# Gravity force on zero distance

1. Apr 1, 2004

### deda

How much will be the gravity force between two weights each of which with 1 kg at zero distance? If you ask Newton the answer will unconditionally be infinity but Archimedes would say extreme for sure but not necessary infinite.

Here is why: The force in Archimedes’s physics is more like geometrical potential the body has. Geometrical potential is sort of storage for the geometrical distance form the center yet to be achieved. Now lets begin from the end i.e. let the weights be on zero distance (in the center of the lever). Now if you arm each weight with 1 N in opposite direction the weights wont end in infinity but their extreme distance i.e. the distance when all the force is exhausted will be finite. Now arm them with 2 N per each. When they combust that force they’ll achieve twice longer distance than before. So, the only case of having infinite force at zero distance is when they were released from infinite distance with zero force.

2. Apr 1, 2004

### Antonio Lao

The combination of infinity and zero pop-up frequently in calculations. It is agreed that

infinity over zero is infinity.

zero over infinity is zero.

infinity is the inverse of zero and vice versa.

But the is the product of infinity and zero a finite quantity?

3. Apr 1, 2004

### mathman

To completely satisfy the Newton paradox, the weights would both have to have zero volume and thus be of infinite density. It won't happen!

4. Apr 2, 2004

### Michael D. Sewell

$$F = Gm_1 m_2/r^2 = G m_1 m_2/0^2$$

This equation makes no sense. The answer is not zero. The answer is not infinity. It is undefined, there is no answer, because it is not a legitimate situation.

Last edited by a moderator: Apr 3, 2004
5. Apr 2, 2004

### chroot

Staff Emeritus
Zero distance is unphysical. No one ever said physical laws should have to produce sensible answers in unphysical situations.

- Warren

6. Apr 2, 2004

### deda

It is again the traditional way of doing physics that cosider the basic matter quanta solid so at it's center there are two sequences of that basic quanta that can be considered at zero distance.

I don't believe anybody understood what my original post is all about.

7. Apr 2, 2004

### Antonio Lao

deda,

Aren't you trying to define or "finitize" the product of infinity and zero? Maybe a mathematician can help you? There seem to be a lot of knowledgeable math experts in this forum.

8. Apr 2, 2004

### Michael D. Sewell

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