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Dr.Doom
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Homework Statement
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.
Homework Equations
Solar Irradiance = [itex]S_{o}[/itex]
Irradiance = F = [itex]S_{o}[/itex]cos(θ)
The Attempt at a Solution
Using geometry, I can easily show that the average solar irradiance is [itex]S_{o}[/itex]/4 by multiplying [itex]S_{o}[/itex] by the ratio of the incident area and total surface area of a sphere:
[itex]\frac{S_{o}*∏r^2}{4∏r^2}[/itex]=[itex]\frac{S_{o}}{4}[/itex]
My question is how can I use calculus to show this? I was thinking that I could integrate [itex]S_{o}[/itex]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!
[Edit] I realize this is probably not the right forum to post this question in but I don't know how to change it.
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