# Temperature of planets from their Luminosities at specific wavelengths.

1. Oct 17, 2012

### 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.

2. Oct 17, 2012

### SHISHKABOB

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

3. Oct 17, 2012

### mystupidmouth

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

4. Oct 17, 2012

### SHISHKABOB

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

5. Oct 17, 2012

### Chronos

6. Oct 17, 2012

### 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

7. Oct 17, 2012

### Drakkith

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

8. Oct 17, 2012

### mystupidmouth

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.

9. Oct 17, 2012

### Drakkith

Staff Emeritus
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. Oct 17, 2012

### mystupidmouth

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

11. Oct 17, 2012

### Drakkith

Staff Emeritus
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. Oct 18, 2012

### Staff: Mentor

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. Oct 18, 2012

### 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].