Monday February 1st 1999
Announcements:

Lecture notes:

Class 10
 

Moving on to stars
Title is why does the Sun Shine?
Will start giving the basic properties of the sun
Sun is basically a big ball of gas

Radius = 700 000 km = R(.)
    = 110 Earth radii
Mass = 2x10³³ g = M(.)
    = 330 000 Earth masses
How dense is the sun?  on average
density = mass/volume = 2x10³³g/[4pi/3 * (7x10¹⁰)³]
    = 1.4 g/cm³
cork = .24 g/cm³
water = 1 g/cm³
rock = 2-4 g/cm³
earth = 5.5 g/cm³

Temperature
5500 C surface.  Hotter than typical fires on Earth
However we know Sun is even hotter in center = 14 million degrees C.
Energy output
    energy made in 1 second compared to a light bulb
100 Watts = 1x10⁹ erg/sec
sun radiates 4x10³³ erg/s
about 4x10²⁴ light bulbs
more than have been made in the history of people.

How does the sun make all this energy?
Fundamentally the sun shines because it converts matter into
energy in its center through nuclear fusion

famous Einstein equation
E=mc² relates mass to the energy
Energy = mass (speed of light)²
speed of light = 3x10¹⁰ cm/s
Energy = mass (9x10²⁰ cm²/s²)
so for one gram
energy = 9x10²⁰ ergs
huge amount!
explosive energy of 20 000 tons of TNT
matter has an incredible amount of energy locked up inside.

Luckily for us energy only liberated under quite extreme conditions like those in the center of the sun.

We said that the sun makes 4x10³³ erg/s
using Einstein's formula
4x10³³ ergs = Mass (9x10²⁰ cm²/s²)
mass = 4.4x10¹² g
=4.4x10⁹ kg
about 4 million cars mass

In center of sun high T = 14 million deg
    density = 16 g/cm³
due to weight of all particles pushing down
particles in the center jostle around and bang into each other causing fusion to occur

The reactions that make sun shine are nuclear reactions.
Kind of like chemical reactions but caused by nuclei
Have special notation like chemical reaction paths you saw in high school.
for hydrogen ¹H = number of particles in nucleus both protons and neutrons
H = name of the element
How to do helium?
⁴He - 2 protons and 2 neutrons
also it turns out that ³He and ²H exist.  Just different numbers of neutrons.  Fairly rare on Earth but important for solar reactions.

Now the main reaction in the sun converts H -> He
proton - proton chain
fairly complicated.  You don't need to memorize all the details but do need to understand the basic ideas.
First you need to know about 2 other subatomic particles
positron - positively charged version of electron ( antimatter)
neutrino - elusive elementary particle that almost never interacts with other particles

Here are the reactions
¹H + ¹H -> ²H + positron + neutrino + energy
²H + ¹H -> ³He + photon + energy
³He + ³He -> ⁴He + ¹H + ¹H + energy

in summary basic process is 4 ¹H -> ⁴He + energy
should know this one

While it seems a little boring on paper a lot more interesting when you consider that these reactions occur billions of times each second in the sun.
This powers life on earth

now where does energy come from?
mass of ⁴He < mass of 4 ¹H
4 protons have mass = 6.6943x10^-24 g
⁴He has mass of 6.6466x10^-24g
a difference of 4.77x10^-26 g
convert to energy
energy - 4.77x10^-26g(9x10²⁰)
    = 4.29 x10 ^-5 erg for this fusion
This powers the sun