# Question on Gravity at the equator. more or less?

Discussion in 'Astronomy, Exobiology, & Cosmology' started by nebel, Oct 13, 2018.

1. ### Janus58Valued Senior Member

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Gravity at the pole does not get stronger at the poles as the oblateness increases, it decreases, it just doesn't decrease as fast as it does at the equator.

If we start with a uniformly dense Earth and squash it so that the polar radius is 1/2 the equatorial radius while maintaining a constant volume, the gravity at the pole decreases to ~85% of its former value, but the gravity at the equator decreases even more.
If you reduce the thickness of the disk to zero, you have to expand the equatorial radius to infinity. An object an infinite distance away feels zero gravity.

At best you can say is that as the oblateness increases, both gravity forces tend toward zero, but at different rates.
Much like this graph of two functions.
They both start at 1 (pole and equatorial gravity equal for sphere)
Both decrease towards zero as X (the numbers across the bottom) increases towards infinity. (it may look like the red function reaches zero before this, but that is just due to the limitations of the graph's scale.)
But in between the extremes, the red function always has a smaller value than the blue function. ( equatorial gravity remains less than polar gravity)

3. ### nebel

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but we are not talking about the gravitaional field/ strength at any heights, but surface gravity. of course at nearly 0 heights at the centre, where is zero gravity to start with there has to be o gravity at that polar point. and if Gravity is higher anywhere than parity, it has to fall through patity again. in y thought experiment anyway.
you vastly overestimate my old age capacity. thank you.
If that constant heights is close to the surface, it would go from near 0 at the centre to maximum at the periphery, the equator. In that outer area, the escape velocity, and resident** orbital velocity would be normally highest there., as additionally dark matter beyond also requires. Again, I can not see how reducing the polar radius from the perfect globe will rise the gravity there for long.
Because, as the long awaited Chef d'oeuvre graphic will clearly show, that as in the assertions on Wiki &Co, gravity starts as parity with the globe, then starts to rise as flatness increases, that is polar radius shrinks, then at some point the equatorial gravity gets the upper hand. so, at some point the strength of Polar and equatorial gravity strength must cross, be equal, and:
I assume it would be 2 parity points, one at 0 oblateness, for the next crossing, the golden ratio would come to mind, because Nature has a way to use the same efficiencies over and over again.

Not distorted it, taken it to another level. thank you again for post#2, No.1!

5. ### originIn a democracy you deserve the leaders you elect.Valued Senior Member

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No, there is mass so there is gravity.
The pole will always have the higher gravity
For the example I gave the gravity would be constant no matter where you went on the plain.
Dark matter? Could you work on the basics first?
So it is safe to assume that you didn't understand the post from Janus58 at all?
Not only ignorant, but arrogant. Cool...

7. ### nebel

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Yes I can see that because that near infinite area is filled only with the finite earth mass.
Thank you! my impression was that the values had risen and fallen from the benchmark of a perfect globe. The many references I checked state that "There is more gravity at the poles by x percent, because of the reduced radius, implying that reduction equals increase. thank you, great help, and will sleep on that.

8. ### nebel

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Sorry, I believe I typed my question/clarification/comments while Janus58 send his message. Now I would qualify and amend those answers. Yes, I am a slow learner, and so could be some interested viewers.

9. ### NotEinsteinValued Senior Member

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nebel: it seems you've accidentally skipped post #36.

10. ### RainbowSingularityValued Senior Member

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from my very laymens understanding of mathamatics, infinity has not yet been proven as a factual numerical value.
but i could be wrong(if so please post a link to the mathamatics publication from the university[or person] that has done so)
while this may not seem very important, mathamatics is the linchpin and corner stone of quantum mechanics.

when speaking of "infinite gravity" as popularised in some conversations, there is no real scientific mathamatical representation of infinity.

this is why i am quite interested in the development of random number generation and the idea of quantifying a value of infinity as being or not being a real value.
(you cant get a true random number when infinity is not the total pool of values availible)

11. ### originIn a democracy you deserve the leaders you elect.Valued Senior Member

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Infinity isn't a number it's a concept
I don't recall anyone talking about infinite gravity, a body with infinite gravity would cause the universe (at least to the light horizon) to collapse to that point.
The 'true value of infinity' is an oxymoron. Infinity isn't a number.

12. ### originIn a democracy you deserve the leaders you elect.Valued Senior Member

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I personally get annoyed with you because you are not a learner at all. You have a belief and you ask questions to see if the answers support your preconceived notions. If the answers do not support your preconceived notions then you ignore the answers or bastardize the answer to support your position.

That is anti-science, disingenuous and frankly very annoying.

13. ### nebel

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re post 36, of what merits attention:
Nebel said: put yourself in the spot and kind of feel it
I meant
, rather than trying to see where an equation would lead me, I like to get a feel what gravity would feel like, such as in origin's #2 center of a shell.
The OP mentioned the Earth, and changing the volume as you would have it, without having changed the mass, would change the density, specific weights. obviously not the intend of the question.
The fact that it is about the Earth, while treating it as an ideal globe mathematically, and you ignoring that, shows your 2 following criticisms of my wording are just nitpicking. pathological naysaying.
It has become apparent be now that not every word of yours merit comment. But those that do will be gladly dealt with.
Of course you are not directly accusing all, but have singled out one instance where there was no attribution, and chose to claim that was not a "fair use" incident, and then using that mis-judgement of yours to repeatedly attribute the T word .
The moderators have better things to do than worry about your selective analysis of fair usage of the vast mass of unattributed (and not original self-created) material here.

14. ### nebel

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Yes, sorry, as an example, from the existing material: I had the pre-existing notion, that the authors had meant that the Earth had changed from an ideal spherical globe situation and had increased gravity above and beyond the maximum value , which exists only with equal polar and equatorial radii. It took one post (#41) , one sentence and graph by Janus 58. to snap me into understanding, thank you.
That I did not have that response to your good efforts, has to to do with the fact that my diminishing capacities are over estimated!. On the other hand,
Even much better minds than mine have annoyed people by their reluctance, inability to change their minds, drag out arguments, incorporate objections into their final opus. sorry.

Last edited: Oct 18, 2018
15. ### NotEinsteinValued Senior Member

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Just so you know: if everybody used that approach, nobody would be responding to you. Also, who made you the judge on merits? Especially after that great showing of your ethical standards I've been referencing.

People studying physics at a university level learn very quickly that that approach doesn't work very well. Our human intuition simply isn't good enough. Take this entire thread for example: the math is relatively simple and straightforward, yet your intuition has lead you to wrong assertions multiple times. Doesn't seem like an efficient or even worthwhile approach to me?

You've missed the point: the oblateness parameter has a very specific definition, and you are using it incorrectly. Quite an important error on your part, even if it is a nitpick or naysaying.

So you are just going to ignore all those issues I've brought up? Well, I'm glad you are showing your level of intellectual honesty so openly.

I think I used the word "thief" (or was it "stealing"?) only in the first post back then, and later apologized for using it. I now retract that apology, because it's now clear that's what you desire: me repeatedly calling you a thief.

Funny; I distinctly remember that it was you who failed to perform any analysis on "fair use". You linked the US laws as if they are somehow applicable internationally, and when I pointed this out to you, you failed to address that.

Great, so no moderation involvement; just you slinging false accusations my way, while I'm reminding you of what really happened in the past, not just your purposefully selective recollection. Again, thank you for showing your level of intellectual honesty so openly.

Also very interesting to see what you judge as having merit. Apparent it's nothing directly related to the topic of the thread, because you ignored all those bits of my post. So if you don't think discussing the topic of this thread has merit, why are you still here? Oh right, you're (still) a person with bad morals, with all the lying, intellectually dishonesty, and flaunting your ignorance in the science section. You know, I think you're right: I should go back to only responding to what merits attention.

16. ### nebel

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Thank you, Great insight. It is for me a kind of corollary to the shell theorem, in that it would state, that
There can never be greater surface gravity than on a perfect sphere. or
words to that effect.

17. ### nebel

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So:

Is Nebel not correct all along by saying in the OP that " --more gravity at the poles because they are closer to the centre --But is this not incorrect, despite the majority opinion--" and if this is so, as Janus58 (thank you) confirmed,
by who and by whom would any too simple Wiki et al references be amended to read " yes more, but only in comparison to actual decreases in overall, and equatorial values? " or words to that effect?
PS: Is my assertion in the OP, that surface gravity can not be increased by shrinking the pole radius proven to be factual by Janus58's great work in his post#41?
nebel knew it all along. or?

Last edited: Oct 20, 2018
18. ### nebel

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Janus, your answer is appreciated and supported by the measurements, but my gut feeling says it is not quite right for a perfect, even mattered, non-spinning globe,-- or any deviation from that even shape.imho Here is why:
Under gravity and in surface tension, bodies tend to find the perfect balance, greatest strength, the perfect spherical shape. Any uprising is put down, as quickly as possible. It works, because there is this additional higher matter that has to be pulled down to the common level.
Smaller radii by themselves , do not generate more gravity, if it were true, we would have runaway pimples all over the planets.

19. ### RainbowSingularityValued Senior Member

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for theory, would it be possible to have the centre of the planet hollow so a tube would run right through ?
it remains spinning...
is the removal of mass in the centre, equal to the reduction in the gravitational field ?
is more spin required to maintain the same gravitational force/field on the surface ?
would gravity in the centre of the tube be changed ?
i assume so as the field generation would be a donut so there would be a pulling force inside the sides of the tube pulling toward the mass of the spinning surfaces... ?

this reminds me of a question i have
is there some range/point of creation/terminal start point... of a planets gravity field once it gets past a certain mass ?
... is the field generated from a point of perfect centre, OR is the field subject to a type of cascade mass collection that creates a field that is like a donut rather than a perfect equation from a centre point ?

20. ### nebel

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This thread has one question in the Op, your questions seem unrelated, calling for you starting your own topic .

21. ### nebel

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Australian National University. "Earthâ€™s inner core is solid, 'J waves' suggest." ScienceDaily. ScienceDaily, 19 October 2018. <www.sciencedaily.com/releases/2018/10/181019135124.htm>

Janus, that was a great contribution to the enigma of the increasing of comparable surface gravities, we know that the globe we are standing on is not uniformly dense, having even a solid Nickel/iron core, that would not have any oblateness. so,imagine what your graphs would look like, when 1/2 way to a flat disk, the polar surface would be getting close to touching that heavy solid inner ball. similarly,
The core's contribution to polar gravity at the pole would have already really increased as that radius shrank.
The polar gravity increases because it is getting closer to the solid, big, massive core, while it would decline in a uniformly dense model Earth.

22. ### James RJust this guy, you know?Staff Member

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33,979
Actually, in that case, the gravitational field would be constant at all distances from the infinite plane. Constant height isn't needed. A given mass will experience the same constant force anywhere above or below the infinite plane of matter.

23. ### originIn a democracy you deserve the leaders you elect.Valued Senior Member

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Absolutely, thanks for pointing that out.