Temperature of planets from their Luminosities at specific wavelengths.

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Discussion Overview

The discussion revolves around determining the temperatures of planets based on their luminosities at specific wavelengths using Planck's equation. Participants explore the implications of the provided luminosity values and the challenges associated with calculating temperatures, particularly in the context of potential additional heat sources affecting the measurements.

Discussion Character

  • Exploratory
  • Technical explanation
  • Debate/contested
  • Mathematical reasoning

Main Points Raised

  • One participant reports obtaining negative Kelvin temperatures, which they acknowledge as incorrect, suggesting that the expected temperatures should be around 600K.
  • Another participant questions the validity of the luminosity values, particularly noting that the luminosity at 2100nm should not be lower than those at 500nm and 10000nm due to the nature of blackbody radiation.
  • Some participants propose that if there are multiple heat sources, the standard equations for determining temperature may not apply, as they would require additional parameters to be defined.
  • There is a suggestion that the reported luminosity values might be misinterpreted, possibly being orders of magnitude off.
  • One participant mentions that using spectroscopy to determine blackbody temperature could yield the temperature of the light source being reflected rather than the actual temperature of the planet.

Areas of Agreement / Disagreement

Participants express differing views on the validity of the luminosity values and the implications of having multiple heat sources. There is no consensus on the correct approach to calculate the temperatures based on the provided data.

Contextual Notes

Participants highlight potential limitations in the measurements and assumptions, such as the need for clarity on whether the luminosity values are accurate and how multiple heat sources might complicate the temperature calculations.

mystupidmouth
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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.
 
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really low as in like what? Generally a planet would have a pretty low effective temperature, I'd imagine.
 
I go negative Kelvin. Which is incorrect. The real answer for atleast two of them should be around 600K.
 
can you try to show how you tried to solve it?
 
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
 
Are those values supposed to be 10-x by chance? If so I think that would make them make sense.
 
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.
 
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)
 
  • #10
why would we need to mix temperatures? Its just trying to find the blackbody model for these values
 
  • #11
mystupidmouth said:
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?
 
  • #12
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.
 
  • #13
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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