Temperature of planets from their Luminosities at specific wavelengths.

[mystupidmouth]

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.

 

[SHISHKABOB]

really low as in like what? Generally a planet would have a pretty low effective temperature, I'd imagine.

 

[mystupidmouth]

I go negative Kelvin. Which is incorrect. The real answer for atleast two of them should be around 600K.

 

[SHISHKABOB]

can you try to show how you tried to solve it?

 

[Chronos]

Space based infrared telescopes, in particular Spitzer, have managed to take direct measurements of the temperature of exosolar planets - e.g., http://www.spacedaily.com/reports/Spitzer_Takes_Temperature_of_Closest_Exoplanet.html and http://www.sfgate.com/news/article/Scientists-measure-temperature-of-distant-2468253.php

 

[willem2]

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

 

[Drakkith]

Are those values supposed to be 10^-x by chance? If so I think that would make them make sense.

 

[mystupidmouth]

No, those are definitely the correct values.
There is supposed to be abnormality in the temperatures as there's an extra heat source on the planet.

 

[Drakkith]

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)

 

[mystupidmouth]

why would we need to mix temperatures? Its just trying to find the blackbody model for these values

 

[Drakkith]

why would we need to mix temperatures? Its just trying to find the blackbody model for these values

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?

 

[mfb]

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.

 

[Chronos]

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].