How to find the intensity of radiation

[zaf]

Hello Forum members

I need help on a homework problem that I am unable to solve. the problem is as follows

Given the radius of a star of 9.0 * 10^3 m and surface temperature of
10000 k (blackbody)find the intensity of radiation (watts/m^2) incident on a planet that is located 2.4 * 10^11 m from the star

I found the total power radiated from the star by using stefans and taking the area to be 4 pi r^2 so P = sAeT^4

s is the stefan-boltzman constant
and e is emissivity of 1 for a blackbody

then I could also find the brightness for that star as seen from another planet 2.4*10^11 m away from the star by using

b = P / (4*pi*d^2)

d being the distance...but i do'nt think that this is the answer

can someone help ?

 

[HallsofIvy]

I'm no great physicist but I don't see how you can answer the question without know what portion of the star's "sky" the planet subtends. That's is a really large planet will intercept more of the stars total radiation (which is what you have calculated) than a small planet will.

 

[zaf]

I understand your response...but i guess that issue has not been taken into consideration by the prof...basically it is know that the intensity of radiation is inversely propotional to the distane...I need to somehow incorporate that in my solution

 

[Claude Bile]

Originally posted by HallsofIvy
I'm no great physicist but I don't see how you can answer the question without know what portion of the star's "sky" the planet subtends. That's is a really large planet will intercept more of the stars total radiation (which is what you have calculated) than a small planet will.

This statement is correct, however notice that the question asks for the intensity, not the total power. The intensity of an isotropic radiator, such as a star will be uniform for a given distance, d.

I see no problem with how the problem is worked out, other than you suddenly switch to solving for the brightness (all the equations are still correct, just need to replace b with I (Intensity).

Claude.

 

[zaf]

Ok..maybe you are correct...but i am not so sure whether brightness and intensity mean the same thing...brightness is a measure of the maximum wavelength of the color spectrum of a star...intensity is the measure of energy.

 

[arcnets]

I think intensity = energy per time per surface area.
Or power per surface area.
So your original answer is OK, I think.