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Temperature of planets from their Luminosities at specific wavelengths.

  1. Oct 17, 2012 #1
    Hi!
    I have worked on this for a while and cannot seem to get a reasonable answer.

    I have been given the Luminosities of planets at different wavelengths and I need to determine the Temperature.
    I re-arranged planck's equation to find T but I keep getting really low temperatures

    Planet A
    Wave length : 500nm Luminosity 6.43*10^22Wnm
    2100nm 1.07*10^14Wnm
    10000nm 3.99*10^14Wnm

    Planet B
    Wavelength 500nm Luminosity 1.97*10^12
    2100 9.47*10^9
    10000nm 8.51*10^11

    Any input would be very much appreciated.
     
  2. jcsd
  3. Oct 17, 2012 #2
    really low as in like what? Generally a planet would have a pretty low effective temperature, I'd imagine.
     
  4. Oct 17, 2012 #3
    I go negative Kelvin. Which is incorrect. The real answer for atleast two of them should be around 600K.
     
  5. Oct 17, 2012 #4
    can you try to show how you tried to solve it?
     
  6. Oct 17, 2012 #5

    Chronos

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  7. Oct 17, 2012 #6
    These numbers can't be right, The number for 2100nm can't be lower than both both the 500nm and 10000nm numbers, because the distribution has 1 maximum and goes to 0 as the wavelength goes to 0 or infinity, so at least one of the numbers must be wrong for both planets.

    6.43 * 10^22 Wnm seems very large for something planet sized
     
  8. Oct 17, 2012 #7

    Drakkith

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    Are those values supposed to be 10-x by chance? If so I think that would make them make sense.
     
  9. Oct 17, 2012 #8
    No, those are definitely the correct values.
    There is supposed to be abnormality in the temperatures as theres an extra heat source on the planet.
     
  10. Oct 17, 2012 #9

    Drakkith

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    Well if you have a mix of two emitting objects at different temperatures, and you are unable to separate the signal from them, I don't think you can use the normal equation. Isn't that just for one object at one temperature? (This coming from someone who hasn't ever done the math, I am just guessing)
     
  11. Oct 17, 2012 #10
    why would we need to mix temperatures? Its just trying to find the blackbody model for these values
     
  12. Oct 17, 2012 #11

    Drakkith

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    You said there was an extra heat source. Wouldn't you then have one temperature from the planet, and one from the heat source mixed together?
     
  13. Oct 18, 2012 #12

    mfb

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    With a single heat source, you have 2 degrees of freedom - temperature and overall brightness (which corresponds to the solid angle the source has in the sky). With two heat sources, you have 4 degrees of freedom, so you cannot determine all parameters based on 3 measurements. You can assume that both heat sources have the same area and emittance, but that looks a bit odd.
     
  14. Oct 18, 2012 #13

    Chronos

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    If you try to get a blackbody temperature using spectroscopy, you will end up with the blackbody temperature of the light source being reflected [i.e., the host star].
     
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