Infinite Flat Plane Pull

Since there was some confusion, I decided to repost this for discussion.  I have verified that this is a legimate solution a number of places.  I am open to argument though.   Since it is a 2d problem, density refers to surface density.  If anything else needs clarification, please let me know.




Edit: New location:

I guess no one had an issue with it afterall.

Wrong.

1) It's not a 2-d problem.

2) Quote your sources.

3) Name all your parameters.

4) Units would be nice too.

5) State your objectives.

For reason 2 alone I won't read further.

There is a better, step by step explanation here:
http://www.pgccphy.net/1030/gravity.pdf

Wrong.

1) It's not a 2-d problem.

2) Quote your sources.

3) Name all your parameters.

4) Units would be nice too.

5) State your objectives.

For reason 2 alone I won't read further.

When is a plane not 2d?
Carl Friedrich Gauss, 1835
What parameters did I not name?
Use any units that fit.
My object was to get from (1) to (4).

When is a plane not 2d?

First of all, even if the Earth is flat, it wouldn't be a plane. Because it would be 3d.

http://i34.tinypic.com/9hs6mx.jpg

http://i34.tinypic.com/9hs6mx.jpg

That isn't the infinite plane model of Earth. I believe John has made this thread solely for the math of the infinite plane model, hence his topic title

Quote from: bl4ke360 on September 26, 2009, 07:38:49 PM

http://i34.tinypic.com/9hs6mx.jpg

That isn't the infinite plane model of Earth. I believe John has made this thread solely for the math of the infinite plane model, hence his topic title

It would still be 3d, because the ground obviously has width. Otherwise you could stick a pencil into the ground and you would see black space on the other side.

The fact that Gauss's Law can be used to calculate the gravitational potential of an infinite plane is not evidence that the earth is an infinite plane.  Gauss's Law is merely a tool to calculate Newtonian gravity for odd shapes and/or sizes (in other words, not a point source).

There actually is a relativistic version too.  It states similar.  I'll post on the rest of this when I wake.

The fact that Gauss's Law can be used to calculate the gravitational potential of an infinite plane is not evidence that the earth is an infinite plane.  Gauss's Law is merely a tool to calculate Newtonian gravity for odd shapes and/or sizes (in other words, not a point source).

It is not evidence.  The fact that gravitational pull does not decrease with altitude in real life, and does not here either is.

However, this is not what this thread is about.  Specifically, its about the mathematical errors crustinator thinks are wrong with this problem.

There is a better, step by step explanation here:
http://www.pgccphy.net/1030/gravity.pdf

Yes, he seems to use the same method I am.  Since those are notes for a class, it explains it in a much more detailed manner.

Quote from: Crustinator on September 26, 2009, 12:16:32 PM

Wrong.

1) It's not a 2-d problem.

2) Quote your sources.

3) Name all your parameters.

4) Units would be nice too.

5) State your objectives.

For reason 2 alone I won't read further.

When is a plane not 2d?

In which case you are assuming that the earth is a plane. Congratulations.

Carl Friedrich Gauss, 1835

That's an insufficient response. Gauss did quite a bit of work you know. Also, since you are making some form of derivation (lord knows what) then there must be more than one formulae involved. Try again.

What parameters did I not name?

"S - the closed surface"

Of what? The earth?

"A - area"

Of what? The earth? The same as S?

"n a normal unit vector"

Meaning what?

"m - mass"

Of what? The earth?

...and so on and so forth...

Use any units that fit.

I'm starting to suspect you have no idea what you've posted and probably copied it from a book.

My object was to get from (1) to (4).

I'm now certain you copied it from a book and haven't the remotest idea what you just posted.

However, this is not what this thread is about.  Specifically, its about the mathematical errors crustinator thinks are wrong with this problem.

Wrong. It's not just the mathematical errors it's the logic errors too.

Otherewise I could say...

The earth is a pyramid.

Proof...

A² + B² = C²

Unless the FE is infinitely deep, could an infinite plane can be approximated to be 2D for the purposes of this calculation since variation along the vertical axis by any finite amount is negligible compared to the infinite horizontal planar expanse?

It directly follows from Gauss's Law for gravitation applied to a plane.  Gauss's Law is obviously the base of this.  

This isn't designed to be a proof of the earths shape.  Its designed to show an infinite amount of matter  (in a slab or specifically a plane)  can cause a finite gravitational pull.  If you don't have any legitimate concerns, please bugger off.

I have a degree in Mathematics.  If I were to copy it from a book, I would just have used the method I posted earlier that uses a slab and would have cited it to avoid your crap.  If I were to copy it from a book, its fairly obvious that the math is solid, in which case you are trolling.

It is clear you have no background in mathematics at all.  If you don't know what a unit vector is then you shouldn't be even trying to understand what is going on.  Furthermore, it is silly to make me state which units.  Just use units that fit, like almost any other math formula based in physics.

It is perfectly legitimate to use a 2d surface to approximate.

If you don't know whats going on, please just state so and move on.  If anyone else has issues with the op, please let me know.

Unless the FE is infinitely deep, could an infinite plane can be approximated to be 2D for the purposes of this calculation since variation along the vertical axis by any finite amount is negligible compared to the infinite horizontal planar expanse?

 If one does this in with slabs, it turns out that G*2*pi*rho*h = g.

Edit: where h = height or thickness of the slab.

Since it has been shown this math is correct for what it aims to show (an infinite plane can cause finite gravitational pull AND an infinite slab can cause finite gravitational pull) I'm going to go ahead and lock this thread.  If you have further issues with this and are qualified, please let me know and I'll unlock this thread.