 - Prob. 2PCh. 1 - One astronomical unit (AU) is about 1.5 108 km....Ch. 1 - A typical galaxy is shown on the first page of the...Ch. 1 - Prob. 5PCh. 1 - Venus orbits 0.72 AU from the Sun. What is that...Ch. 1 - Light from the Sun takes 8 minutes to reach Earth....Ch. 1 - The Sun is almost 400 times farther from Earth...Ch. 1 - If the speed of light is 3.0 × 105 km/s, how many...Ch. 1 - Prob. 10PCh. 1 - Prob. 11PCh. 1 - Prob. 12PCh. 1 - How many galaxies like our own would it take if...Ch. 1 - Arrange the following in order of increasing size:...Ch. 1 - Arrange the following in order of increasing...Ch. 1 - Prob. 3SPCh. 1 - Prob. 4SPCh. 1 - Look at the center of Figure 1–4. Approximately...Ch. 1 - Look at Figure 1-6. How can you tell that Mercury...Ch. 1 - Prob. 3LLCh. 1 - Look at Figure 1-9. Would you say that the...Ch. 1 - Prob. 5LLCh. 1 - Prob. 6LL
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