# THE NATURE AND EVOLUTION OF STARS

• For the next week ``we'' will look at one of the most fundamental questions about a star

### How is all that energy that radiates away into space produced?

The answer to this explains the existence of the main sequence in the H-R Diagram and leads into the next big topics the Formation and Evolution of Stars.

### Coal or Wood burning:

• What is ``burning''? Conversion of molecular binding energy into E-M radiation

This is not very efficient!

• So, a 3000 gram bucket of coal is good for about ergs or 300 Kilowatt-hours. This would run a little space heater for about an hour.

• Now, the Sun's mass is grams. If it was coal and producing energy via conventional combustion it could generate a total energy of:

• The Question: How long would the Sun shine for the case of coal power?

Lifetime is given by taking the total energy available divided by the rate at which you are using up the energy.

• Note: is equivalent to 1 ton of coal burned per hour for every square foot of the Sun's surface

• By the mid-1800's it was recognized that the Earth and Sun were at least millions of years old. This was a puzzle - the most common source of energy on Earth could not be used to explain the energy production and longevity of the the Sun.

## Another Energy Source possibility: Gravitational Potential Energy

Anytime you have a collection of mass (for example a gas of atoms and molecules) it has an associated Gravitational Potential Energy - GPE. For a big ball of gas, the GPE goes like:

where R is the radius of the ball of gas, M is the total mass and G is the ``gravitational constant''.

Similarly, if because the Earth exerts a gravitational pull on objects at the surface and in space, objects all have an associated GPE.

• So, if a gas cloud shrinks in size without changing mass, it must Release GPE. Energy is always conserved, so as a cloud shrinks it heats up and emits radiation.

• At the surface of the Earth, an object at a large radius from the center of the Earth has more GPE than the same object at a smaller radius (here the radius is the radius of the Earth plus the height of the object above the surface of the Earth

• Perhaps the Sun is slowly shrinking in size and radiating away the lost GPE.

• How much total GPE does the Sun have that could be turned into radiation as the Sun shrinks?

• This shows that converting GPE is a pretty efficient process compared to chemical burning.

This is about 250 times more efficient than chemical burning.

• OK, how long would the Sun last at its current luminosity if it was GPE powered? (Note that it would contract at about 40m per year)

This converts to 16 million years - still too short! The Earth is around 4 billion years old (plus the Sun would have been much bigger in the past).

• Another possibility considered was the GPE of comets and meteors falling into the Sun. To produce would require about 1 Earth mass per year to be accreted (not that much). This can be ruled out because the resulting change in the Earth's orbit has not been measured.