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glittle
Canada
37 Posts |
 Posted - 08 Jan 2003 : 01:55:44
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From my understanding of the Meta view of gravity, if there was a room sized hollow at the center of the earth, a person there would be floating in free-fall with no net effect from gravity.
Is that correct?
What would the "standard" explanation be? I've always heard that the pressure at the center is extreme... but where does that come from, since there is no weight at the center?
Thanks,
Glen
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dholeman
USA
79 Posts |
Posted - 08 Jan 2003 : 02:54:32
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quote:
From my understanding of the Meta view of gravity, if there was a room sized hollow at the center of the earth, a person there would be floating in free-fall with no net effect from gravity.
Is that correct?
Correct for any model of gravity not just the Meta Model.
quote:
What would the "standard" explanation be?
The standard model says that because you would be equally surrounded by matter in all directions the gravity emanating from that matter would exert an equal force 'pulling' on you in all directions - hence a net zero directional force, or 'weightlessness'. The Meta Model says that the matter surrounding you shadows you from gravitons pushing on you equally in all directions to the same net effect.
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I've always heard that the pressure at the center is extreme... but where does that come from, since there is no weight at the center?
Just because the net vector of gravity - that is, the 'direction' of gravity - equals zero at the center does not mean the total force of gravity is zero. The total force is quite large because it is the the sum of the gravitational forces acting in all directions.
A simple thought experiment illustrates the point. Have someone split the earth in half and hold the two pieces apart a couple of feet from each other. Insert yourself in the middle centered between the pieces. Then have your partner let go of the pieces and wait a few moments. The two pieces would be attracted to each other and squeeze you with a total force equal to the sum of the gravitational force that they exert on each other.
All the Best,
Don
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Jim
1582 Posts |
Posted - 08 Jan 2003 : 19:24:34
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I think the example that shows that the pressure at the center of the Earth (or any sphere of great mass)is not related to the zero gravity is incorrect and the true pressure at the center of a sphere is zero. The reason is simply that pressure requires mass on an area and the mass of a sphere at the center is resting upward in all directions. So, I agree with glittle and not dholeman.
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dholeman
USA
79 Posts |
Posted - 09 Jan 2003 : 04:09:39
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quote:
I think the example that shows that the pressure at the center of the Earth (or any sphere of great mass)is not related to the zero gravity is incorrect and the true pressure at the center of a sphere is zero. The reason is simply that pressure requires mass on an area and the mass of a sphere at the center is resting upward in all directions. So, I agree with glittle and not dholeman.
I'm not surprised. 
In the first place Glen asked a question, so there's nothing to agree with him about.
I pointed out the distinction between gravitational force and the pressure due to gravity because they are two different things. You are certainly correct in saying that the mass at the very center of the earth is 'resting upward in all directions', which basically repeats what I said. Hence, it is 'weightless'. That does not mean it does not experience pressure though. It carries all the weight of all the matter above it in all directions. In order to know what that adds up to you need to first determine the pressure (force per unit area) and then multiply it by your surface area.
I'm not smart enough to do the math but if I were I would express the pressure as the integral of the gravitational acceleration acting on the mass present in a column of constant cross section with the radius of the earth expressed as the differential of density with depth but we can simplify the problem by assuming a constant for earth's density. We can also take advantage of somebody else's work in putting all the funny squiggly Greek characters on the web for us:
http://burro.astr.cwru.edu/Academics/Astr221/SolarSys/hydrostat.html
It comes to something like 350 gigapascals, which is the same order of magnitude force that can be achieved by a diamond anvil.
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tvanflandern
USA
2793 Posts |
Posted - 09 Jan 2003 : 11:17:50
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For those unfamiliar with physics, there is a major difference between "force" and "pressure". As we stand here on Earth, we experience a downward force of 1 g. But we also experience a pressure in all directions of 14 pounds per square inch. (Because the pressure is equalized, we don't notice it much except when we try to go to high altitude, or when we try to remove the air from a container.)
Likewise, in the ocean, the downward force of gravity is the same, but the bouyancy of fish easily cancels that. Nonetheless, the deeper one goes, the greater is the water pressure in all directions. There comes a theoretical depth when it could crush anything. -|Tom|-
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Jim
1582 Posts |
Posted - 10 Jan 2003 : 12:25:43
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The pressure at the center of a sphere is no greater than the pressure at the surface. This is a very important fact that is now not known in the field. Assuming as you do that the accepted math is correct is not going to show this, however. First let me say why this issue is a vital detail. Being a low pressure zone a mass center will not support current models of fusion.
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MarkVitrone
USA
386 Posts |
Posted - 10 Jan 2003 : 12:36:13
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| If some fusion reactions were occuring at a planet's core, what would the gravity be at the core assuming that the fusion was under extreme high pressures? Would there be exponential shielding effects as the gradient of pressure increased? MV |
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tvanflandern
USA
2793 Posts |
Posted - 10 Jan 2003 : 14:31:59
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[Jim]: The pressure at the center of a sphere is no greater than the pressure at the surface. This is a very important fact that is now not known in the field.
Indeed. To my knowledge, it is not known anywhere outside of your mind.
If a fluid planet has uniform density, then the force of gravity gets weaker as one goes deeper into the planet. It goes to zero at the center.
In the same planet, the pressure continually rises as one goes deeper. (We measure this in Earth's oceans.) Exactly how and why does it behave on the way down so that it reverses and ends up at zero pressure at the center? This is contrary to all experimental evidence that I am familiar with.
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[MV]: If some fusion reactions were occuring at a planet's core, what would the gravity be at the core assuming that the fusion was under extreme high pressures? Would there be exponential shielding effects as the gradient of pressure increased? MV
Gravitational force would still be zero at the core. Pressures are high, but forces come equally from all directions and cancel. It might be possible for densities to rise to the point where shielding became major, but probably not without a total core collapse first. -|Tom|-
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Jim
1582 Posts |
Posted - 10 Jan 2003 : 17:26:04
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You have refered to experimental evidence that shows pressure continues to increase with depth without any reguard to gravity. Can this proof be accessed and where? I guess a new idea has to begin somewhere so I suppose as you said at this time this one only exists in my mind. Look at the units for pressure and see that it is simply mass per unit of area. What you are saying is quite impossible. The pressure at the center would reach infinity. The mass at the center of a sphere is all around and resting at the gravity center and that is near the surface not near the center.
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tvanflandern
USA
2793 Posts |
Posted - 10 Jan 2003 : 17:41:55
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You have refered to experimental evidence that shows pressure continues to increase with depth without any reguard to gravity. Can this proof be accessed and where?
Are you really unfamiliar with the knowledge that water pressure increases with depth? Every diver knows this. I don't keep citations in that field. Jim. Please read a book.
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What you are saying is quite impossible. The pressure at the center would reach infinity. The mass at the center of a sphere is all around and resting at the gravity center and that is near the surface not near the center.
I don't understand a word of this. Earth's center of gravity is at its center. The pressure there is just the weight of all the higher layers pressing down. That is hardly infinite.
Unless someone else has the patience to carry on, I give up. Jim, you know too little, but assume that your knowledge is nearing completion. With a little more experience you will come to realize that none of us knows how much we don't yet know until we have learned nearly all there is to learn in a given field. That is why it typically takes 20+ years of education to reach the doctorate level -- the level that nominally qualifies someone as a researcher. -|Tom|-
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Ben
USA
7 Posts |
Posted - 10 Jan 2003 : 19:39:08
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Hum, Would not the pressure "weight" toward the core of a planet decrease somewhat, Say once you pass to within less then 25 percent of the plant radius (I guess this assumes a cold core). This as more of the planets mass would be above you which would tend to decrease gravity a tad and corresponding drop in pressure.
I think Jim's comment about the pressure at the core of a sphere being the same as the surface would only apply if the sphere was composed of gas inside say a steel shell. I suspect that that would only apply for gas filled sphere's of say less then 10-20 kM in diameter.
For much larger gas spheres you would see an increase in pressure toward the center ( Up to a point inward that is) once there was enough mass for gravity to have some effect. Eventually if you had enough gas the pressures would build up enough to generate heat which would generate more pressure, which generates more heat, etc. etc till you had yourself a star. Takes a fair amount of gas though. Even though the pressure would be high due to heating the gravity at or near the center would be quite low.
I'm probably still an idiot. But hey I've just a practical engineer. I am hopping to learn though.
Ben
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tvanflandern
USA
2793 Posts |
Posted - 10 Jan 2003 : 20:46:43
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Hum, Would not the pressure "weight" toward the core of a planet decrease somewhat, Say once you pass to within less then 25 percent of the plant radius (I guess this assumes a cold core). This as more of the planets mass would be above you which would tend to decrease gravity a tad and corresponding drop in pressure.
No, this mixes force and pressure. No matter how deep the atmosphere or the ocean was, there would never come a point where pressure started to decrease. Pressure, in a manner of speaking, is the accumulated weight of all the layers directly above. For example, 14 psi means that a column of air one square inch in area from the ground to the top of the atmosphere would weigh 14 pounds.
At the center, force (gravity) goes to zero. But the pressure at the center is still coming in from all sides because each layer squeezes on the one below it. That lower layer relays the pressure it feels from above, and adds its own weight to it. And so on to the center.
quote:
I think Jim's comment about the pressure at the core of a sphere being the same as the surface would only apply if the sphere was composed of gas inside say a steel shell. I suspect that that would only apply for gas filled sphere's of say less then 10-20 kM in diameter.
A steel shell is a rigid structure that resists pressure (up to some crushing point) and does not relay exterior pressure into its interior. But everything inside the Earth below the crust is already getting pressures way above the crushing point, and so has no significant ability to resist relaying those pressures on down to the center.
quote:
I'm probably still an idiot. But hey I've just a practical engineer. I am hoping to learn though.
You ask good questions. No one is an idiot for not knowing something, and the exercise of asking and answering questions is how we all probe the limits of our knowledge and our understanding. I ask plenty of questions every day -- every time I pick up a journal.  -|Tom|-
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Ben
USA
7 Posts |
Posted - 10 Jan 2003 : 23:32:48
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Ok, Thought about it and your right. There would be quite a bit of pressure at the center but zero or near zero gravity too. I wonder how far from the center of a planet the zero G extends and does the gravity increase linearly with distance or increase steeply only a short distance from the center.
Thanks again,
Ben |
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tvanflandern
USA
2793 Posts |
Posted - 11 Jan 2003 : 01:00:25
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I wonder how far from the center of a planet the zero G extends and does the gravity increase linearly with distance or increase steeply only a short distance from the center.
Remember the uniform spherical shell theorem? Consider a point a distance x from the center. All planet-centered spherical shells with radius greater than x contribute nothing to the force on x. All planet-centered spherical shells with radius less than x act as if all their mass were concentrated at the center. So x feels an acceleration of Gm/x^2, where m is the mass in all shells interior to x.
If these all had the same density rho, then their combined mass would be m = rho (4/3 pi x^3) [the product of density and volume]. That makes the force on x equal to 4/3 G pi rho x. It goes up linearly with x until the density starts to drop off significantly. -|Tom|-
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Ben
USA
7 Posts |
Posted - 11 Jan 2003 : 10:46:11
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OK did the math and sketched it out (my brain is visually orientated) I've got it now. Thanks for the help.
Ben
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jacques
Canada
87 Posts |
Posted - 11 Jan 2003 : 11:46:52
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Remember the uniform spherical shell theorem?
I understand this theorem and I see that it is widely used in astronomy, but sorry for my ignorance, was that theorem proved?
Will a limited range for gravity break that theorem?
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tvanflandern
USA
2793 Posts |
Posted - 11 Jan 2003 : 12:26:38
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[jacques]: I understand this theorem and I see that it is widely used in astronomy, but sorry for my ignorance, was that theorem proved?
Yes. It is proved rigorously by setting up volume integrals and evaluating them. It is an easy proof if one knows integral calculus.
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Will a limited range for gravity break that theorem?
No. The limited range is so large compared to the size of stars or planets that the effect is negligible. For the structure of galaxies, limited range of gravity is significant, and the uniform spherical shell theorem no longer holds. -|Tom|-
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jacques
Canada
87 Posts |
Posted - 11 Jan 2003 : 12:28:32
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Thank you!
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Jim
1582 Posts |
Posted - 15 Jan 2003 : 19:04:47
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As everyone except myself is convinced the pressure at the mass center of a sphere increases as the distance from the mass center is reduced maybe I should forget this and not ask, but after reviewing the past posts on this topic I'm puzzled about several details. First how does the model of inceasing pressure keep the pressure from going to infinity as I said early on? If the pressure goes higher because the area of the sphere is less and less it seems to me at the mass center the area gets so small as the radius of the sphere goes to a very small size. The pressure at a millimeter radius must be very great(too much for anything I would suggest). The other points are hard to put in words.
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tvanflandern
USA
2793 Posts |
Posted - 18 Jan 2003 : 02:15:28
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[Jim]: how does the model of inceasing pressure keep the pressure from going to infinity as I said early on?
The pressure is just a measure of all the weight above that point. How can the weight above a point go to infinity? -|Tom|-
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dholeman
USA
79 Posts |
Posted - 18 Jan 2003 : 02:28:14
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If the pressure goes higher because the area of the sphere is less and less it seems to me at the mass center the area gets so small as the radius of the sphere goes to a very small size.
Not all functions taken to their limits go to either "nothing" (infinitessimly small) or infinity. Neither, too, do all inverse functions whose limits are "nothing" always go to infinity. It happens that the function that describes the pressure at the infinitessimly small point at the center of the sphere goes to a finite value that is the sum of all the "weight" of all the mass "above" it. The arithmetic is worked out in a reference I provided way at the top of this thread.
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Topic |
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Gravity at the center of the Earth?
