Why is the law of the inverse square not it self the explanation for olber's paradox?

Question

I can view an galaxi that is 200,000 light years in diamiter as a speck in the night sky,thus, the law of the inverse sqeare.
I can aim a hundred flashlights at you and provided that they are at a suficiant distence you would not see so much as a pin head
of light.

Answer 1

The flux from any given source varies inversely with the square of the distance from it. But the radiant intensity (in units of watts per steradian) does not.

Olber's paradox assumes that the universe is infinite and that all space is populated with stars. In such a universe, every straight line from anywhere would sooner or later intersect a star's surface. That fact does not depend on the angular size of any particular star.

The assumptions of Olber's paradox would require that the entire sky have the radiant intensity of a stellar surface, and that would require that the temperature of space be equal to the temperature of a stellar surface.

Since that result obviously isn't factual, there must be something wrong with the assumptions in Olber's paradox.

Two of the needed adjustments are: (1) the universe is finite in space, meaning that not every line from a place intersects a star, and (2) the red shift, increasing with distance, fades the radiant intensity (the color temperature) of the luminous sources that those lines do intersect. Chief among those sources, of course, is the Big Bang, itself.

Answer 2

The inverse square law is part of Olber's paradox. While the intensity of radiation falls off as the square of the distance, the number of stars increases as the square of the distance, so the net radiation on the earth should be the sum of radiation of all the stars in the universe. Of course, this assumes a uniform distribution of stars (which is roughly true). The real resolution comes from the expansion of the universe (which reduces radiation intensity from distant stars) and the finite speed of light, which mean distant stars are older (we are looking into the past), and at far enough distance they decrease in number because fewer stars have formed.

Answer 3

<>Please explain how you relate the two. I, personally, cannot see the relationship. Coulomb's Law (Inverse Square) does not explain why the sky is dark at night (Olber's).