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“I always wanted to be somebody, but I
should have been more specific.”
Lilly Tomlin
Any late HW2 are due before class on
Wednesday. HW2 solutions posted after
class on Wednesday.
You will want to bring a calculator to class.
This next part is math-rich, but we will do
many sample problems in class.
Test 1 is Friday- be sure to bring a pencil
and a calculator.
There is a study guide and sample test on
the course web page.
Next section:The power of light!
We want to know:

How hot are stars?

How BIG are stars (size)?

How massive are stars?

What are stars made of?

How far away are stars?

Are they in motion?

How much energy do stars emit?

Where does that energy come from?
A spectrum
Blue light has more energy (is hotter)
than red light.
Quiz 8: Which light has the most energy?
A) X-rays B) Green light C) Microwaves D) Radio waves
Temperatures given in Kelvins T=2.9x106/max for  in nm.
Shorter wavelengths
= hotter object.
Objects glowing blue
are hotter then objects
glowing red.
Stefan-Boltzmann Law

Can determine energy per square
meter from the temperature.
2
4
 E/m = T
-8 W/m2K4
 Where = 5.67x10
Example:
Our Sun looks yellow. So from the chart below,
let's assume the peak of the continuous spectrum
is at 575nm. What are the temperature and
energy per square meter of our Sun?
400
575
700 nm
Example: our Sun
First find the temperature:
6
T=2.9x10 / = ?
=575
Now find the energy associated
with that temperature.
4
-8
4
2
E/m = T =(5.67x10 )(T )=?
Example: our Sun
First find the temperature:
T=2.9x106/ = 2.9x106/575 = 5043K
Now find the energy associated with that
temperature.
4
4
E = T =(5043 )=
(5.67x10-8)(6.47x1014)
=3.7x107 W/m2
That's 37 million watts for each square
meter at the surface of the Sun!
Example: our Sun
6
T=2.9x10 /
=
6
2.9x10 /575
= 5043K
E = T4=(50434)=3.7x107 W/m2
That's 37 million watts for each square
meter at the surface of the Sun!
But it's not the total energy of the Sun.
How do we find the total energy of the
Sun?
Example: our Sun
T= 5043K
2
7
2
E/m =3.7x10 W/m
To get the total energy,
multiply by the surface
area of the Sun:
A=4pR2 where R is
the radius of the Sun:
8
6.96x10 m.
Example: our Sun
T=2.9x106/ = 2.9x106/575 = 5043K
E=
4
4
7
2
T =(5043 )=3.7x10 W/m
To get the total energy, multiply by the
surface area of the Sun: A=4pR2 where
8
R is the radius of the Sun: 6.96x10 m.
Etot= 2.25x1026 watts.
This energy has a special name:
Luminosity
Luminosity:
The total energy emitted by a star:
2
4
L=4pR T
We want to know:

How hot are stars?

How BIG are stars (size)?

How massive are stars?

What are stars made of?

How much energy do stars emit?

Where does that energy come from?

How far away are stars?

Are they in motion?
INVERSE SQUARE LAW
Light drops off as the square of the distance (1/d2)
The light received at 2m is ¼ the light received at 1m.
The light received at 3m is 1/9 the light received at
1m and so on. This is called the apparent luminosity
(Lap). So Lap at 3m is 1/9L.
Put it all together:
Apparent Luminosity
Include distance into the calculation.
Lap=4pR2T4/d2
This is how bright stars appear to us when we look
up into the sky at night.
Units: Temperature must be in Kelvin, size and
distance must be in meters.
How to make a star brighter

Make it hotter: E~T4

Make it bigger: E~R2

Make it closer: E~1/d2
Hotter is most powerful.
The motions of stars.
Parallax
Parallax
From parallax we can determine distances
to nearby stars. This is the first step in
determining the distances in our
Universe.
This method is only good for nearby
stars.
Parallax
From parallax we can determine distances
to nearby stars.
This method is only good for nearby
stars.
The closest star to us is 4 light years away
(~25,000 AU)
Most stars we see are tens to thousands of
light years away.
We want to know:

How hot are stars?

How BIG are stars (size)?

How massive are stars?

What are stars made of?

How much energy do stars emit?

Where does that energy come from?

How far away are stars?

Are they in motion?
Parallax is due to the motion of Earth
around the Sun.
But stars are in motion too!
(everything in the Universe is)
Parallax is due to the motion of Earth
around the Sun.
Proper motion is a stars motion across
the sky. (not towards or away from us)
Again, closer stars will have larger proper
motion, and faster stars will have larger proper
motion.
Radial velocity
But stars are also moving towards and
away from us. To measure this motion,
we use the Doppler shift.
Parallax is due to the motion of Earth
around the Sun.
Proper motion is a stars motion across
the sky. (not towards or away from us)
Radial velocity uses the Doppler shift to
measure a star's motion towards or away
from us.
The complete picture.
Arrow shows true motion of star
We want to know:

How hot are stars?

How BIG are stars (size)?

How massive are stars?

What are stars made of?

How much energy do stars emit?

Where does that energy come from?

How far away are stars?

Are they in motion? Yes!
Luminosity (brightness)
When we look at a star from Earth, we measure its
APPARENT LUMINOSITY (BRIGHTNESS): Lap
We call the TOTAL energy emitted from a star its
LUMINOSITY: L
We also have a standard called ABSOLUTE
LUMINOSITY: Labs which is how bright a star
would appear if it were at 10 parsecs (pc) from us.
Parsecs
16
1pc=3.1x10 m
1pc = 206,667 AU
1pc = 3.26 light years (ly)
Kirchoff
In the 1850s, Gustav Kirchhoff
took another look at Wien's work.
He discovered 3 types of spectra
He also heated ceramics and got the spectrum on the
left.
Then he put a cool gas in front of the ceramic and
got the center spectrum.
Then he just heated the gas (with electricity) and got
the spectrum on the right.
So now we have 3 types of spectra
Continuous
spectra are
made by
objects under
high pressure
(like solids)
Absorption line Emission line
spectra are spectra are made
made by cool
by
(comparatively) (comparatively)
low pressure
hot,
gases.
low pressure
gases.
Below are the 3 kinds of spectra again.
As you can see from the labels on the left, different
elements produce different spectral lines.
A spectrum of our Sun:
The lines give us composition!
So we can see what our Sun is
made of !
Now we can get the Sun's composition.
By Mass
Astronomers
call this stuff
“metals”

76% Hydrogen

22% Helium

0.8% Oxygen

0.4% Carbon

0.2% Neon

0.1% Iron and Nitrogn

~0.08% Silicon and Magnesium

~0.24% Everything else
We want to know:

How hot are stars?

How BIG are stars (size)?

How massive are stars?

What are stars made of?

How much energy do stars emit?

Where does that energy come from?

How far away are stars?

Are stars in motion? Yes!
Now we can ask, What
provides the energy our
Sun emits?
How to solve the problem.
To determine the energy source of the Sun,
astronomers tried to calculate the total energy
emitted by the Sun in its lifetime. To do this, you
simply multiply the amount of energy the Sun
radiates each second (L=3.9x1026W) by its age.
In the beginning....
Chemical burning is a way to generate heat.
Chemical reactions (burning) could power the Sun
for ~3,000 years.
This agreed with religious dogma at the time.
Another way
Back in the 1850s, scientists thought the Sun's
energy came from gravity- the Sun was converting
gravitational energy to heat.
Egrav=GMm/R. So as R get smaller, energy can be
released. Lord Kelvin estimated the Sun could last
30 million years based on this.
The Earth's age
By late in the 19th century, Darwin had determined
that the Earth must at least be hundreds of millions
of years old.
Early in the 20th century, radiation provided a new
power source and the age of atomic physics was
born.
Einstein
We now know that the Sun is 4.6 billion years old
and converts hydrogen to helium via nuclear
fusion. This releases energy based on Einstein's
famous equation: E=mc2. In each reaction, the Sun
converts a little bit of mass into energy.
The Sun puts out a million billion tons of TNT
worth of energy each second.
By converting hydrogen to helium.