Download ASTR100 Homework #5 Solutions Chapter 11 #29, 31 Due

ASTR100 Homework #5 Solutions
Due Thursday Nov 19, 2007
Chapter 11
Chapter 12
Chapter 13
Extra Credit
Chapter 12
#29, 31
#22, 26
#25
#46
Chapter 11
#29
Choose the best answer to each of the following, and explain your reasoning with one or more
complete sentences.
Which of these stars has the coolest surface temperature?
(a) A star
(b) F star
(c) K star
The order of Hottest to Coldest is O B A F G K M.
You can memorize it using “Oh Be A Fine Girl/Guy Kiss Me”
Therefore c) K stars are coldest
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#31
Which of these Stars has the longest lifetime?
(a) main-sequence A star
(b) main-sequence G star
(c) main-sequence M star
The colder the star, the longer it takes to burn through its energy source.
Hottest stars are O, coldest stars are M
(again… O B A F G K M)
c) M stars are the coldest, so those will live the longest
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Chapter 12
#22
Decide whether the statement makes sense or does not. Explain clearly.
If you could look inside the Sun today, you’d find that its core contains a much higher proportion of
helium and a lower proportion of hydrogen than it did when the Sun was born.
This statement makes sense because over the last 4.5 billion years the Sun has been busy converting its
Hydrogen into Helium via the Proton-Proton Chain. During this process the Sun will lose mass and
radiate it away as energy. When the sun was born the percentages were about 94% hydrogen and 4%
Helium, but now we can expect the percent of Hydrogen still available for fusion is closer to 60%. Don’t
worry, because there’s still plenty left!
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#26
The Gold in my new ring came from a supernova explosion.
This statement makes sense. In the final stages of a high mass star’s life, the star has exhausted all of its
energy sources, resulting in an inert iron core, which is supported by the degeneracy principle. This
prohibits the electrons from getting too close together, but once gravity pushes the electrons past this
quantum limit, they combine with protons, to form neutrons. Within seconds the core, with a mass
comparable to our sun, is collapsed into a ball of neutrons the size of only a few kilometers. The collapse
stops at this point because now the neutrons are supported by their own form of degeneracy pressure.
This gravitational collapse of the core releases tons of energy in the form of a SUPERNOVA, which blows
away the outer layers of the star. All elements heavier than iron which includes gold, were created in
these massive supernova explosions.
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Chapter 13
#25
Choose the best answer to each of the following, and explain your reasoning with one or more
complete sentences.
Which of these objects has the smallest radius?
(a) 1.2 Msun White Dwarf
(b) 0.6 Msun White Dwarf
(c) Jupiter
The smallest object is (a) the 1.2 Msun White Dwarf.
This is because a White Dwarfs is comparable to the size of the Earth, which rules out Jupiter.
Also the more massive a white dwarf is, the smaller it is! This is because the more mass a white dwarf
has, the more its electrons must squeeze together to maintain enough outward pressure to support the
extra mass. There is a limit on the amount of mass a white dwarf can have, however. This limit is 1.4
times the mass of our Sun.
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Extra Credit
Chapter 12
#46
The distance from Earth of the read supergiant Betelgeuse is approximately 427 light-years. If it were to
explode as a supernova, it would be one of the brightest stars in the sky. Right now, the brightest star
other than the Sun is Sirius, with a luminosity of 26 Lsun and a distance of 8.6 light-years. How much
brighter than Sirius would the Betelgeuse supernova be in our sky if it reached a maximum luminosity of
1010 Lsun?
Distance
Luminosity
Betelgeuse
427 light-years
𝟏𝟎𝟏𝟎 Lsun
Sirius
8.6 light-years
26 Lsun
For this problem we need to find the ratio of Apparent Brightness for the two objects…
where
B = L / 4πR^2
or
Apparent
Brightness
=
Luminosity
4 (π) (𝑅𝑎𝑑𝑖𝑢𝑠)2
Therefore, the Betelgeuse supernova would be 156015.52 times brighter than Sirius in our sky.
There are no units to worry about since the problem was set up as a ratio.