1. Feb 5, 2012

### Dr.Doom

1. The problem statement, all variables and given/known data
I am trying to show that the average solar irradiance over earth's surface is 1/4 of the total solar irradiance using only calculus.

2. Relevant equations
Solar Irradiance = $S_{o}$
Irradiance = F = $S_{o}$cos(θ)

3. The attempt at a solution
Using geometry, I can easily show that the average solar irradiance is $S_{o}$/4 by multiplying $S_{o}$ by the ratio of the incident area and total surface area of a sphere:
$\frac{S_{o}*∏r^2}{4∏r^2}$=$\frac{S_{o}}{4}$

My question is how can I use calculus to show this? I was thinking that I could integrate $S_{o}$cos(θ), but I'm not sure what my integration bounds should be. I'm having trouble visualizing how I can integrate over the entire surface area of a sphere.

Any suggestions would be greatly appreciated!

 I realize this is probably not the right forum to post this question in but I don't know how to change it.

Last edited: Feb 5, 2012
2. Feb 5, 2012

### Spinnor

Googling the definition of solar irradiance your problem came up in one of the links, looks like you need to consider the rotating Earth in your problem.