How Does Radiation Intensity from a Star Change with Distance?

[stunner5000pt]

but somehow my brain is not working...
how does the intensity of radiation emitted by a star (but really any hot sphere, really) vary with distance from the star?

at the surface the intensity is
$$I = 4 \pi \sigma T^4 R_{star}^2$$

as we move away
$$I = 4 \pi \sigma T^4 (R_{star} + r)^2$$ where r is the distnace from the star to some point.

is that how the intensity varies?
Square of the sitance from the center of the star?

 

[finchie_88]

I think the equation that you want might be $$I = \frac{I_0}{4 \pi r^2}$$, but I'm not entirely sure if that is what you are looking for.

 

[Meir Achuz]

but somehow my brain is not working...
how does the intensity of radiation emitted by a star (but really any hot sphere, really) vary with distance from the star?

at the surface the intensity is
$$I = 4 \pi \sigma T^4 R_{star}^2$$

as we move away
$$I = 4 \pi \sigma T^4 (R_{star} + r)^2$$ where r is the distnace from the star to some point.

is that how the intensity varies?
Square of the sitance from the center of the star?

$$I = 4 \pi \sigma T^4 R_{\rm star}^4/ (R_{star} + r)^2$$