## Calculation of the Earth's Effective Temperature.

The effective temperature of a planet is the temperature it would have if it acted like a black body, absorbing all the incoming radiation received at its surface and reradiating it all back to space.

With the following facts you can easily calculate the effective temperature of the Earth and, if you know the distance to the other planets, their effective temperatures as well.

Distance from Earth to Sun = 150x106 kilometers.
Radius of the Sun = 6.96x108 meters.
Radius of the Earth = 6.4x106 meters.
Surface area of a sphere = 4pr2.
Area of a circle = pr2.
p = 3.1416.
Maximum output from the Sun occurs at a wavelength of 0.5 microns.

Lets walk through the steps together:

1. Since we know the wavelength of the Sun's maximum output, we can use Wein's law to calculate the Sun's temperature. Go ahead and do it. You should get a number near 5796 K. For convenience you can round this off to 5800 K.

2. If we know the Sun's temperature, we can calculate the intensity of the solar output (I, flux per square meter), by using the Stephan Boltzman equation. Go ahead and calculate it. (To calculate the fourth power of a number with your hand calculator square it twice.)

3. To calculate the Sun's total output (total flux or luminosity, L) we must multiply the intensity (I, flux per square meter) by the total number of square meters on the Sun's surface. Use the radius of the sun and the equation for the surface area of a sphere, given above, to do this.

4. Now, since energy is conserved, any sphere of any radius with the Sun at its center will receive the same total radiation from the Sun as is emitted from the Sun's surface. Therefore the intensity of solar radiation at the Sun-Earth distance is related to that distance by the intensity to distance relationship you learned about earlier.