What is a formula for determining how much of the sun's energy reaches the earth?

Answer 1

Let's do a little math. The radius of the earth is about 4000 miles. Since area is pi(r2), the surface area of the earth exposed to the sun at any one time is about 50 million square miles.

When there is cloud cover or lots of ice, much of the solar energy is reflected back into space. Otherwise, the earth's albedo is not all that high--not nearly as high as that of Venus, and much of the energy that reaches the earth is absorbed.

Although the earth presents a surface area of 50 million square miles, we want to know what fraction of the sun's output strikes the earth's surface. So we need the area of a sphere with a 93 million miles radius (earth's average distance from the sun). That area works out to 108,686,539,000,000,000 square miles. The ratio is 4.6e-10, or 0.0000000046%. Actually, slightly less, as transits of Mercury and Venus intercept tiny fractions of the sun's output also. We don't have to concern ourselves with the outer planets, as they would never intercept energy bound for the earth. What we see is that most of the sun's output streams off into the interstellar depths.

What we need to do is erect a sphere around the sun, a big solar collector, and use all that energy for ourselves. This concept originated with a physicist named Freeman Dyson, who suggested that as civilizations progress, their energy demands increase exponentially. Just think of what we could do with cheap, abundant energy of such magnitude.

See the related question:

What_percentage_of_incoming_solar_radiation_is_reflected_back_into_space

Answer 2

Calculate the surface area of a sphere about 93,000,000 miles in radius. 4 pi r^2=Area of a sphere. Now envision a disk about 8,000(d) miles across and see how much that takes up by dividing that huge number by pi r(4000)^2=Area and seeing how small a percent that is.

Answer 3

The sun puts out energy over its whole surface the earth gets only a small fraction The ratio is (Rsun/Rdistance)^2 Radius of sun to the radius to earth squared;

(.7Gm/150 gm)^2 = 21.8E-6 is the ratio.

Answer 4

c = speed of light (300,000 km/s)

AU = Astronomical Unit (149,598,000 km)

x = Unknown

x = AU ÷ (c × 60 sec.)

x = 149,598,000 km ÷ (300,000 km/s × 60 sec.)

Answer 5

About one half of one billionth

Answer 6

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