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Law of Universal Gravitation?
What happens if r = 0
Yes, I see what you mean. I was pondering this question, and it seemed to me that the objects would have to exist as a singularity or something of that nature.
2 Answers
- ?Lv 51 decade agoFavorite Answer
If you consider that the bodies involved have constant density, ρ then (at least for spherical masses) M=4π/3 ρr^3
So the gravitational potential energy for a body of mass M will be
U = -GM/r = -4/3 πρr²
which tends nicely to zero as r->0
Note that this even works for non-spherical bodies since all that matters is that the mass = ρV and the volume, V, is proportional to r^3.
- Old Science GuyLv 71 decade ago
the m's in the equation are physical objects which have non-zero dimensions
for r to be zero these objects would have to be dimensionless points
so as a practical matter this cannot be
remember that r is the distance between the 'centers of mass' for the two objects, not just the distance between surfaces
mathematically, as r approaches 0, 1/r approaches infinity
so F would be infinitely large