# Gravitation force

#### jobyts

If the distance between two objects is zero, won't there be infinite gravitational attraction force between them? How would the objects can get separated?

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#### Landru

Gravity is't really a force and the amount of attraction between the objects wouldn't be infinate. Gravity can be defied with relatively little force.

#### jobyts

I'm talking about F = G*m1*m2/(d^2).

If d is zero, won't the F be infinite?
Or, is there a lower limit to d between two molecules/atoms, that eventually puts an upper limit to F?

#### DaleSwanson

In the formula d is the distance between the centers of gravity. So even if two objects were touching their centers of gravity wouldn't be.

#### gendou2

jobyts said:
If d is zero, won't the F be infinite?
Congratulations jobyts, you just discovered a problem in classical physics.
When distances are very small (approaching zero in this case), you have to use quantum mechanics.
Since we don't have a working theory of quantum gravity, it's not quite clear how gravity will behave in this case.

jobyts said:
is there a lower limit to d between two molecules/atoms
Good question. In quantum mechanics, there is always uncertainty in position. With like-charged particles, the repulsive force will overwhelm all others, so the distance should never become zero. But with neutral or dissimilar charged particles, we have to consider further. When two dissimilar particles, (take proton and electron) are put together, you get an atom of hydrogen. The force of gravity cannot be infinite because the atom can be ionized (pulling the electron away). I would speculate that the uncertainty in position of the electron keeps the distance non-zero. I don't think two neutral particles (two neutrons) can occupy the same space because they are fermions, and thus obey the Pauli exclusion principle.

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#### Phrak

Congratulations jobyts, you just discovered a problem in classical physics. When distances are very small (approaching zero in this case), you have to use quantum mechanics.
That's wouldn't be necessary, nor asuccessful endeavor, without a theory of quantum gravity. It would be sufficient, to eliminate infinites, that mass density be finite.

I don't know of any infinitely dense masses. Newtonian gravity will suffice in avoiding infinities in force and energy, in this case, if you don't assume infinite densities as a premise.

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#### gendou2

Phrak said:
It would be sufficient, to eliminate infinites, that mass density be finite.
Good point, Phrak.
Have the mass density of the fundamental particles been measured?
I have seen fundamental particles treated as point-like particles of infinite density.
I suspect this is not how they really are, and that they should have finite density.
Also, it would be interesting to find out wether the charge density looks like the mass density (for particles that have charge).

Phrak said:
I don't know of any infinitely dense masses.
The singularity in a black hole? :)

EDIT
I just learned that the charge density distribution of the neutron is not constant zero.
So, in testing gravity between two particles approaching zero distance using protons, electrons, or even neutrons, the electromagnetic force will overwhelm the experiment.
http://www.terra.es/personal/gsardin/news13.htm

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#### Phrak

Good point, Phrak.
Have the mass density of the fundamental particles been measured?
I have seen fundamental particles treated as point-like particles of infinite density.
I suspect this is not how they really are, and that they should have finite density.
Also, it would be interesting to find out wether the charge density looks like the mass density (for particles that have charge).

The singularity in a black hole? :)
I missed that one. (But is the map the territory?)

That's not a bad question. In quntum mechanics, a measurement can localize a particle's postion, but does locaize it's mass?

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