h2g2 The Hitchhiker's Guide to the Galaxy: Earth Edition

So as a result objects can't touch, ie have a seperation of 0, because it isn't possible to divide by 0^2...

define touching. A distance of 0 would only be conceivable in a singularity. Otherwise stuff is separated (by electron shells, nuclei etc..)

Isn't "r" (radius between objects) measured from the centre of mass rather than the distance between the objects. Which raises the interesting idea of an object which has a centre of mass outside its own volume (an easy example to picture, a horseshoe), which space can then be occupied... again giving a distance for r of 0.

I know that this does not occur, but I believe it is an implication of the theory, if applied to objects rather than particles.

Math

No r is the distance between the object here.

Newton's law is no long valid for very small r, this awaits a (as yet unwritten) law for quantum gravity.

In practice when two objects move together the nuclear and electromagnetic forces between atoms are much stronger than gravity and keep them apart.

Really... I doubt it but lets test this idea of yours...

1kg mass being held 1m above the earth's searface.

F=(G * M1 * M2)/r^2

F=(6.67*10^-11 * 6*10^24 * 1)/1

now I don't have a calculator to hand (and being in work its not installed as that would be useful...) so I'll just give an approx answer.

F=6.67*6*10^13

F=4*10^14
F=400,000,000,000,000

Which is obviously inaccurate...
the answer should be closer to 10.

I believe this demonstrates quite amply that it is the centre of mass which has to be taken into account.


Now perhaps we can consider the case I put forward of ojects for which the centeer of gravity is not within its own volume.

Sorry, misunderstanding there

I thought you were refering to the distance from an object to the centre of mass of the 2 body system (which is used in some equations).

But you're quite right, it's the distance between the centres of mass of each objects.

No problem , I just reread that and I apologize for the tone which could have been more polite .

Math

...may I interfere?

Well, in your question you were talking about touching... that's why I asked about your definition of 'touching'. If you just mean 'coinciding with centre of mass' then we have something different than the nuclar repulsion stuff I was mumbling about.

About your horseshoe (interesting example BTW)... I guess we mustn't dive into quantum gravitation to think about an abswer to your proposition. It's easier than it seems, actually. In the centre of mass of a horseshoe you would have some kind of equilibrium of forces, a whole complicated shape dependent non-spheric field of gravity is in there, which is probably something that the equation does oversimplify. I think, that the given equation is only valid for vaguely spheroidical things that are separated by a radius r. Furthermore I think, that by definition a radius must have a value >0, otherwise it would be a point... Maybe this should have been mentioned in the Entry that the equation is just a very rough simplification that works most of the times, except if you are sitting on a horse-shoe shaped planet with a moon right in it's centre of mass.


HELL

Well said Hell, certainly seems to make sense to me

Math

HELL