Sunlit earth

  • Thread starter quietrain
  • Start date
  • #1
655
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Homework Statement


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.)

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!
 

Answers and Replies

  • #2
Doc Al
Mentor
45,379
1,758
but the correct answer is half of this. so where did i go wrong? thanks for help!
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.)
 
  • #3
655
2
ooo! thanks a lot doc! now i remembered my lecturer said this too !
 

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