• 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.

 E = x T4 Area

Where E is the energy radiated away from the star in the form of E-M radiation, T is the surface temperature of the star and is a constant known as the Stephan-Boltzmann constant.

This means that if you double the temperature of an object, it will radiate   2 x 2 x 2 x 2 = 16   times as much energy per square unit of area and in total if its surface area doesn't change.

• Now let's look at the Sun and Alpha Ori.

 SUN: 1 L ; T = 5500 K Ori: 27,500 L ; T = 3400 K

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 Ori is 187,000x the surface area of the Sun. This star has a radius (remember area is proportional to r2) which is 432 times larger than the Sun. The star is cool, but large.

• ### Size and the HR Diagram

Let's look at the sizes of stars as they relate to the HR diagram.

• Stars such as Ori which are cool in temperature yet huge in size are found in the upper right of the HR diagram and are given the name Red Giants.

• We 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. Thus they must have small surface areas and so get called White Dwarfs .

• You can play this game with all the stars and find an enormous range of sizes from around 1/100 R to nearly 1000 R .