# Blackbody Radiation and the Inverse Square Law

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1. Aug 25, 2015

### ecastro

I am currently confused with the concept of the blackbody radiation and the inverse square law.

Planck's function for the radiation of a blackbody is in $W sr^{-1} m^{-3}$, is this somehow a form of intensity (because of the watts per square meter unit)? If it does, doesn't intensity decreases with distance, and that would mean that the radiation from a blackbody differs depending on the distance of the subject? If temperature will be calculated using Planck's function, does that mean that the temperature of the object is dependent on the distance to the object?

2. Aug 25, 2015

### soarce

It is also defined per unit solid angle, and this removes the dependence on the distance (see wikipedia for instance). I think that although the total intensity will decrease with the distance from the source, the temperature fingerprint is the shape of spectra not the intensity.

3. Aug 25, 2015

### ecastro

$I = \sigma T^4$

4. Aug 25, 2015

### soarce

Ok, I misused the term "total intensity". I was thinking of the energy received by a detector calculated as the integral over the detector area, I wasn't referring to the total intensity of the source.

5. Aug 25, 2015

### ecastro

I found out that the equation I just showed is luminosity. So, is the total intensity of the source is luminosity, or otherwise?

6. Aug 25, 2015

### soarce

I think it is luminosity, $j(T) = \int d\nu d\Omega I(\nu,T)$ and you are left with the energy radiated per unit time (power). Further you will probably need to integrate over the source area.

7. Aug 25, 2015

### ecastro

Alright. Going back to my original question, does this mean that the value of the radiation from a blackbody is independent of distance? The spectra of the Sun is the same whether here on Earth or on Mars?

8. Aug 25, 2015

### Staff: Mentor

That equation describes the spectral radiance of a surface. That is, the power emitted in watts per solid angle per wavelength per square meter.

It does not.

As best I can tell, luminosity is a term used in astronomy to refer to the total amount of energy emitted by an astronomical object like a star or planet. The equivalent SI unit is radiant flux. Intensity doesn't seem to be used by itself, but only in conjunction with another term, such as in radiant intensity.

See the full list of units here: https://en.wikipedia.org/wiki/Radiometry

Note the explanation of irradiance in the table: Radiant flux received by a surface per unit area. This is sometimes also confusingly called "intensity".

9. Aug 25, 2015

### ecastro

Thanks for the information. I will not be using the term intensity for awhile. Is there a relationship between the spectral radiance and the absolute square of an electric field (this is also sometimes referred as an intensity)?

10. Aug 25, 2015

### Staff: Mentor

That I can't answer. If you're referring to the amplitude of the EM waves emitted from the surface of the object, I'm sure there's a relationship, I just don't know what it is.

11. Aug 25, 2015

### my2cts

A perfect blackbody radiator follows Lamberts cosine law so that the surface brightness is independent on distance or viewing angle.
In general the angular extent of the emissor is distance dependent so that the energy received becomes distance or orientation dependent
https://en.wikipedia.org/wiki/Lambertian_reflectance

12. Aug 26, 2015

### GTOM

Last edited: Aug 26, 2015
13. Aug 26, 2015

### Staff: Mentor

It refers to the resolution of the prism or grating. See this link: http://hyperphysics.phy-astr.gsu.edu/hbase/phyopt/gratres.html

I believe that refers to the signal to noise ratio. For example, the NIRSpec instrument page says this: R=100 mode shall reach a limiting continuum flux of 132 nJy at 3.0 µm at S/N=10 in t=10,000 s.

I think this means that in R=100 mode, which has less resolution but concentrates light better than the R=1000 mode, a flux of 132 nJy (nano Janskys) at a wavelength of 3 microns will generate a S/N ratio of 10 in 10,000 seconds worth of exposure time.

14. Aug 27, 2015

### GTOM

Thanks. MJ radiation, i meant, a body that radiates a MJ energy in less than 10.000 second, so overall radiated energy is MJ.

15. Aug 27, 2015

### Staff: Mentor

Oh, okay. The correct phrase should be "A MJ of energy", since a megajoule is a quantity. Like a "gallon of milk" or "meter of fabric".

I don't know, honestly. Probably not very far in astronomical distances. Certainly not outside of the solar system.