• 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.

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