ASTR 109 HOMEWORK #5 (Hamilton)
due Wednesday August 20
1. A Star's Life.
a) Will the Sun age gracefully? Go to the
Life of the Sun program at http://janus.astro.umd.edu/astro/stars/SunsLife.html/
to find out. Watch the animation through once to see what happens and
note the timer at the top left. Write down the following events:
Present Day Earth, Earth's Oceans Boil, Red Giant, Helium Burning,
White Dwarf. Then get a pen ready and run the simulation, noting
rough times for each event. You will have to be quick and will need to
watch several times! Make a table of the event and its timing. How
long does the Sun live as a Red Giant? How much time does the
Sun burn Hydrogen (beginning until Helium Burning) and how much time
does it burn Helium (Helium Burning to White Dwarf)? So for what small
fraction of its life (up to the onset of the White Dwarf phase) will the
Sun burn Helium?
b) Different stars live for different amounts of time. Go to the
Star Race program at http://janus.astro.umd.edu/astro/stars/StarRace.html. The
length of this simulation scales with the true lifetimes of the stars
- some of them seem to live forever! Choose pairs of stars and race
them noting, in each case, the total lifetime of the star, the large
remnant that it spreads across space (supernova explosion or Planetary
Nebula) and the small remnant that it leaves behind (black hole, white
dwarf, neutron star). Make a table of these results. What pattern do
you see in the stellar lifetimes? Describe the possible fates for
small, larger, and the largest stars.
2) Fueling the Sun.
a) The Sun generates energy at a rate of
about 3.8 * 1026 Watts (1 Watt = 1 Joule/second). So in 1
second, 3.8 * 1026 Joules of energy are produced.
Use Einstein's famous E=mc2 formula to convert the
Sun's energy generation rate into a mass destruction rate. Here
c=3*108 m/s is the speed of light. A direct usage of the
formula will give you the number of kg of mass that the Sun destroys
every second. Now convert your answer to millions of tons per second.
b) Take the mass of the Sun and divide by your answer to part a) in
kg/s. This gives you the maximum number of seconds that the Sun can
shine at its current rate of expending energy. Convert your answer
into billions of years. You will need to work out the number of
seconds in a year. Compare this number with the current age of the
Sun (4.5 billion years) and its expected total lifetime (12 billion
years). It will not be a perfect match!
c) If your answer to part b) is much shorter than 12 billion
years, then the Sun will need another fuel source to survive this
long. If your answer is much greater than 12 billion years, then
either the Sun won't burn up all of its Hydrogen or it will burn it at
a faster rate in the future. In fact, all of these points are true!
What is the Sun's other fuel source? When do you think that it burns
the most Hydrogen fuel and why? And where do you think that the
unburned fuel goes?
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