Astronomy
1st Edition
ISBN: 9781938168284
Author: Andrew Fraknoi; David Morrison; Sidney C. Wolff
Publisher: OpenStax
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Textbook Question
Chapter 23, Problem 35E
Say that a particular white dwarf has the mass of the Sun but the radius of Earth. What is the acceleration of gravity at the surface of the white dwarf? How much greater is this than g at the surface of Earth? What would you weigh at the surface of the white dwarf (again granting us the dubious notion that you could survive there)?
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Check out a sample textbook solutionStudents 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 23 Solutions
Astronomy
Ch. 23 - How does a white dwarf differ from a neutron star?...Ch. 23 - Describe the evolution of a star with a mass like...Ch. 23 - Describe the evolution of a massive star (say, 20...Ch. 23 - How do the two types of supernovae discussed in...Ch. 23 - A star begins its life with a mass of 5 MSunbut...Ch. 23 - If the formation of a neutron star leads to a...Ch. 23 - How can the Crab Nebula shine with the energy of...Ch. 23 - How is a nova different from a type Ia supernova?...Ch. 23 - Apart from the masses, how are binary systems with...Ch. 23 - What observations from SN 1987A helped confirm...
Ch. 23 - Describe the evolution of a white dwarf over time,...Ch. 23 - Describe the evolution of a pulsar over time, in...Ch. 23 - How would a white dwarf that formed from a star...Ch. 23 - What do astronomers think are the causes of...Ch. 23 - How did astronomers finally solve the mystery of...Ch. 23 - Arrange the following stars in order of their...Ch. 23 - Would you expect to find any white dwarfs in the...Ch. 23 - Suppose no stars more massive than about 2 MSunhad...Ch. 23 - Would you be more likely to observe a type II...Ch. 23 - Astronomers believe there are something like 100...Ch. 23 - Would you expect to observe every supernova in our...Ch. 23 - The Large Magellanic Cloud has about one-tenth the...Ch. 23 - Look at the list of the nearest stars in Appendix...Ch. 23 - If most stars become white dwarfs at the ends of...Ch. 23 - If a 3 and 8 MSunstar formed together in a binary...Ch. 23 - You have discovered two star clusters. The first...Ch. 23 - A supernova remnant was recently discovered and...Ch. 23 - Based upon the evolution of stars, place the...Ch. 23 - What observations or types of telescopes would you...Ch. 23 - How would the spectra of a type II supernova be...Ch. 23 - The ring around SN 1987A (Figure 23.12) initially...Ch. 23 - What is the acceleration of gravity (g) at the...Ch. 23 - What is the escape velocity from the Sun? How much...Ch. 23 - What is the average density of the Sun? How does...Ch. 23 - Say that a particular white dwarf has the mass of...Ch. 23 - What is the escape velocity from the white dwarf...Ch. 23 - What is the average density of the white dwarf in...Ch. 23 - Now take a neutron star that has twice the mass of...Ch. 23 - What is the escape velocity from the neutron star...Ch. 23 - What is the average density of the neutron star in...Ch. 23 - One way to calculate the radius of a star is to...Ch. 23 - According to a model described in the text, a...Ch. 23 - Do the same calculations as in Exercise 23.42 but...Ch. 23 - If the Sun were replaced by a white dwarf with a...Ch. 23 - A supernova can eject material at a velocity of...Ch. 23 - A supernova remnant was observed in 2007 to be...Ch. 23 - The ring around SN 1987A (Figure 23.12) started...Ch. 23 - Before the star that became SN 1987A exploded, it...Ch. 23 - What is the radius of the progenitor star that...Ch. 23 - What is the acceleration of gravity at the surface...Ch. 23 - What was the escape velocity from the surface of...Ch. 23 - What was the average density of the star that...Ch. 23 - If the pulsar shown in Figure 23.16 is rotating...
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