AST 301
Spring 2003
Exam #2
1.a) Describe the first reaction in the chain of nuclear reactions that
are occurring in the Sun.
Two protons fuse, with one of them turning into a neutron and releasing a
positron and a neutrino, to make a deuterium (Heavy hydrogen) nucleus.
The following reactions in the chain result in the formation of helium.
b) How can we use Einstein's equation E = mc^2 to calculate the energy that
is generated in a nuclear reaction?
Mass is converted into energy, and the energy generated equals the mass
destroyed multiplied by the square of the speed of light.
2. Describe one method astronomers use to measure the surface (or
photospheric) temperature of a star.
Three options:
1) Observe the star's color. Hotter stars are bluer, cooler stars are
redder.
2) (better) Measure the wavelength at which the star is brightest. The
temperature is inversely proportional to the wavelength at which it is
brightest.
3. Answer ONE of the following two questions:
a) Explain the connection between distance and parallax. That is, say
what the relation is between these two quantities, and explain why they
are related in the way they are. (A figure might help.)
Draw the picture we drew in class. From it you can see that more distant
stars have smaller parallaxes. The distance is inversely proportional to
the parallax.
b) Explain the connection between distance and apparent brightness.
That is, say what the relation is between these two quantities, and
explain why they are related in the way they are. (A figure might help.)
Draw the picture we drew in class. From it you can see that as light goes
out from a star it spreads out in two directions. So the flux (power per
area) falls off with distance as distance squared.
4.a) Explain why a star must be big and cool to be found in the upper
right region of the H-R diagram.
The axes on the diagram are temperature and luminosity. Upper right means
luminous and cool. So cool is obvious. To be luminous in spite of being
cool, a star must be big, so it has a lot of surface area to radiate.
b) Explain why white dwarfs move down and to the right on the H-R diagram
as they cool.
White dwarfs don't change size as they cool. Cooling means moving to the
right. If a star cools while keeping constant size, so constant surface
area, it gets fainter, so moves down on the diagram. This is because cooler
objects emit less light per surface area than hotter objects.
5. A 2 solar mass star has a luminosity of about 10 solar luminosities.
a) How does the amount of fuel (for nuclear fusion) in a 2 solar mass
star compare to the amount of fuel in the Sun?
The star's mass is its fuel. They are both the hydrogen it is made of.
So twice as much mass means twice as much fuel.
b) How does the amount of fuel a 2 solar mass star uses in a second compare
to the amount of fuel the Sun uses in a second?
If a star is in thermal equilibrium, it must burn the amount of fuel needed
to generate the energy it radiates (its luminosity). So if a star has 10
times the luminosity of the Sun, it must be burning 10 times as much fuel
each second as the Sun does.
c) With the additional information that the Sun will have a lifetime as a
main-sequence star of about 10^10 years, explain how you would combine your
answers to parts a and b to calculate the lifetime of a 2 solar mass star.
If the star has 10 times as much fuel as the Sun, but burns twice as much
each second, its fuel will last only 1/5 as long, or 2x10^9 years.
6. Describe one of the two types of supernova. Specifically, say what
events lead to the explosion, what happens during the explosion, and what
is left behind after the explosion. For extra credit, say how an astronomer
can tell which type of supernova he or she is seeing when one happens.
I) A white dwarf gains mass from a companion star until its mass exceed
1.44 M_sun. It then collapses because degereracy pressure can't support it.
That ignites fusion of carbon and oxygen, which blows it apart, leaving
nothing.
II) A massive red giant fuses elements in its core until it starts fusing
iron to make heavier elements. This fusion reaction takes energy from the
core, causing it to collapse. It collapses to make a neutron star. The
star's envelope falls in on the neutron star and bounces back out in an
explosion.
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