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Homework Help: Average Solar Irradiance

  1. Feb 5, 2012 #1
    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 = [itex]S_{o}[/itex]
    Irradiance = F = [itex]S_{o}[/itex]cos(θ)

    3. 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:

    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.
    Last edited: Feb 5, 2012
  2. jcsd
  3. Feb 5, 2012 #2
    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.
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