- With another relation from the physics of the 19th century we can figure
out the
**Sizes**of stars.- This gets quantified with a relation known as
**Stephan's Law**. - This gets quantified with a relation known as

Where **E** is the energy radiated away in the form of E-M radiation,
**T** is the surface temperature and is a constant called the
Stephan-Boltzmann constant.

- This means that if you
**double**the temperature of an object, it will radiate times as much energy per square cm and in total if it's surface area doesn't change. -
**Now lets think about the Sun and Alpha Ori**.**Sun: 1Lo; T=5500K****Alpha Ori: 27,500 Lo; T=3400K**So, something funny is going on. The Sun has a higher surface temperature so it must radiate more energy per unit surface area. There is only one way that Ori could radiate more total energy -

**it must have a larger total surface area**. - How much larger is Ori?
for the Sun is larger than that of Ori by:

- If the two stars had the same radius and surface area, the Sun would
radiate 6.8 times as much energy. But Ori has a total energy radiated that is 27,000 times more than that of the Sun.
We can

**quantify**the difference in the size of the two stars using Stephan's Law. - So the surface area of Alpha Ori is 187,000x the surface
area of the Sun. This star has a radius 432 times larger than the Sun. It is
cool, yet huge hence the name
**Red Giant** - Can play the same game with the low-luminosity hot stars at
the left side of the H-R Diagram. Despite the fact that they have
lots of energy radiated per unit surface area, they have a small
total energy radiated - they must have small surface areas and get
called
**White Dwarfs**. - You can play this game with all the stars and find an enourmous
range of sizes from around 1/100 R to nearly 1000 R

*Michael Bolte*

Thu Jan 29 09:33:26 PST 1998