Gravity on an infinite plane

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Kami

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Gravity on an infinite plane
« on: May 25, 2016, 08:21:38 AM »
I was bored and did some math regarding John Davis' approach of an infinite plane. Since I don't know how to embed formulas here, I uploaded a PDF. https://www.docdroid.net/abhC8KU/infplane.pdf.html
Feel free to debate/criticize/point out errors.

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rabinoz

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Re: Gravity on an infinite plane
« Reply #1 on: May 25, 2016, 10:20:26 PM »
I was bored and did some math regarding John Davis' approach of an infinite plane. Since I don't know how to embed formulas here, I uploaded a PDF. https://www.docdroid.net/abhC8KU/infplane.pdf.html
Feel free to debate/criticize/point out errors.
As far as I know the calculations are correct, but that doesn't mean it explains gravity on earth.

For me I would first determine the shape of the Earth, then everything falls into place.

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Kami

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Re: Gravity on an infinite plane
« Reply #2 on: May 26, 2016, 01:43:10 AM »
Of course, a sphere makes way more sense, since in this case you can explain its formation and you don't need an infinite mass (not to mention the sun and other planets whou would, in this scenario, fall down on earth pretty quickly). I'm just saying that it would be theoretically possible.

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FalseProphet

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Re: Gravity on an infinite plane
« Reply #3 on: May 26, 2016, 03:48:23 AM »
That's most interesting. Unfortunally I'm bad in math.

Re: Gravity on an infinite plane
« Reply #4 on: May 26, 2016, 04:09:52 AM »
Interesting, thanks!

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John Davis

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Re: Gravity on an infinite plane
« Reply #5 on: May 26, 2016, 06:45:20 AM »
I haven't taken a look at this in depth, but it seems to match my ballpark estimate for the depth using Gaussian Pillboxes instead.

Here is the Wolfram for that: http://scienceworld.wolfram.com/physics/BouguerGravity.html
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sokarul

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Re: Gravity on an infinite plane
« Reply #6 on: May 26, 2016, 07:02:54 AM »
An infinite plane requires infinite energy, which is said not to exist.
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John Davis

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Re: Gravity on an infinite plane
« Reply #7 on: May 26, 2016, 07:05:52 AM »
I haven't taken a look at this in depth, but it seems to match my ballpark estimate for the depth using Gaussian Pillboxes instead.

Here is the Wolfram for that: http://scienceworld.wolfram.com/physics/BouguerGravity.html

And here is the longer version on our upcoming site: http://www.theflatearthsociety.org/home/index.php/blog/infinite-flat-earth-mathematics

Would you mind if I verified yours was correct and included it as well on this page?

An infinite plane requires infinite energy, which is said not to exist.
Really? I'm pretty sure we just said it did exist. Of course, a constantly expanding and accelerating universe always requires infinite energy (or energies approaching infinity very quickly.)
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Kami

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Re: Gravity on an infinite plane
« Reply #8 on: May 26, 2016, 02:30:59 PM »
Would you mind if I verified yours was correct and included it as well on this page?
Sure, feel free to use it, i hereby declare this open source  ;D. If you want to edit this I can send you the .tex file.
Your derived formula for the gravitational acceleration seems to be the same as mine, although the derived depths differ slightly. Probably we used different numbers for the density of the earth :).

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John Davis

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Re: Gravity on an infinite plane
« Reply #9 on: May 27, 2016, 06:47:23 AM »
The Tex would be useful. We could even post it here then

[jstex]2\pi Gp\int_{0}^{d} \frac{\left | h + l \right |}{h + l}[/jstex]
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MaNaeSWolf

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Re: Gravity on an infinite plane
« Reply #10 on: May 27, 2016, 07:14:30 AM »
Just a thought. Would gravitational pull not stay consistent regardless of altitude on a infinite plane?
As your altitude increases, you move to a more perpendicular position to more mass, meaning higher downward attraction.
Its the inverse square law working against itself.
At a infinite plane world the only point with consistent zero gravity is in a plane in the middle of the "earth" or infinite plane itself.

Re: Gravity on an infinite plane
« Reply #11 on: May 27, 2016, 10:47:55 AM »
If gravity didn't change as you got higher, nether would air pressure, and we know air pressure does decrease.

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John Davis

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Re: Gravity on an infinite plane
« Reply #12 on: May 27, 2016, 12:21:33 PM »
Just a thought. Would gravitational pull not stay consistent regardless of altitude on a infinite plane?
As your altitude increases, you move to a more perpendicular position to more mass, meaning higher downward attraction.
Its the inverse square law working against itself.
At a infinite plane world the only point with consistent zero gravity is in a plane in the middle of the "earth" or infinite plane itself.
Yes, altitude would not diminish gravitational pull if the plane is infinite and uniform. Local mass differences would cause diminishing effects though, since in reality we aren't dealing with an infinite plane that is uniform. So, at high altitudes you'd still be further away from the local mass differences that would add to this finite non-diminishing pul and then would still note air pressure differences.

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Kami

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Re: Gravity on an infinite plane
« Reply #13 on: May 27, 2016, 03:34:01 PM »
If gravity didn't change as you got higher, nether would air pressure, and we know air pressure does decrease.
That is not true, on a round earth the graviy at 400km (height of ISS) is about 80% of the gravity on earth, still there is almost no air. For the same reason the water pressure increases when you dive deep.
Yes, the gravitational pull would not decrease at higher altitudes, and the sun, stars and other planets might have Problems with that, but the air pressure would behave almost the same as on a spherical earth.
There would be a layer of zero gravity in the middle of the plane.
John davis I will send you the file in a few hours when I'm home.
« Last Edit: May 27, 2016, 03:36:16 PM by Kami »

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rabinoz

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Re: Gravity on an infinite plane
« Reply #14 on: May 27, 2016, 04:35:20 PM »
If gravity didn't change as you got higher, nether would air pressure, and we know air pressure does decrease.
As you know I certainly accept the Globe, gravitation and gravity varying with altitude etc, but I do believe you are quite wrong with the statement "If gravity didn't change as you got higher, nether would air pressure"

Take a look at:
Quote from: University of Illinois
Pressure with Height,
pressure decreases with increasing altitude
The pressure at any level in the atmosphere may be interpreted as the total weight of the air above a unit area at any elevation. At higher elevations, there are fewer air molecules above a given surface than a similar surface at lower levels. For example, there are fewer molecules above the 50 km surface than are found above the 12 km surface, which is why the pressure is less at 50 km.
What this implies is that atmospheric pressure decreases with increasing height. Since most of the atmosphere's molecules are held close to the earth's surface by the force of gravity, air pressure decreases rapidly at first, then more slowly at higher levels.
From: http://ww2010.atmos.uiuc.edu/(Gh)/guides/mtr/prs/hght.rxml

Likewise the variation in pressure with water depth is for the above reason, not variation in "g".

The variation of"g" with altitude is quite slow.

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John Davis

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Re: Gravity on an infinite plane
« Reply #15 on: May 27, 2016, 05:37:53 PM »
So slow in fact, that its hard to detect. So hard, that when we find an issue with it, the earth suddenly becomes 'pear shaped.'
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Blue_Moon

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Re: Gravity on an infinite plane
« Reply #16 on: May 27, 2016, 06:24:41 PM »
So slow in fact, that it's hard to detect. So hard, that when we find an issue with it, the earth suddenly becomes 'pear shaped.'

"Pear shaped" is a gross exaggeration/oversimplification.  And it's not hard to detect if you have a gravimeter. 
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Bom Tishop

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Re: Gravity on an infinite plane
« Reply #17 on: May 27, 2016, 06:37:55 PM »
I was bored and did some math regarding John Davis' approach of an infinite plane. Since I don't know how to embed formulas here, I uploaded a PDF. https://www.docdroid.net/abhC8KU/infplane.pdf.html
Feel free to debate/criticize/point out errors.

Wow that is the first time I have seen math on this site. COOL!!

First off, good job, seemed like a fun little exercise. This is also a perfect (yet disturbing) point of being about to make things feasible on paper. Just go to Tesla's views on this subject.

I will say, with the estimated mass and trajectory of the sun and moon, this model would not work. Though, I am not jumping your ass, I know you were just playing with a fun exercise.

Edit: flat earth sun and moon, not speaking about he heliocentric sun/moon
« Last Edit: May 27, 2016, 08:34:31 PM by Babyhighspeed »
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MrDebunk

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Re: Gravity on an infinite plane
« Reply #18 on: May 27, 2016, 07:00:10 PM »
I'm going to ask you to keep an open mind on this one. OK.

@John Davis thinks that we all live on an infinite plane, but only in a specific section. The infinite plane would of course have infinite mass. Infinite mass = infinite gravitational pull = not in our reality.

Nice try.

P.S. "but gravity doesn't exist!" prove it.
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JerkFace

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Re: Gravity on an infinite plane
« Reply #19 on: May 27, 2016, 07:55:04 PM »
I'm going to ask you to keep an open mind on this one. OK.

@John Davis thinks that we all live on an infinite plane, but only in a specific section. The infinite plane would of course have infinite mass. Infinite mass = infinite gravitational pull = not in our reality.

Nice try.

P.S. "but gravity doesn't exist!" prove it.


The infinite plane and the globe have some topological similarities,  for example no edges....  :)   

Maybe we live on the surface of a globe?   Wouldn't that explain the variation of pressure with altitude?   


Stop gilding the pickle, you demisexual aromantic homoflexible snowflake.

Re: Gravity on an infinite plane
« Reply #20 on: May 27, 2016, 08:06:01 PM »
.....Of course, a constantly expanding and accelerating universe always requires infinite energy (or energies approaching infinity very quickly.)

No it doesn't
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MrDebunk

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Re: Gravity on an infinite plane
« Reply #21 on: May 27, 2016, 09:38:34 PM »
I'm going to ask you to keep an open mind on this one. OK.

@John Davis thinks that we all live on an infinite plane, but only in a specific section. The infinite plane would of course have infinite mass. Infinite mass = infinite gravitational pull = not in our reality.

Nice try.

P.S. "but gravity doesn't exist!" prove it.


The infinite plane and the globe have some topological similarities,  for example no edges....  :)   

Maybe we live on the surface of a globe?   Wouldn't that explain the variation of pressure with altitude?

Yes. I see where you're going and will respect you on this thinking. (and yes I know you're a round earther)

I'm talking about mass here. Earth has a finite mass, so do tennis balls, basketballs, and bowling balls. An infinite plane has infinite mass.
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You sound like shill.

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rabinoz

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Re: Gravity on an infinite plane
« Reply #22 on: May 28, 2016, 01:56:48 AM »
So slow in fact, that its hard to detect. So hard, that when we find an issue with it, the earth suddenly becomes 'pear shaped.'
Not you going "pear shaped" as well?
The equatorial diameter is c.7,926 mi (12,760 km) and the polar diameter 7,900 mi (12,720 km) from Hypertext Book Facts.

::) ::) That's some pear  ::) ::)

The infamous "Pear Shaped" was just an out of context quote quite maliciously aimed at making Neil deGrasse Tyson look foolish! Just a little on in the video he explained that the earth was almost as spherical as a billiard ball, but a little "chubbier" south of the equator than northnorth.

There have been a number of recent posts just as disingenuous as this. 
I'm sure the posters thought they were "smart", but in my book it's simply dishonest.

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Kami

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Re: Gravity on an infinite plane
« Reply #23 on: May 28, 2016, 02:08:23 AM »
Infinite mass = infinite gravitational pull = not in our reality.
If I made no mistake (and John Davis came to the same conclusion with another way, so I tend to believe that the math is correct), then this is not true.
Quote
The infinite plane and the globe have some topological similarities,  for example no edges....  :)   
Maybe we live on the surface of a globe?   Wouldn't that explain the variation of pressure with altitude? 
Actually, if you add the point "infinity" to the plane, it topologically becomes a sphere. If you assume it to be non-euclidean and apply the right metric, you get a sphere. But in my case I assumed the distance to be euclidean, otherwise my formula would be moot.

Edit: corrected an error
« Last Edit: May 28, 2016, 02:25:45 AM by Kami »

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John Davis

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Re: Gravity on an infinite plane
« Reply #24 on: May 28, 2016, 08:13:57 AM »
I'm going to ask you to keep an open mind on this one. OK.

@John Davis thinks that we all live on an infinite plane, but only in a specific section. The infinite plane would of course have infinite mass. Infinite mass = infinite gravitational pull = not in our reality.

Nice try.

P.S. "but gravity doesn't exist!" prove it.
We just provided you with two mathematical models that show that an infinite plane would not have infinite gravitational pull.

So slow in fact, that it's hard to detect. So hard, that when we find an issue with it, the earth suddenly becomes 'pear shaped.'

"Pear shaped" is a gross exaggeration/oversimplification.  And it's not hard to detect if you have a gravimeter. 
It actually still is hard to detect. That is why we supposedly use satellites to gather this data. The differences are so small that one can easily make a flat earth an oblate spheroid. Its not about the silliness of calling it "pear shaped", its about taking minute differences and curve fitting them to an already existing model. If the existing model is wrong, so is the adjusted one, even if it happens to describe well enough.
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Re: Gravity on an infinite plane
« Reply #25 on: May 28, 2016, 02:25:07 PM »
You forgot a few things in your assumptions ...

"The earth is an infinite plane"

-> That means, no matter how thick, that V - Volume - is infinite

-> That means, no matter how low the density, M - Mass - is infinite

-> That means that gravity would be infinite on every possible point on this "plane"

-> But that also means that this plane does not actually have a centre of gravity, because all points on this plane are equally - infinitely - far away from the - technically non-existing - edge. You trying to glance over that problem by "assuming the plane to be symmetrical via rotations" doesn't just make it so - either infinite or a centre, not both

-> That means the distance between the centre of gravity of the two attracting masses r is undefined and can't be used in a calculation

Basically, the whole thought-experiment has already broken down at this point ... twice, on your first formula. Infinite planes can be used in math and geometry, but it doesn't work with actual physical properties, genius.

This is like one of those math "problems" created by "dividing by zero" or other tricks that make any calculation after that point mute ... "Einstein would love that!"

Re: Gravity on an infinite plane
« Reply #26 on: May 28, 2016, 02:36:59 PM »
Next Problem ...

"we can assume that all horizontal parts of the attractive force cancel out"

-> No, we cannot, because the gravity formula calculates the force between the two centres of gravity of the two objects, there are no other vectors cancelling anything out, the formula is already reduced to exactly one vector ... so yes, your "infinite plane" gravity - that can't exists, but lets humour you there  - would not be vertically, except right above your imaginary centre (that doesn't exists on an infinite plane, either, as I already mentioned in my previous post).

Stop making shit up.

I better stop reading this ...

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Kami

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Re: Gravity on an infinite plane
« Reply #27 on: May 28, 2016, 04:25:54 PM »
PeKu, the approach "calculating gravitational force just by watching their center of masses" is only correct when you have objects which are small compared to the distance that seperates them. In the other case you have to integrate over the whole mass.

The funny thing is that an infinite plane is symmetrical everywhere, therefore you can say that the horizontal parts of the forces cancel out.

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rabinoz

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Re: Gravity on an infinite plane
« Reply #28 on: May 28, 2016, 10:45:32 PM »
PeKu, the approach "calculating gravitational force just by watching their center of masses" is only correct when you have objects which are small compared to the distance that seperates them. In the other case you have to integrate over the whole mass.

The funny thing is that an infinite plane is symmetrical everywhere, therefore you can say that the horizontal parts of the forces cancel out.
Another interesting point is that the thickness does not matter, so long as the mass per unit area stays the same.

And then, if the average density of the material in this plane is the same as the average density of the earth, the thickness needed to make the gravity over the flat plane the same as earth's gravity just "happens" to be the radius of the Globe.
I think John Davis brings this out.

Re: Gravity on an infinite plane
« Reply #29 on: May 29, 2016, 02:13:09 AM »
PeKu, the approach "calculating gravitational force just by watching their center of masses" is only correct when you have objects which are small compared to the distance that seperates them. In the other case you have to integrate over the whole mass.

The funny thing is that an infinite plane is symmetrical everywhere, therefore you can say that the horizontal parts of the forces cancel out.

Blabla, blabla ...

So the earth is "small compared to the distance"? The formula is correct when you assume an average, uniform dencity accross the whole object ... which is exactly what the paper does. Oh my god ...

And the funny thing is that saying "an infinite plane is symmetrical everywhere" actually supports my statement, it's just a different way of saying "there is no centre".

Try harder ...