1. Not finding help here? Sign up for a free 30min tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

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:
    [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.
     
    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.
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook




Similar Discussions: Average Solar Irradiance
  1. Radiance, Irradiance? (Replies: 1)

Loading...