A SHINING STAR
What is the relationship between distance to a star and its brightness (that is the intensity of light we receive from it)? As we can see in the diagram, as we move away from a star, the radiation it emits has to cover a greater surface area. Imagine a sphere at a distance r from the star. Assuming a star is spherical and emits radiation equally in all directions the intensity of the energy at distance r over an area A will be I. If we double the distance from the star to 2r this same amount of energy is now distributed over four times the surface area, that is 4A. This means that the intensity per unit A is only ¼ the amount at r. At 3× the distance it will only be 1/9th the intensity per unit A and so forth.
Voila'! That was actually a pretty cool thing to learn.
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