Calculating Mass Increase of Earth in a Day Due to Solar Energy

[quietrain]

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 anyone time, half of the Earth is lit.

so surface area lit = 1/2 x 4$$\Pi$$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 kgbut the correct answer is half of this. so where did i go wrong? thanks for help!

 

[Doc Al]

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.)

 

[quietrain]

ooo! thanks a lot doc! now i remembered my lecturer said this too !