Question

Calculate the fraction of the total emitted sunlight that reaches Earth. (Hint: Imagine a sphere around the Sun the size of Earth’s orbit (area = 4πa2), then calculate the fraction of that area taken up by the disk of Earth (area = πr2planet). Earth's reflectivity is 29%)

Answer 1

Answer:

1.305 * 10⁻¹⁰

Explanation:

The earth disk is circular, hence the area of the earth disk is given as:

$Area\ of\ earth\ disk=\pi r_{planet}^2\\\\but\ r_{planet}=6371\ km=6371000\ m\\\\Area\ of\ earth\ disk=\pi (6371000)^2\\\\a=1.5*10^8\ km=1.5*10^{11}\ m\\\\Area\ of\ earth\ orbit=4\pi a^2=4\pi (1.5*10^{11})^2.\\\\Therefore:\\\\\frac{Area\ of\ earth\ disk}{Area\ of\ earth\ orbit}=\frac{\pi (6371000)^2}{4\pi (1.5*10^{11})^2} =4.5*10^{-10}$

This ratio represents the fraction that would be blocked if the planet did not reflect any light, hence:

fraction of the total emitted sunlight reflected by earth = 29% of 4.5 * 10⁻¹⁰ = 0.29 * 4.5 * 10⁻¹⁰ = 1.305 * 10⁻¹⁰