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Announcements
• Welcome back to Standard Time!
• Wednesday night star parties begin this week, 8:45
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…
Nuclear Reactions in Stars
30 October 2006
Today:
• Measuring masses of stars
• What makes the stars shine?
Binary Star Systems
• Period of orbit is
determined by m1+m2
• Relative amounts of
motion are determined
by mass ratio m1/m2
Binary Star Systems
• Period of orbit is determined by m1+m2 (and orbital size)
• Relative amounts of motion are determined by mass
ratio m1/m2
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, Newton’s laws
Masses of Stars
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 mainsequence 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.
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?
Types of energy
Motion (“kinetic”)
Gravitational
Elastic
Thermal
Chemical
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.
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!
?
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 sun’s mass and present
size, Kelvin calculated an
age of about 20 million years
(at its current luminosity).
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!
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
Nuclear Fusion Details
For 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
How much energy is released?
E=
Energy content of any
object (including all
forms except kinetic
energy of overall
motion), in joules
2
mc
Mass of object,
in kilograms
Conversion
factor,
numerically
equal to 3x108
m/s, squared
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.
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