Could Zero Distance Create Infinite Gravitational Force?

[schaefera]

If the separation between two objects (say, me and my chair) is zero, shouldn't the gravitational force between those two objects be infinite because in the equation for force you divide by r?

And I understand that the centers of my atoms are not literally touching the chair, so maybe the separation is miniscule... but as they get so close that they are only TINY distances apart, the gravitational force should at least APPROACH infinity? But this seems to defy logic...

 

[Curl]

They are tiny distances apart but the mass of those atoms is also tiny and the gravitational constant is also tiny, so you get a tiny number.

 

[schaefera]

Ok well take the mass of my foot and the mass of the ground with which it is in contact. Shouldn't this be a magnificentally large force?

 

[HallsofIvy]

The gravitational force between two extended (not point) masses is
$$\frac{GmM}{r^2}$$.

where r is the distance beween their center of masses. For your body and the earth, that is a very large distance.

If you want to calculate forces between, say, atoms that are very close together then you have to deal with those very, very small masses at very small distances.

 

[schaefera]

So would this be an example of the equations of classical mechanics breaking down when you get to quantum levels?

 

[Curl]

Ok well take the mass of my foot and the mass of the ground with which it is in contact. Shouldn't this be a magnificentally large force?

No, only a few atoms are close to the ground, the rest aren't.

 

[gomunkul51]

It's simple: Newton's Law for gravitation brakes down when you look at very small distances. Greetings! you're entering the realm of Quantum effects.
As do Newton's Laws of motion brake down when you travel at velocities close to the speed of light. Say hello the world of Relativity! :)