Would an inverse-cube law obey Newton's shell theorem?

I think we have with simple proof in post 13 for all power laws (including 3) at http://www.sciforums.com/showthread...hell-theorem&p=3052484&viewfull=1#post3052484 where I show that ONLY for the inverse square law is the internal gravitational potential constant - all other power laws have gravity forces inside except at the center.

I showed that if the inverse power is less than 2 then the net force is towards the farthest point of the sphere away from the off-center point considered and conversely if power is greater than 2 net force is towards the closest point of the sphere.

I assume "3-sphere" is a hollow 3D sphere somewhat like a basket ball as that is what my proof concerned.

 

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Actually, a 3-ball (as Tach said), which is a higher dimensional analog to a sphere.

 

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In which posts was it answered?

 

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Go back through the thread, you'll find my post and BIlly T's post right after mine on page 1.

 

Zero dimensional eh? How many dimensions are in a 1-ball? How would you propose that we discuss the three points A, B and r if we're speaking in zero dimensions?

I also know the difference between my ass and a hole in the ground; neither point is relevant when disproving the following statement.

 

Yes, you can stop trolling now. Actually, you should have stopped long ago.

Based on your posts, no, you don't.

 

Only in the World of Tach is it considered trolling to prove him wrong.

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You shouldn't contradict the Supreme Tach.

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hmm, let's see

Billy T was only talking about the second half of Newton's shell theorem. Besides can we show that it is applied to 4-D space?


Just in case Tach accuses me of trolling, here's a quoteception

I don't think it's been answered. :scratchin:

 

The math says clearly that it doesn't apply inside the shell for functions different from \(1/r^2\). This means it doesn't apply, period. Why do you have so much difficulty in understanding?

 

Why do YOU have so much difficulty understanding?

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"Inside the shell" is only half of the theorem. And as I said

 

If it fails for a subcase it means that it fails , period. I take it that you flunked basic logic as well, not only trigonometry.

 

Hmm, logic and mathematics....

Are you sure? We still need the math. We can't just say "period" in an assertive tone like a boss

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And everything that does not fully agree with what you say is considered "flunking". Strict teaching. I like that.

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Yes, I am sure. If a theory has two parts and one part fails, then the whole theory fails.

You are flunking because you post nonsense.

 

Being sure doesn't really help. Perhaps rpenner can shed some light on this, since you aren't to keen on explaining.

So you say. Well you can believe whatever you want to believe.

 

It is basic textbook stuff, I suggest you suspend your posting for a while and spend the time studying.

 

Well if you are so well read then you could explain a bit more instead of "asking me to learn". It's difficult to learn what you want me to learn because you only give minimal guidance. And then you'll just say that I'm wrong. So you're just extending the process for everyone.



I think you should spend some time studying your own posts. Self-reflection.

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Theorem: "If both A and B are true then C is true".
Particular case: "If Newton Shell theorem applies to attractive functions that vary with \(1/r^p, p>2\) both inside and outside the shell, then Newton Shell theorem is true"

Study case for you: It was shown that Newton Shell theorem does NOT apply to attractive functions that vary with \(1/r^p, p>2\) inside the shell. What can be said about Newton Shell theorem in this case?

 

But first you must prove that we cannot get the first half of the shell theorem without the second half.


Doing some dimensional analysis, I do think you're right though.

 

Duh...the whole space is divided by the shell surface into two regions: interior and exterior.

 

So I guess you consider yourself a genius and/or me ignorant and dumb.

I don't think we can say "duh" when it comes to mathematical proofs, even the parallel postulate was being deeply considered by past mathematicians.



I mean, just a while ago you said