This morning the weather lady on a local TV station stated there would be “tons of sunshine” today. I thought, “Really? Tons of sunshine?” Sunshine isn’t very heavy. Let’s see how much it weighs on just my state, the Commonwealth of Virginia.
The pressure of light on the ground is highest at high noon, when the sun is closest to being directly overhead. It really isn’t directly overhead – not on May 20 in Virginia. But to keep the math simple, I will assume it is. This is just an approximate calculation.
The distance to the sun is 92.96 million miles, or 149,600,000 kilometers, and a kilometer is one thousand meters. Using scientific notation, the distance to the sun is 1.496e+11 m.
Virginia has an area of 110,785 square kilometers and a square kilometer is one million square meters. Using scientific notation, Virginia has an area of 1.10785e+12 m2.
Radiation pressure is Prad = (2 x I)/c
where I is Intensity and c is speed of light (3e+8 m/s)
I = power/area = power/(4 x pi x r2)
The power emitted by the sun in the form of EM waves (visible light, infrared, ultraviolet, etc.) is 4e+26 Watts. So the intensity at the earth-sun distance is,
I = 4e+26 W/(4 x 3.14 x 2.24e+22 m2) = 1.42e+3 W/m2
Now that we have the intensity, we can calculate radiation pressure,
Prad = (2 x I)/c = (2 x 1.42e+3 W/m2)/3e+8 m/s = 9.47e-6 Newton (per m2)
(A Newton is the force required to accelerate a mass of 1 kilogram to a rate of 1 meter per second per second. 1 N = 1 kg⋅m/s2)
The force associated with the radiation pressure is Frad = Prad x A,
where Prad is the radiation pressure and A is the area receiving sunlight.
Frad = 9.47e-6 N/m2 x 1.10785e+12 m2 = 1.05e+7 Newtons
1 Newton = 0.2248 pounds so, converting from metric to avoirdupois units,
Frad = 2.36e+6 lb = 1180 tons.
It appears the weather lady was correct; we did get “tons of sunshine” today. How did she know? The weather lady must have done the math, too.
Next time she should probably simply say that we will be having a sunny day.
There’s a lot less math.
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