# STELLAR LUMINOSITIES

Remember that Luminosity is the total amount of energy produced in a star and radiated into space in the form of E-M radiation. The Sun radiates ergs/sec.

• How do we figure out the luminosity of the Sun?

It's easy. Measure its (apparent) brightness, measure it's distance and use the inverse square law.

The apparent brightness is a measure in photon energy passing through a square whatever at the distance of the Earth. One way to determine the total energy release in photons is to multiply the photon energy per square whatever, times the total area of the sphere with radius 1 AU (remember an astronomical unit is the distance between the Earth and Sun) in units of square whatevers.

• One measure of the apparent brightness of the Sun is ``Solar Constant''. At the Earth's surface we receive:

1,400,000 ergs/square cm/second

where ``erg'' is not a joke, it is a unit of energy.

(Note that a normal-sized human emits 100 watts in IR power).

Strangely enough a black horse in a field on a sunny day absorbs around 800 watts = 1 horsepower.

• How about the top of this building?

ergs/cm /sec (roof area) gives the energy beating down per second in Solar photons.

Roof Area: 100m  100m m cm .

Is this alot? Total campus usage is 3.5 MW.

• So, given the solar constant, how do we find the total radiant energy of the Sun?

We have the energy per square cm per second:

The Surface Area of a sphere with radius R= 1AU is:

• The total energy flowing through the surface of this sphere is therefore:

• This is the total energy produced by the Sun:

• How much energy is this? It is pretty hard to get a feeling for numbers this large. At PG&E rates, the price of the Sun's energy would be \$/second.

Q. What is the Solar Luminosity at the distance of Mars (1.5 AU)?

Still the same, 1 solar luminosity. The Martian ``solar constant'' will be smaller by a factor of 1.5 x 1.5, but added up over the entire surface of the sphere centered on the Sun with radius 1.5AU, the luminosity is the same. Luminosity is an intrinsic property of the Sun.

Q.
What is the Solar Luminosity at the surface of the Sun?

A REALLY GOOD QUESTION: How does the Sun manage to produce all that energy and maintain that production for at least 4.5 billions years?

What about the Luminosity of those other stars?

Once we have the distance to any other star, we can combine that with the apparent brightness and the inverse-square law for light dimming to determine the ``intrinsic brightness'' or luminosity.

We can therefore determine the Luminosity for all the stars for which we have trigonometric parallax measurements. Find out that there is a pretty big range from down to 0.00001 .

Michael Bolte
Mon Jan 26 12:32:25 PST 1998