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Sunlit earth

  1. Mar 3, 2010 #1
    1. The problem statement, all variables and given/known data
    At Earth’s location, the intensity of sunlight is 1.5 kW/m^2. If no energy escapes
    Earth, by how much would Earth’s mass increase in a day? (Radius of Earth is
    6.37 × 10^6 m.)

    3. The attempt at a solution

    ok so, at any one time, half of the earth is lit.

    so surface area lit = 1/2 x 4[tex]\Pi[/tex]r2 =
    2.55x1014m2

    intensity = 1500 W/m2

    so energy per second on earth = 1500 x 2.55x1014 = 3.82 x 1017 J

    energy per day = 3.82 x 1017 x 60 x 60 x 24 = 3.3 x 1022

    so E = mc2
    so m = E / c2 = 3.67 x 105 kg


    but the correct answer is half of this. so where did i go wrong? thanks for help!
     
  2. jcsd
  3. Mar 3, 2010 #2

    Doc Al

    User Avatar

    Staff: Mentor

    You are treating the light as being perpendicular to the surface area of the sphere, but it's not. The light comes in parallel. (Treat the earth as a disk, not a sphere.)
     
  4. Mar 3, 2010 #3
    ooo! thanks a lot doc! now i remembered my lecturer said this too !
     
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