Chapter 15--Our Sun - Geological Sciences

Problems
9. Gravitational Contraction. Briefly describe how gravitational
contraction generates energy and when it was important
in the Sun’s history.
10. Solar Characteristics. Briefly describe the Sun’s luminosity,
mass, radius, and average surface temperature.
11. Sunspots. What are sunspots? Why do they appear dark in
pictures of the Sun?
12. Solar Fusion. What is the overall nuclear fusion reaction in
the Sun? Briefly describe the proton–proton chain.
13. Models of the Sun. Explain how mathematical models allow
us to predict conditions inside the Sun. How can we be
confident that the models are on the right track?
14. Sun Quakes. How are “sun quakes” similar to earthquakes?
How are they different? Describe how we can observe them
and how they help us learn about the solar interior.
15. Energy Transport. Why does the energy produced by fusion
in the solar core take so long to reach the solar surface?
Describe the processes of radiative diffusion and convection
in the solar interior.
16. The Photosphere. Describe the appearance and temperature
of the Sun’s photosphere. What is granulation? How would
granulation appear in a movie?
17. Observing the Sun’s Atmosphere. Why is the chromosphere
best viewed with ultraviolet telescopes? Why is the corona
best viewed with X-ray telescopes?
18. An Angry Sun. A Time magazine cover once suggested that
an “angry Sun” was becoming more active as human activity
changed Earth’s climate through global warming. It’s
certainly possible for the Sun to become more active at the
same time that humans are affecting Earth, but is it possible
that the Sun could be responding to human activity? Can
humans affect the Sun in any significant way? Explain.
*19. Number of Fusion Reactions in the Sun. Use the fact that each
cycle of the proton–proton chain converts 4.7 10 29 kg
of mass into energy (see Mathematical Insight 15.1), along
with the fact that the Sun loses a total of about 4.2 10 9 kg
of mass each second, to calculate the total number of times
the proton–proton chain occurs each second in the Sun.
*20. The Lifetime of the Sun. The total mass of the Sun is about
2 10 30 kg, of which about 75% was hydrogen when the
Sun formed. However, only about 13% of this hydrogen
ever becomes available for fusion in the core. The rest remains
in layers of the Sun where the temperature is too low
for fusion.
a. Based on the given information, calculate the total
mass of hydrogen available for fusion over the lifetime
of the Sun.
b. Combine your results from part (a) and the fact that the
Sun fuses about 600 billion kg of hydrogen each second
to calculate how long the Sun’s initial supply of hydrogen
can last. Give your answer in both seconds and years.
c. Given that our solar system is now about 4.6 billion years
old, when will we need to worry about the Sun running
out of hydrogen for fusion?
*21. Solar Power Collectors. This problem leads you through the
calculation and discussion of how much solar power can be
collected by solar cells on Earth.
a. Imagine a giant sphere surrounding the Sun with a
radius of 1 AU. What is the surface area of this sphere,
in square meters? (Hint: The formula for the surface
area of a sphere is 4pr 2 .)
b. Because this imaginary giant sphere surrounds the Sun,
the Sun’s entire luminosity of 3.8 10 26 watts must
pass through it. Calculate the power passing through
each square meter of this imaginary sphere in watts per
square meter. Explain why this number represents the
maximum power per square meter that can be collected
by a solar collector in Earth orbit.
c. List several reasons why the average power per square
meter collected by a solar collector on the ground will
always be less than what you found in part (b).
d. Suppose you want to put a solar collector on your roof.
If you want to optimize the amount of power you can
collect, how should you orient the collector? (Hint: The
optimum orientation depends on both your latitude
and the time of year and day.)
*22. Solar Power for the United States. The total annual U.S. energy
consumption is about 2 10 20 joules.
a. What is the average power requirement for the United
States, in watts? (Hint: 1 watt 1 joule/s.)
b. With current technologies and solar collectors on the
ground, the best we can hope is that solar cells will
generate an average (day and night) power of about
200 watts/m 2 .(You might compare this to the maximum
power per square meter you found in problem 22b.)
What total area would we need to cover with solar cells
to supply all the power needed for the United States?
Give your answer in both square meters and square
kilometers.
c. The total surface area of the United States is about
2 10 7 km 2 .What fraction of the U.S. area would have
to be covered by solar collectors to generate all of the
U.S. power needs? In one page or less, describe potential
environmental impacts of covering so much area with
solar collectors. Also discuss whether you think these
environmental impacts would be greater or less than
the impacts of using current energy sources such as coal,
oil, nuclear power, and hydroelectric power.
chapter 15 • Our Star 519