Announcements

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Announcements

• Welcome back to Standard Time!
• Wednesday night star parties begin this week,
  845 pm, weather permitting. Attend one for 4
  points extra credit! (Staff signature required.)
• Milky Way bars! (For a bigger one, solve the
  Monty Python song puzzler.)
• Telescopic trick-or-treat tomorrow at 1444
  Binford Street (weather permitting)
• Turn in Homework 9
• Pick up Homework 10
• Sorry about the delay in grading projects, tests

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Nuclear Reactions in Stars

• 30 October 2006

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Today

• Measuring masses of stars
• What makes the stars shine?

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Binary Star Systems

• Period of orbit is determined by m1m2
• Relative amounts of motion are determined by mass
  ratio m1/m2

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Binary Star Systems

• Period of orbit is determined by m1m2 (and
  orbital size)
• Relative amounts of motion are determined by mass
  ratio m1/m2

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Summary of Stellar Properties
Distance Measure using parallax (if close enough)
Velocity Proper motion and Doppler shift
Luminosity Calculate from apparent brightness and distance
Temperature From overall color or spectral class
Composition From detailed analysis of spectral lines
Size Calculate from temperature and luminosity
Mass From binary star orbits, Newtons laws
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Masses of Stars
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Masses of Stars

• The most massive stars area about 100 times as
  massive as our sun (msun 2 x 1030 kg).
• The least massive stars have about 1/10 the mass
  of our sun.
• The full range of masses occurs among
  main-sequence stars, for which mass correlates to
  temperature and luminosity.
• Red giant stars tend to be more massive than
  our sun, but otherwise are no more massive than
  main-sequence stars.
• White dwarf stars tend to have about the same
  mass as our sun.

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What makes the stars shine?
Stars give off huge amounts of radiant energy
over very long time periods, yet undergo little
noticeable change. Where does all this energy
come from?
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Types of energy
Motion (kinetic) Gravitational Elastic Thermal C
hemical Nuclear Electrical Radiant (light)
Energy can be converted from one type to another,
but cannot be created or destroyed. The total
amount of energy in the universe never changes.
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Possible energy sources

• Chemical. 1030 kilograms of gasoline, each
  providing 10,000 Calories of energy (40 MJ),
  would yield 4 x 1037 joules of energy. If the
  energy is released at a rate of 4 x 1026 J/s,
  this fuel would last 1011 seconds, or about 3000
  years. Not long enough!

?
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Possible energy sources

• Gravitational. Our sun formed from a collapsing
  gas cloud, and may still be contracting. As
  material falls inward, gravitational energy is
  converted to kinetic and then thermal energy.
  From the suns mass and present size, Kelvin
  calculated an age of about 20 million years (at
  its current luminosity).

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Possible energy sources

• Nuclear! Nuclear reactions typically give off a
  million times as much energy, per atom, as
  chemical reactions, so the sun could last
  billions of years.
• Problem The sun is made mostly of stable
  isotopes, 1H and 4He. Its energy source is not
  ordinary radioactive decay!

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Nuclear Fusion Reactions

• Small nuclei (such as hydrogen) combine to form
  larger nuclei (helium, etc.), releasing energy.
• But First the nuclei must touch each other,
  despite electrostatic repulsion. This requires
  high-speed collisions, that is, very high
  temperatures (except at the U. of U. Chemistry
  Department).

4 1H (protons)
4He
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Nuclear Fusion DetailsFor the sun and most
main-sequence stars
(Not shown Positrons (beta) annihilate with
electrons into gamma rays.)
Net result 4 protons plus 2 electrons convert
to a 4He nucleus, 2 neutrinos, and 6 gamma-ray
photons
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How much energy is released?
E mc2
Conversion factor, numerically equal to 3x108
m/s, squared
Energy content of any object (including all forms
except kinetic energy of overall motion), in
joules
Mass of object, in kilograms
The total energy content of a 1-kg object is 9 x
1016 joules! Chemical reactions typically involve
mass changes of only one part in a billion -- too
small to measure. Nuclear reactions typically
involve mass changes of a few parts in a thousand
-- easy to measure.
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How much energy is released?
For each kilogram of hydrogen converted to
helium, the mass decreases by 7 grams, so the
energy released is 6 x 1014 joules. In one
second, the sun releases 4 x 1026 joules of
energy, so its mass must decrease by about 4
billion kilograms!
Hans Bethe, 1906 - 2005