What fraction of the light from the Sun is intercepted by the Earth? Clearly, th

Question

What fraction of the light from the Sun is intercepted by the Earth? Clearly, this gives an upper bound to how much light the Earth reflects. To compute it, compare the cross section of the Earth (the area of a circle with radius REarth) to the area of a sphere centered on the Sun that has a radius equal to the radius of the orbit of the Earth (meaning, take the ratio of those two numbers). You can easily find sizes and distances on the Internet. Please express them in the same units to take a meaningful ratio (meter or kilometers will work best). SHOW YOUR WORK!

Explanation / Answer

You can easily calculate this on WolframAlpha, you just need to break it into 2 steps:

1. Get the surface area of the "sphere" of earth's rotation around the sun:
(surface area of sphere with radius = 1 astronomical unit)
This returns 12.5664 au^2
(1 au is the average distance between the earth and the sun.)

2. Calculate the size of Earth's "disk" (remember  [math]pi*r^2[/math]) and divide that by the above sphere's area to get your answer:
((pi*(earth's radius)^2)) / 12.5664 au^2
This returns 4.5292×10^-10

= 0.000000045292%

(This is an estimate since it ignores certain details such as the varying distance of the Earth from the Sun.)

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