Foundations of Astronomy (MindTap Course List)
14th Edition
ISBN: 9781337399920
Author: Michael A. Seeds, Dana Backman
Publisher: Cengage Learning
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Textbook Question
Chapter 22, Problem 5RQ
Describe a hypothesis explaining why Jupiter emits more energy than it receives from the Sun.
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Students have asked these similar questions
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 22 Solutions
Foundations of Astronomy (MindTap Course List)
Ch. 22 - Describe four differences between the Jovian...Ch. 22 - Why is Jupiter more oblate than Earth? Just...Ch. 22 - Which molecules and atoms are Jupiter and Saturn...Ch. 22 - What determines which cloud layers are found at...Ch. 22 - Describe a hypothesis explaining why Jupiter emits...Ch. 22 - How does beltzone circulation transport energyby...Ch. 22 - Why are belts and zones wrapped entirely around...Ch. 22 - What ingredients are needed to power a dynamo...Ch. 22 - Why are magnetic phenomena such as extensive...Ch. 22 - How do the interiors of Jupiter and Saturn differ?...
Ch. 22 - Which planet formation step did the Jovian planets...Ch. 22 - Why is Jupiters moon lo called a regular...Ch. 22 - Why is Saturns moon Phoebe called an irregular...Ch. 22 - If Jupiter had a satellite the size of our own...Ch. 22 - The density of Earths Moon is 3.3 g/cm3. Which of...Ch. 22 - Ganymede was once completely molten on the inside....Ch. 22 - Describe evidence of tectonic features seen on...Ch. 22 - Why are no craters seen on lo and few seen on...Ch. 22 - Why should you expect lo to suffer more impacts...Ch. 22 - How can you be certain that Jupiters rings do not...Ch. 22 - Why are the belts and zones in the atmosphere of...Ch. 22 - Describe the composition of Saturn from its center...Ch. 22 - If Saturn had no moons, do you think it would have...Ch. 22 - How can Titan keep an atmosphere when Titan is...Ch. 22 - What should the interior composition of Titan be...Ch. 22 - If you were able to stand on the surface of Titan...Ch. 22 - Does Titan experience volcanism today? Impact...Ch. 22 - Describe the types of geological activity observed...Ch. 22 - More Jovian moons are geologically active than...Ch. 22 - Prob. 30RQCh. 22 - If you piloted a spacecraft to visit Saturns moons...Ch. 22 - The ring systems around Jupiter and Saturn lie...Ch. 22 - Saturns rings are primordial, meaning that they...Ch. 22 - What is understood to be the cause of gaps in ring...Ch. 22 - What is understood to be the cause of ripples in...Ch. 22 - Why would you expect research in archaeology to be...Ch. 22 - What is the angular diameter of Jupiter as seen...Ch. 22 - Prob. 2PCh. 22 - What is the angular diameter of Jupiter as seen...Ch. 22 - What is the escape velocity from the surface of...Ch. 22 - Calculate the mass of Callisto using a value for...Ch. 22 - Prob. 6PCh. 22 - Calculate the radius of Jupiters Roche limit for a...Ch. 22 - How long does the eastward wind at the equator of...Ch. 22 - What is the orbital velocity and period of a ring...Ch. 22 - If you were to record the spectrum of Saturn as...Ch. 22 - Prob. 11PCh. 22 - Jupiter is about 71,000 km in radius. The...Ch. 22 - Saturn is about 60,000 km in radius, and its rings...Ch. 22 - Look at Figure 22-4b. Compare the visual and UV...Ch. 22 - Prob. 2LTLCh. 22 - Prob. 3LTLCh. 22 - The Cassini spacecraft recorded the image shown...
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