HORIZONS (LL) W/WEBASSIGN ACCESS CARD
14th Edition
ISBN: 9780357537565
Author: Seeds
Publisher: CENGAGE L
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Textbook Question
Chapter 15, Problem 8RQ
Why is almost every solid surface in our Solar System scarred by craters?
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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]
Page 2
SECTION A
Answer ALL questions in Section A
[Expect to use one single-sided A4 page for each Section-A sub question.]
Question A1
SPA6308 (2024)
Consider Minkowski spacetime in Cartesian coordinates th
=
(t, x, y, z), such that
ds² = dt² + dx² + dy² + dz².
(a) Consider the vector with components V" = (1,-1,0,0). Determine V and V. V.
(b) Consider now the coordinate system x' (u, v, y, z) such that
u =t-x,
v=t+x.
[2 marks]
Write down the line element, the metric, the Christoffel symbols and the Riemann curvature
tensor in the new coordinates. [See the Appendix of this document.]
[5 marks]
(c) Determine V", that is, write the object in question A1.a in the coordinate system x'. Verify
explicitly that V. V is invariant under the coordinate transformation.
Question A2
[5 marks]
Suppose that A, is a covector field, and consider the object
Fv=AAμ.
(a) Show explicitly that F is a tensor, that is, show that it transforms appropriately under a
coordinate transformation.
[5 marks]
(b)…
Chapter 15 Solutions
HORIZONS (LL) W/WEBASSIGN ACCESS CARD
Ch. 15 - What produced the helium now present in the Sun’s...Ch. 15 - What produced the iron and heavier elements like...Ch. 15 - What evidence can you cite that disks of gas and...Ch. 15 - According to the solar nebula theory, why is the...Ch. 15 - Why does the solar nebula theory predict that...Ch. 15 - Prob. 6RQCh. 15 - If you visited another planetary system, would you...Ch. 15 - Why is almost every solid surface in our Solar...Ch. 15 - What is the difference between condensation and...Ch. 15 - Why don’t Terrestrial planets have rings like the...
Ch. 15 - How does the solar nebula theory help you...Ch. 15 - How does the solar nebula theory explain the...Ch. 15 - What does the term differentiated mean when...Ch. 15 - What processes cleared the nebula away and ended...Ch. 15 - Why would astronomically short lifetime of gas and...Ch. 15 - Prob. 16RQCh. 15 - What evidence can you cite that planets orbit...Ch. 15 - Why is the existence of “hot Jupiters” puzzling?...Ch. 15 - How Do We know? The evidence is overwhelming in...Ch. 15 - How Do We know? How can scientists know anything...Ch. 15 - If you could visit another planetary system while...Ch. 15 - Prob. 2DQCh. 15 - If the solar nebula hypothesis is correct, do you...Ch. 15 - If you observed the Solar System from the nearest...Ch. 15 - Prob. 2PCh. 15 - Prob. 3PCh. 15 - Prob. 4PCh. 15 - Prob. 5PCh. 15 - Prob. 6PCh. 15 - Suppose that Earth grew to its present size in 1...Ch. 15 - Prob. 8PCh. 15 - Prob. 9PCh. 15 - Prob. 1LTLCh. 15 - Why do astronomers conclude that the surface of...Ch. 15 - Prob. 3LTL
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