You cannot tell by looking at stars in the sky which ones have the greatest luminosity. The farther away (d) a star of luminosity (L) is, the less bright (B) it appears.
Light spreads out uniformly in all directions from a source so that the amount of starlight shining on a unit area falls off as 1 over the square of the distance away from the star. This relationship is called the inverse square law (Figure 3.13). The equation is: B = L/4nd2.
Our Sun is exceptionally bright because it is so close to us. If it were located 100,000 times deeper in space, how many times fainter would it look?
Answer: 10 billion times fainter, or about like the brilliant blue-white star, Sirius.
Figure 3.13. Inverse square law. The same amount of starlight that shines on a square at 1 spreads out to illuminate four equal squares at 2 and nine equal squares at 3. Thus, if two stars have exactly the same luminosity but one is twice as far away from you as the other, the distant one will look only V22 = V4 as bright as the closer one, because you get one fourth the light in your eyes.
(100,000)2 10,000,000,000 as bright (or 10 billion times fainter)
2 times as far away, % of the light
3 times as far away, % of the light
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