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I Calculated solar irradiation not matching up with measured

  1. Mar 24, 2016 #1
    Hi all! I'm trying to build up a solar model, using real-world data where available, and filling in the weak low and high frequency extremes of the spectrum with a simple blackbody curve. All well and good. But when I apply Planck's law to the known data it goes awry!

    Here's what I'm working with.

    Effective radius of the sun's radiating surface: said to be about 7,00e8m
    Blackbody temperature of the sun: Said to be 5778
    Earth distance to the sun: 149597870700m
    Calculated radial angle: 9,36e-3 (actual said to be 9,35 - so far, so good)
    Calculated steradians: 6,88e-5 (actual said to be 6,87e-5 - again, so far so good).
    Misc constants:
    Planck: 6,6260700400E-34
    Speed of light: 299792458
    Stefan-Boltzman: 1,3806485200E-23

    ... that is, staying with SI units.

    Okay, now we get to planck's equation (in terms of wavelength). When I apply it first to short wavelengths - say, 280nm - I come up with 9,5045e12 W/m^2/sr (6,5377e-1 W/m^2/nm). Actual reported:


    ... is said to be 8,2000e-2 W/m^2/nm. Okay, my value is significantly higher, but that's not necessarily a problem because the sun isn't a perfect blackbody, there's plenty of gaps. As I start going to longer wavelengths, the numbers start to converge toward a perfect blackbody, and then.... the real-world power figures *pass* the calculated figures! For example, at 495nm the real-world spectrum is 2,0510e0 W/m^2/nm, but I calculate that a perfect blackbody would emit 1,8135e0.

    Obviously the real-world should never be higher than the calculated! So something's wrong here. What do you think the problem might be?
  2. jcsd
  3. Mar 24, 2016 #2
    Wait, never mind, I've got it; that figure is just an apparent temperature, not an actual temperature; it's based on how hot a blackbody would have to be to emit the same amount of energy. So since some areas will be under the ideal blackbody curve, some areas have to be over for the total energy represented to match up with the equivalent blackbody.

    Okay, good, I didn't mess up my equation setup. :)
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