I'm trying to calculate the amount of power from the sun hitting the earth, but I am getting a number which is off by a factor of ~4.
I calculate the "area" of the earth, as seen from the sun, and then divide that by the surface area of a sphere of radius 1 AU, to get the portion of the sun's rays we absorb, and then I multiply that by the solar luminosity.
Mathematica gives me this:
![\text{UnitConvert}\left[\frac{\pi \text{Quantity}[\text{AstronomicalData}[\text{Earth},\text{Diameter}],\text{m}]^2}{4 \pi \text{Quantity}[1,\text{astronomocal units}]^2} \text{L}_{\odot },\text{W}\right]](https://i.sstatic.net/516fe.png)
But when I put it into Wolfram|alpha, I get this result:
Am I doing something wrong? where could that big an error be introduced? Is "mean power intercepted by earth" different than what I'm calculating?