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Inverse Square Laws

© Copyright 2001, Jim Loy

On the left, we see a drawing of light from a star. The light is falling on three squares. The light gets fainter and fainter the farther it travels, because it is spreading out as it goes. When it strikes the most distant and largest square, it is much fainter than it was when it struck the much closer and smaller squares. The observed brightness (B) of the star is B=L / (4 pi d^2), where L is luminosity of the star, d is our distance from the star, and d^2 means the distance squared. If the last square is three times farther from the star than the first square, then the light that strikes it is 1/9 as bright. This is called an "inverse-square law." The brightness varies inversely with the square of the distance.

You may be familiar with Newton's Law of Gravity. This states F=GMm/(d^2), where F is force, G is the universal gravitational constant, M and m are the masses of two objects, and d is the distance between them. This too is an "inverse-square law." Gravity gets weaker with the square of the distance.

There are other inverse-square laws, dealing with electricity, magnetism, and other physical phenomena. In general, these various forces and intensities weaken with the square of the distance. In nuclear physics, the nuclear forces are not inverse square forces; their strengths decrease much more rapidly than that.

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