Infinite Flat Earth Gravity

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Username

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Re: Infinite Flat Earth Gravity
« Reply #60 on: October 01, 2007, 03:41:46 AM »
...
Anyways so as it stands, there are more than a few solutions for an infinite earth having finite gravity.  Anyone else have anything to add?
Just to clarify for the casual reader: Username and I agree that for an infinite Flat Earth with a positive minimum density with a positive minimum thickness in a Universe with a positive gravitation constant, gravity at any point on above the top surface must be infinite. We have shown this by both logic and calculus.

Username suggests correctly that there are geometric configurations, not entirely flat, that should have a finite gravity.

(Username, please correct me if I've misstated our agreement. Thanks.)
Seems about right to me
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Re: Infinite Flat Earth Gravity
« Reply #61 on: October 01, 2007, 02:44:10 PM »
(Sorry weak, immature moment follows...)

Hehe.  I can't help but notice the [Rules Violation] (aka [Rules Violation] ) is quiet now.
« Last Edit: October 07, 2007, 04:13:51 PM by Gulliver »

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Colonel Gaydafi

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Re: Infinite Flat Earth Gravity
« Reply #62 on: October 02, 2007, 12:48:55 AM »
tut tut tut so immature
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narcberry

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Re: Infinite Flat Earth Gravity
« Reply #63 on: October 02, 2007, 07:31:34 AM »
(Sorry weak, immature moment follows...)

Hehe.  I can't help but notice the dingleberry (aka Dumbicus) is quiet now.

You didn't notice my profile had shown me to not even have read this site in several days. I travel a lot, and end up being offline for days at a time very frequently.

Anyhow, thanks for the calculus work. I will go over it later to see if I agree, skimming it shows you considered the two factors of worry for me. It would be nice to have an absolute answer about an infinite plane.

Re: Infinite Flat Earth Gravity
« Reply #64 on: October 02, 2007, 10:03:20 AM »
(Sorry weak, immature moment follows...)

Hehe.  I can't help but notice the dingleberry (aka Dumbicus) is quiet now.

You didn't notice my profile had shown me to not even have read this site in several days. I travel a lot, and end up being offline for days at a time very frequently.

Anyhow, thanks for the calculus work. I will go over it later to see if I agree, skimming it shows you considered the two factors of worry for me. It would be nice to have an absolute answer about an infinite plane.
You falsely assume that you can only read the messages while logged in.

The absolute answer is there. The gravity for a FE would always diverge.

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Username

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Re: Infinite Flat Earth Gravity
« Reply #65 on: October 02, 2007, 05:12:35 PM »
(Sorry weak, immature moment follows...)

Hehe.  I can't help but notice the dingleberry (aka Dumbicus) is quiet now.

You didn't notice my profile had shown me to not even have read this site in several days. I travel a lot, and end up being offline for days at a time very frequently.

Anyhow, thanks for the calculus work. I will go over it later to see if I agree, skimming it shows you considered the two factors of worry for me. It would be nice to have an absolute answer about an infinite plane.
You falsely assume that you can only read the messages while logged in.

The absolute answer is there. The gravity for a FE would always diverge.
I agree, if it is flat all the way out, it would diverge. 
The illusion is shattered if we ask what goes on behind the scenes.

Re: Infinite Flat Earth Gravity
« Reply #66 on: October 04, 2007, 01:25:21 AM »
1) As the distance from each ring grows, the gravity force vector becomes more parallel with the surface of earth. This means that each ring provides more horizontal force (which cancels itself out since it is a ring) and less vertical force (what you would actually feel as gravity) as it is further from the observer.

2) As the distance from each ring grows, the gravity force becomes exponentially weaker.

Smarticus I don't know where to begin.  Firstly, your argument does not need calculus.  An 8th-grade conceptual understanding of geometry and algebra is sufficient.  Throwing in calculus is a red herring (although I don't think borne of malicious intent...just a desire to impress with your [at least] 12th-grade education probably).

Secondly we can dispense with logical "rings" as an unnecessarily complicating device.  An imaginary infinite plane is a sufficiently graspable concept.

Even though the infinite plane, as you described, would increasingly pull more "horizontally" as distance increased (in terms of right angle geometry), and would necessarily pull equally so horizontally from all directions no matter where you stand (being infinite as it were), you are missing one critical point: Every point on the disk is also exterting a downward force (the geometry thing again), however small and variable relative to distance it might be, and never a counteracting upward pull--seeing as how our 200 lb man is presumably standing on and above the plane.

Even though the farther away you get from a given point is pulling ever more horizontally than vertically, and even though gravitational attraction falls off exponentially with the square of distance, both components are nevertheless non-zero.  And by using simple geometry and algebra, it can be shown that any given point anywhere on the infinite plane exerts a non-zero downward vertical pull on your 200 lb. man.

Infinite points multiplied by non-zero downward gravitation attraction = infinite downward gravitational attraction.  No sun + moon (be they disks themselves or spheres), being presumably of finite mass pulling you up, can counteract infinite downward pull.  And for that matter it is a chin-scratcher trying to conjure up some mechanism for the sun and moon to resist such infinite gravity themselves.  Especially since they are only 30 miles away.

No calculus required.

Therefore, you may wish to update your argument of an infinite-plane earth, to the seemingly preferred FE infinite sub-theory of an infinite plane Earth that has no mass.  (Yet that somehow also has mountains and crushing water and magma and presumably still has an ice wall...are we getting this yet?)  I'm not saying I won't debunk your points when you switch, but lets take it one step at a time. ;-)
Look you ugly son of a bitch, making up observations and unfounded suppositions is exactly what the Flat Earth Society is about.

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Username

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Re: Infinite Flat Earth Gravity
« Reply #67 on: October 04, 2007, 06:30:14 AM »
No, calculus is needed and you cannot solve this with geometry/algabra alone. Infinite non-zero values can sum to a finite value.
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Re: Infinite Flat Earth Gravity
« Reply #68 on: October 04, 2007, 06:51:51 AM »
Come to think of it, we ignored that gravity cannot travel faster than light.  However, the flat earth could have expanded (with its space) at faster than light speeds like in the RE big bang.
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Re: Infinite Flat Earth Gravity
« Reply #69 on: October 04, 2007, 08:43:18 AM »
No, calculus is needed and you cannot solve this with geometry/algabra alone. Infinite non-zero values can sum to a finite value.
False. You can solve such problems without calculus. I agree that this poster fails to show that the sum his infinite non-zero values  diverges. I, however, have posted a proof, without calculus, that it does.

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narcberry

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Re: Infinite Flat Earth Gravity
« Reply #70 on: October 04, 2007, 04:16:46 PM »
No, calculus is needed and you cannot solve this with geometry/algabra alone. Infinite non-zero values can sum to a finite value.
False. You can solve such problems without calculus. I agree that this poster fails to show that the sum his infinite non-zero values  diverges. I, however, have posted a proof, without calculus, that it does.

Perhaps you can show how this could be solved without calculus.

Re: Infinite Flat Earth Gravity
« Reply #71 on: October 04, 2007, 04:24:07 PM »
No, calculus is needed and you cannot solve this with geometry/algabra alone. Infinite non-zero values can sum to a finite value.
False. You can solve such problems without calculus. I agree that this poster fails to show that the sum his infinite non-zero values  diverges. I, however, have posted a proof, without calculus, that it does.

Perhaps you can show how this could be solved without calculus.
I already have.

Infinite earth would have infinite mass (I think).
An infinite earth without an UA runs into the problem of infinite gravity.

Imagine the FE as a set of concentric rings about a disc in which you're at the center top. Let the disc have even mass to create 1/10 of a g  downward. Let each ring have a monotonically increase mass and distance from inside to outside of the ring, more properly increasing difference between the minor and major radii, so that each ring exerts a downward force of 1/10 of a g. Since there are an infinite number of rings each with 1/10 of a g, the total force would be infinite.

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Username

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Re: Infinite Flat Earth Gravity
« Reply #72 on: October 04, 2007, 11:23:38 PM »
Infinite earth would have infinite mass (I think).
An infinite earth without an UA runs into the problem of infinite gravity.

Imagine the FE as a set of concentric rings about a disc in which you're at the center top. Let the disc have even mass to create 1/10 of a g  downward. Let each ring have a monotonically increase mass and distance from inside to outside of the ring, more properly increasing difference between the minor and major radii, so that each ring exerts a downward force of 1/10 of a g. Since there are an infinite number of rings each with 1/10 of a g, the total force would be infinite.
Is there where?

Cause this looks alot like the lim(x->infinity) for x/10
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Re: Infinite Flat Earth Gravity
« Reply #73 on: October 04, 2007, 11:26:29 PM »
Infinite earth would have infinite mass (I think).
An infinite earth without an UA runs into the problem of infinite gravity.

Imagine the FE as a set of concentric rings about a disc in which you're at the center top. Let the disc have even mass to create 1/10 of a g  downward. Let each ring have a monotonically increase mass and distance from inside to outside of the ring, more properly increasing difference between the minor and major radii, so that each ring exerts a downward force of 1/10 of a g. Since there are an infinite number of rings each with 1/10 of a g, the total force would be infinite.
Is there where?

Cause this looks alot like the lim(x->infinity) for x/10
You looked at this too quickly, I'm afraid. It's the lim(x->infinity) of the Sum of g/10 taken x times, which diverges.

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Username

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Re: Infinite Flat Earth Gravity
« Reply #74 on: October 05, 2007, 02:13:53 AM »
which is still calculus and not geometry/algebra =-)
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Re: Infinite Flat Earth Gravity
« Reply #75 on: October 05, 2007, 05:20:49 AM »
Infinite earth would have infinite mass (I think).
An infinite earth without an UA runs into the problem of infinite gravity.

Imagine the FE as a set of concentric rings about a disc in which you're at the center top. Let the disc have even mass to create 1/10 of a g  downward. Let each ring have a monotonically increase mass and distance from inside to outside of the ring, more properly increasing difference between the minor and major radii, so that each ring exerts a downward force of 1/10 of a g. Since there are an infinite number of rings each with 1/10 of a g, the total force would be infinite.

If the "infinite" Earth is not really infinite but expanding and the UA produces a spin-effect on the earth like a coin (which increases in velocity in conjunction with the expanding), then the centripetal force will counteract with gravitation.
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Re: Infinite Flat Earth Gravity
« Reply #76 on: October 05, 2007, 07:03:33 AM »
which is still calculus and not geometry/algebra =-)
Nope.

Knowledge on how to evaluate the limit of a function, and mathematical analysis in general, has been around much longer than calculus.

Reference: Wiki.

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Username

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Re: Infinite Flat Earth Gravity
« Reply #77 on: October 05, 2007, 11:07:03 AM »
I don't know any 8th grade geometry or algebra courses that include Limits in their curriculum. :P
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Re: Infinite Flat Earth Gravity
« Reply #78 on: October 05, 2007, 12:08:20 PM »
I don't know any 8th grade geometry or algebra courses that include Limits in their curriculum. :P
You're right. It's taught in 6th grade.  :D

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Re: Infinite Flat Earth Gravity
« Reply #80 on: October 05, 2007, 12:33:07 PM »
http://www.cde.ca.gov/be/st/ss/mthalgebra1.asp
http://www.pen.k12.va.us/go/Sols/mathsol2001.pdf

I disagree.
Do you realize that your second link contains:

"MA.5 The student will solve practical problems involving arithmetic and geometric sequences and series. This will include finding the sum (sigma notation included) of finite and infinite convergent series that will lead to an intuitive approach to a limit."

?

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Re: Infinite Flat Earth Gravity
« Reply #81 on: October 05, 2007, 12:45:38 PM »
Yes, under math anal, which has a prereq of Algebra 2, and seems to be a precalc class.

Quote
The standards below outline the content for a one-year course in Mathematical Analysis.
Students enrolled in Mathematical Analysis are assumed to have mastered Algebra II concepts
and have some exposure to trigonometry.
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Re: Infinite Flat Earth Gravity
« Reply #82 on: October 05, 2007, 12:49:15 PM »
Yes, under math anal, which has a prereq of Algebra 2, and seems to be a precalc class.

Quote
The standards below outline the content for a one-year course in Mathematical Analysis.
Students enrolled in Mathematical Analysis are assumed to have mastered Algebra II concepts
and have some exposure to trigonometry.
So we agree that understanding how to find limits is a concept before calculus?

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Username

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Re: Infinite Flat Earth Gravity
« Reply #83 on: October 05, 2007, 01:13:08 PM »
So long as we agree it is taught in neither 6th nor 8th grade algebra/geometry.  Math anal seems to be a class for high school seniors if it is even offered. 

Usually limits and their sums are taught in precalc or above or a similar class.  For example, the standards in TN: http://www.state.tn.us/education/ci/mathhighschool/math912list.shtml we don't see it come up until precalc.

So I will agree, you only need precalc.  However, many many many students don't take precalc until college if at all.  The tone of the poster it was referring to was that we introduced calculus just to sound smart.  This is to say, we introduced limits of sums to sound smart.  That was really not a fair assessment. 

Furthermore, it was you that introduced the rings, not narcberry.

I question whether the poster even read the thread or was just trying to sound smart.  The fact that Potentiall agrees is just silly.


Where it lies in math is not the issue at hand - the issue at hand was whether or not it is, as the poster claimed, 8th grade level which it obviously is not.
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Re: Infinite Flat Earth Gravity
« Reply #84 on: October 05, 2007, 01:20:16 PM »
So long as we agree it is taught in neither 6th nor 8th grade algebra/geometry.  Math anal seems to be a class for high school seniors if it is even offered. 

Usually limits and their sums are taught in precalc or above or a similar class.  For example, the standards in TN: http://www.state.tn.us/education/ci/mathhighschool/math912list.shtml we don't see it come up until precalc.

So I will agree, you only need precalc.  However, many many many students don't take precalc until college if at all.  The tone of the poster it was referring to was that we introduced calculus just to sound smart.  This is to say, we introduced limits of sums to sound smart.  That was really not a fair assessment. 

Furthermore, it was you that introduced the rings, not narcberry.

I question whether the poster even read the thread or was just trying to sound smart.  The fact that Potentiall agrees is just silly.


Where it lies in math is not the issue at hand - the issue at hand was whether or not it is, as the poster claimed, 8th grade level which it obviously is not.
I can definitely say that I remember in 5th grade (Mrs. Campbell was memorable.) introduced to limits and would have had enough of a background at that time to understand the ring proof. We didn't not have the mathematics to handle much more than arithmetic and geometric series, but we could handle the logic of divergence or convergence.

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Re: Infinite Flat Earth Gravity
« Reply #85 on: October 05, 2007, 01:50:26 PM »
Well, from the lists for the above 3 states ( can't say much about the others ) that is no longer the case.  You don't need much background at all to learn about the concepts, but they seem (at least from the sources I see, and personal experience) to only be offered at the upper end final high school courses.

So, yes, I agree that its before calculus.  I was wrong, sorry.

However, it still seems like the poster was wrong in his point when he said that they were taught in 8th grade.  I don't doubt you were taught this in 5th grade.  However, I think if we look at other states, they will have similar standards.  Perhaps schooling isn't what it used to be or you had exceptional or just different curriculum.

The point is that the concept is not introduced into the average persons life until early college or upper end high school courses.  His claims that a) narcberry introduced the rings to complicate things and b) introduced calculus to sound smart is silly and ill founded.  Calculus is introduced at maybe a year later at worst.


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