- 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