1. Limited time only! Sign up for a free 30min personal 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!

Energy from the Sun received at the Earth cross section

  1. Jan 18, 2017 #1
    1. The problem statement, all variables and given/known data

    My homework involves calculating the amount of energy the Earth receives from the Sun in a given year. I actually have the answer, but what I'm confused with is that the calculation says that the Sun "sees the cross section of the Earth, a circle". So in the calculation, we multiply the energy per square meter received at 1AU by pi*R^2 (R is the radius of the Earth).

    Why isn't it multiplied by half of the surface area of Earth? I picture half of the Earth facing the sun as the surface receiving the energy. So I would think to multiply by 2*pi*r^2.



    2. Relevant equations


    3. The attempt at a solution
     
  2. jcsd
  3. Jan 18, 2017 #2

    BvU

    User Avatar
    Science Advisor
    Homework Helper
    Gold Member

    Hi.

    ##\pi r^2## is the area of a circle. That's what the sun 'sees'.

    You seem to be thinking of half a sphere, but then
    1. a sphere has area ##{4\over 3} \pi r^2##
    2. the angle of incidence has to be corrected for -- which brings you back to ##\pi r^2##
    Make a little sketch showing this angle of incidence

    Or check the shadow of a sphere on a wall !
     
  4. Jan 18, 2017 #3

    haruspex

    User Avatar
    Science Advisor
    Homework Helper
    Gold Member
    2016 Award

    Because the Sun doesn't care what shape the Earth is. It sends out the same power per unit solid angle in all directions. The power the Earth gets is proportional to the solid angle it subtends at the Sun.
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Have something to add?
Draft saved Draft deleted



Similar Discussions: Energy from the Sun received at the Earth cross section
  1. Energy from the sun (Replies: 2)

Loading...