We all know that gravitation force between two small (not heavenly) bodies is negligible. We give a reason that their mass is VERY small. But according to inverse square law, as r→0, then F→∞. But in real life we observe that even if we bring two objects very close, no such force is seen.
Why is this so?
Answer
The inverse-square law holds for spherically symmetric objects, but in that case the main problem is that r is the distance between their centers. So "very close" spheres are still quite a bit apart--r would be at least the sum of their radii.
For two spheres of equal density and size just touching each other, the magnitude of the gravitational force between them is F=GM2(2r)2=49Gπ2ρ2r4, which definitely does not go to infinity as r→0 unless the density ρ is increased, but ordinary matter has densities of only up to ρ∼20g/cm3 or so.
Tests of Newton's law for small spheres began with the Cavendish experiment, and this paper has a collection of references to more modern 1/r2 tests.
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