The inverse square law

[Walter Wayne]

Walt,

But why doesn't gravity act directly along a line joining the two objects rather than disperse through a surface?
Or why doesn't it disperse throughout the volume of the sphere rather than just through its surface?

I don't know what you mean by act directly along a line this, appears to me to be exactly how gravity acts. If you draw a bunch of lines straight out from a source point on a piece of paper, you notice that close to the source, the lines are close togethor (dense) and away from it they are further apart (sparse). So the same object close to the source intersect more lines than a distance. If you could draw this in three dimensions you would not that the density of lines from the source was proportional to the inverse square.

Walt

 

[T'ai Chi]

Because God said so?

I'll buy that.

 

[Jimmy]

I don't know what you mean by act directly along a line this, appears to me to be exactly how gravity acts. If you draw a bunch of lines straight out from a source point on a piece of paper, you notice that close to the source, the lines are close togethor (dense) and away from it they are further apart (sparse). So the same object close to the source intersect more lines than a distance. If you could draw this in three dimensions you would not that the density of lines from the source was proportional to the inverse square.

Walt

And I'll buy that. I think that's as good an explanation as any.

 

[Jimmy]

Jimmy: Because God said so?

I'll buy that.

I think there is great wisdom in the idea that God helps those who help themselves.

 

[BillyJoe]

I understand what everyone is saying and I agree with it all but somehow my point is not getting through.
All I am saying, and I assume everyone agrees, is that science describes. It doesn't explain.

Walt,

I don't know what you mean by act directly along a line.

I am trying to illustrate how gravity could decrease in proportion to d rather than d². Rather than lines of force radiating out from the source and therefore decreasing in proportion to d², I am imagining a direct body to body interaction along a line joining them so that the force decreases in proportion to d. I know this is not how it is in our universe but am I wrong in thinking that, in an alternative universe, this could be the case. Similarly, in another universe, gravity could decrease in proportion to d³. In this case our chart could illustrate this by showing how volume increases with distance

In any case, we have already established that d² is only an approximation and hence the so-called explanation cannot be an explanation at all. We can only ever have descriptions or models of gravity (in this case Newton's model of gravity).

Am I winning?

BillyJoe

 

[Iamme]

More posts, in such a short time, than I ever imagined. Can't respond to all at this time. I think poster "Till" summed up your thoughts. He says:

Man there's some cool " magic numbers" that will give you a mind cramp. The existances of such quantities give rise to the " it MUST be by design" senerio. Bottom line ? This stuff is cool ...Pi, e, perfect squares 3,4,5, primes, theres a suitcase full and in our effort to ascribe order to the universe we find them tickleing our imagination..ask a Math guy they have DEEP stories to tell.

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Yes. That indeed has been my thinking. And, the Pythagrean(sp.) theorum, and even the fact that E=MC2. That thing about squaring or inverse squaring something, and having it come out EXACT is very intiguing to me.

Since non-believers claim that we can't "prove" God's existance (although deeply religious people claim they see proof all about us)...the fact that math has such formulations as this shows there is an exacting order which maybe proves no more to some of you the possibility of God, than does how it 'just so happens' that both during a solar and a lunar eclipse...the host object gets PERFECTLY eclipsed. A sign from God...like the rainbow? Well...to say such stuff is what causes many to say that they refuse to argue religion (and politics).

 

[Dancing David]

Lamme ,
I may or may not agree to god, depending on the day of the week, but the universe is a wonder to behold. I finf that the coolest thing we observe is isotropy, the laws seem to apply the same very where.

 

[69dodge]

Originally posted by Walter Wayne
Suppose that we have a source which radiates power uniformly. [. . .] Then look at the relation between energy and force. They are proportional.

I'm not entirely sure what you mean, but it seems like you're saying the inverse square law of gravity follows from energy conservation. That's not right. Any central force that depends only on distance is a conservative force. (Some noncentral forces are conservative too.) Nuclear forces do not obey an inverse square law, but they do not violate conservation of energy.

It is convenient that a force obeying an inverse square law can be represented by continuous field lines whose density is proportional to the field strength, but I don't think that fact qualifies as any sort of ultimate explanation. There is nothing inherently self-contradictory about a force that obeys a different law; we would simply have to find some other way to represent it.

(You talk about radiation of power. Newtonian gravity, which is the kind that obeys an inverse square law, doesn't radiate. Perhaps you were actually thinking about electromagnetic radiation? The field in an electromagnetic wave isn't really analogous to a static gravitational field.)

 

[scribble]

than does how it 'just so happens' that both during a solar and a lunar eclipse...the host object gets PERFECTLY eclipsed.

You must be damn lucky to live someplace where all eclipses are perfect. As far as I know, there's no place on Earth like that.

A sign from God...like the rainbow?

Last time I checked, a rainbow was caused by diffraction. Did I miss something?

Well...to say such stuff is what causes many to say that they refuse to argue religion (and politics). [/B]

You're very difficult to comprehend.

 

[69dodge]

Originally posted by Iamme
it 'just so happens' that both during a solar and a lunar eclipse...the host object gets PERFECTLY eclipsed.

The sun and moon appear from the earth to be approximately the same size, so solar eclipses are sometimes "perfect." But during a lunar eclipse, the diameter of the earth's shadow on the moon is much larger than the diameter of the moon.

Of course, if you look at the moon only when it's completely in shadow, there's no way to see this. Provided the earth's shadow is at least as big as the moon, you'll just see a dark moon, regardless of how much bigger the shadow might be. But, when the moon is partially shadowed, you can see the size difference .

 

[jj]

Right, but why an inverse, and why inverse square?

It would help if you indicated what you don't undestand. Do you nderstand that the area of a 3D shape grows as r^2, and that since it grows as r^2, whatever is coming from the middle obviously has a density of 1/r^2 as a function of 'r'.

(Note, you can set an "r" even for non-conic shapes, you just have to express the shape as an appropriate function. Such a shape will still have an area that scales as "r^2" in 3 spatial dimensions unless you venture into the bizzare mathematical, at least. (I'm not sure I know of such a shape, but I'm not sure that by using some kind of fractal or infinite shape one could not make such a thing. Such a thing, however, would be non-physical.)

 

[jj]

Here's an interesting link I ran across:

Inverse Square Law

I'm not sure I agree with everything that is mentioned, however.



Considering that GR works very well using four dimensions and the inverse square law is a good approximation of how gravity works, something seems flawed with this assertion. *shrug*

It would help if you were more specific.

You would mean x, y, z, t? Three spatial and one time? That's your answer, right there.

 

[69dodge]

Originally posted by jj
It would help if you indicated what you don't undestand. Do you nderstand that the area of a 3D shape grows as r^2, and that since it grows as r^2, whatever is coming from the middle obviously has a density of 1/r^2 as a function of 'r'.

Yes, if whatever is coming from the middle is conserved. But gravitational force is not a conserved substance that travels outward from a massive object. The gravity at a location distant from the object has not travelled there from the object after passing through locations nearer the object; the nearby locations still have their own gravity.

(This refers to Newtonian gravity. It's true that in general relativity, gravitational effects propagate at the speed of light instead of instantaneously, but on the other hand, GR's gravity doesn't obey (exactly) an inverse square law.)

 

[Iamme]

scribble says:

You must be damn lucky to live someplace where all eclipses are perfect. As far as I know, there's no place on Earth like that.
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I must be lucky then. We recently had a lunar eclipse. iI was darn near perfect here. I remember years ago, seeing my first solar eclipse through the little hole you make in paper. It was also perfect. All you could see was the ring of fire, barely, and equally, around the rim of the sun.

Think about this once: If you have 3 objects that sooner or later come into an alignment with each other...and one gives off light, so that a shadow is cast; what is the odds that that shadow cast will be the same size as the object it is cast upon?(If you yourself did not predetermine the objects sizes nor their relative distances from each other.) The distances AND the objects have to have the right size, for this to occur.

Now I suppose a skeptic could simply say, "So what? This doesn't prove that this happened by design. It could simply be a matter of..that it is. It is, because it is. If it wasn't this way...would we think any less of our universe? (Sort of like asking ourselves if we think any less of our forests because the trees are not in perfect rows)." But...because it *IS* perfect, geometrically, to have this occur, just as there is order out of chaos to have it just so happen that there is inverse square properties....it causes someone like myself to contemplate if this is just all random chance, or stems from some sort of order caused by a designer.

We haven't touched on crystral formations yet, have we?

 

[CurtC]

If you consider a line source instead of a point source, the strength of a field drops off as 1/d. The "inverse law" I guess. Does this disprove the existence of god? (by the way, the link in the OP seems to not be working - it times out for me, so I can't really read what is so mystifying about the inverse square law.)

 

[jj]

Yes, if whatever is coming from the middle is conserved. But gravitational force is not a conserved substance that travels outward from a massive object. The gravity at a location distant from the object has not travelled there from the object after passing through locations nearer the object; the nearby locations still have their own gravity.


I see your objection but I also find it pretty much irrelevant.

Gravity doesn't get used up, so what's the problem?


(This refers to Newtonian gravity. It's true that in general relativity, gravitational effects propagate at the speed of light instead of instantaneously, but on the other hand, GR's gravity doesn't obey (exactly) an inverse square law.)

In what frame?

 

[jj]

If you consider a line source instead of a point source, the strength of a field drops off as 1/d. The "inverse law" I guess. Does this disprove the existence of god? (by the way, the link in the OP seems to not be working - it times out for me, so I can't really read what is so mystifying about the inverse square law.)

And if you have a plane source, ...

Then, CurtC, you could ask him about a dipole, a quadrapole, etc, if you want...

 

[69dodge]

Originally posted by jj
Gravity doesn't get used up, so what's the problem?

I'm not sure what you mean. There's no problem with gravity following an inverse square law. But neither would there be any problem if it didn't.

 

[BillyJoe]

....and BillyJoe, struggling at the end of the line, passes the golden baton to 69dodge who strides towards the finish line....

 

[bjornart]

Think about this once: If you have 3 objects that sooner or later come into an alignment with each other...and one gives off light, so that a shadow is cast; what is the odds that that shadow cast will be the same size as the object it is cast upon?(If you yourself did not predetermine the objects sizes nor their relative distances from each other.) The distances AND the objects have to have the right size, for this to occur.

Now I suppose a skeptic could simply say, "So what? This doesn't prove that this happened by design. It could simply be a matter of..that it is. It is, because it is. If it wasn't this way...would we think any less of our universe? (Sort of like asking ourselves if we think any less of our forests because the trees are not in perfect rows)." But...because it *IS* perfect, geometrically, to have this occur, just as there is order out of chaos to have it just so happen that there is inverse square properties....it causes someone like myself to contemplate if this is just all random chance, or stems from some sort of order caused by a designer.

We haven't touched on crystral formations yet, have we?

I can do better than that. The moon started out much closer, it's moving outwards. Orbital mechanics make it more likely that the orbit of the moon around the earth ended up in the same plane as the earth's around the sun. Hence, for a period of time solar eclipses are perfect. That we, instead of the dinosaurs, are around to see them is just coincidence. And anyway not all solar eclipses are perfect, there's also annular eclipses, which will in time be the only kind.
So it isn't perfect, and God hasn't managed to put any bodies in "perfect" circular orbits either. He do that and I'll believe.