Question

In the newton's universal law of gravitation, what happens if r=0? F=G(mM)/r^2.

Does the equality "r=0" has any physical significance?

Answer 1

Other forces come to dominate at very small separations (nuclear)

Answer 2

When r=0 The body are not separate, but the same.
The Law of Gravitation deals with separate bodies

Answer 3

The whole equation relates to the magnitude of the force between two point particles of mass 1 and mass 2, separated by a distance r. A separation of r = 0 implies that there is no separation between the two points, meaning that there cannot be a force between them. Mathematically, you end up with an undefined quantity for the force as you try to divide by zero. The is no physical significance in r = 0 in this case.

Answer 4

Newton's universal law suppose the mass is concentrated in one virtual point. It's absolutely not representative of the reality. So it's normal there's some problem to apply it everywhere.
Though, imagine one seconde you're in the center of Earth, at the point r=0, in a more real world (than one described by Newton) you will be in balance with all gravitation forces of all surrounding material. So the sum of forces is null (but r=0, so the force must be infinity according to the formula) but the mass can't be anymore described like a virtual point at the center of Earth.

Otherwise if you take two atoms which come near each other, there is a scale of distance where you will need to take account of others interactions (electromagnetic, nuclear force) and gravitation force is quasi-nonexistant.
And to conclude, r=0 would mean at least two particules in the same place in the space ; impossible.

Answer 5

r= 0 seems possible with, for example, two concentric spheres.