- 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 T ^{4}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 r^{2}) 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_{}.

- How much larger is Ori?