MadSci Network: Physics

Re: How much solar energy is directed from the sun to earth a day, in watts?

Area: Physics
Posted By: Tom Cull, Grad student Physics, Washington U
Date: Wed Jan 22 20:41:00 1997

The answer is that about 1500 WATTS per METER SQUARED hits the earth, and here is how you could calculate that:

The sun's surface is about 5800 K (degrees Kelvin). That can be deduced because the primary color of the sun is yellow. Using the Stefan-Boltzmann equation for thermal radiation THERMAL FLUX = CONSTANT * TEMPERATURE to the FOURTH POWER.

S = 5.67 x 10^-8 * T^4, where S is in WATTS/METER^2 and T is in degrees Kelvin.

If the sun's surface is 5800 K then at the surface the sun puts out 64 x 10 ^6 WATTS/(METER^2). The sun is supplying a constant amount of power (energy per time) but the POWER PER AREA DEPENDS ON THE AREA, too. The radius of the sun is about 450,000 miles and the earth is about 93 Million miles from the sun (I apologize for the mixed units but it won't matter in the end). Think of a sphere around the sun capturing the power because the power is radiating away from the sun in all directions. This imaginary sphere is the shape of the sun at the sun's surface and is 93 Million miles in radius when it hits the earth. The surface area of of a sphere is 4*PI*(RADIUS^2). So THE POWER AREA goes as 1/(RADIUS^2).

The ratio of the of the two distance is (45/9300). So the power per area is down by (45/9300)^2.

POWER PER AREA from sun at earth = (45/9300)^2 * 64 x 10^6 WATTS/(METER^2) = ABOUT 1500 WATTS/(METER^2).

ON AVERAGE, because the earth is round and rotating only 1/4 of this actually hits the earth. This of it as a ratio of a circle of the same radius of the earth which is facing the sun at any given time. The ratio of surface area of a sphere to the area of a circle of the same radius is 4 to 1.

With these numbers the calculated temperature of earth is about 44 degrees fahrenheit. The actual average temperature is closer to 59 degrees fahrenheit. The difference is accounted for by the necessary GREENHOUSE EFFECT. This is not the "evil" enhanced greenhouse effect caused by human fuel consumption.


Tom Cull

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