EBK FOUNDATIONS OF ASTRONOMY
14th Edition
ISBN: 8220106820612
Author: Backman
Publisher: YUZU
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Chapter 25, Problem 7P
If you detected radio signals with an average wavelength of 20.000 cm and suspected that they came from a civilization on a distant Earth-like exoplanet, roughly how much of a change in wavelength should you expect to detect as a result of the orbital motion of the distant exoplanet? (Hint: Use the Doppler shift formula, Eq. 7-3.) (Note: Earth’s orbital velocity is 30 km/s.)
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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 25 Solutions
EBK FOUNDATIONS OF ASTRONOMY
Ch. 25 - Explain how astrobiology is a science and not a...Ch. 25 - Describe one special quality of water that makes...Ch. 25 - Mars and Europa are two Solar System bodies that...Ch. 25 - How does the DNA molecule produce a copy of...Ch. 25 - What would happen to a life-form if the genetic...Ch. 25 - What would happen to a life-form if the genetic...Ch. 25 - What would happen to a life-form if the...Ch. 25 - Describe an example of natural selection acting on...Ch. 25 - Prob. 9RQCh. 25 - What evidence do scientists have that life on...
Ch. 25 - Define organic, as in organic molecule. How is...Ch. 25 - Why is liquid water generally considered necessary...Ch. 25 - Some meteorites contain organic molecules. What...Ch. 25 - What is the difference between chemical evolution...Ch. 25 - Prob. 15RQCh. 25 - Why was Earths early atmosphere able to support...Ch. 25 - Molecules of which gas were needed in Earths...Ch. 25 - Does intelligence make a creature more likely to...Ch. 25 - Describe one hypothesis for how cells first...Ch. 25 - What is the evidence that the first organisms on...Ch. 25 - Name three locations in our Solar System to search...Ch. 25 - Why are upper-main-sequence (high-luminosity) host...Ch. 25 - Prob. 23RQCh. 25 - How does the stability of technological...Ch. 25 - Prob. 25RQCh. 25 - Prob. 26RQCh. 25 - Why are scientists confident Earth has never been...Ch. 25 - Why does the Drake equation implicitly assume the...Ch. 25 - A single human cell encloses about 1.5 m of DNA....Ch. 25 - If you represent Earths history by a line that is...Ch. 25 - Consider Figure 25-8. What is the ratio of the...Ch. 25 - Suppose a human generation is defined as the...Ch. 25 - If a star must remain on the main sequence for at...Ch. 25 - Prob. 6PCh. 25 - If you detected radio signals with an average...Ch. 25 - Prob. 8PCh. 25 - The first radio broadcast was made on January 13,...Ch. 25 - Prob. 10PCh. 25 - The DNA in a single cell in your body contains...Ch. 25 - Prob. 2SOPCh. 25 - Look at Figure 25-11. Since the time we sent the...Ch. 25 - The star cluster shown in this image contains a...Ch. 25 - If you could search for life in the galaxy shown...
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