Cold Core Model of Earth's Structure

[Pyrotex]

pyrotex etal

For the life of me, I cannot think of an experiment to verify my trigonometric findings. It is frustrating, because the horizontal forces described act in a 360 degree plane, only when you try to disturb that plane does the horizontal force show it ugly head. I can describe what it is like, such as comparing it to restorative force in the skin of a rubber baloon, but as for an experiment I'm wide open to any suggestions. ...

Okay!

I think I finally have an insight into what you are doing.

The "force" you are describing above with the balloon analogy is "strain". The air inside the balloon creates pressure, which is a force per unit area, and the elastic nature of the rubber generates a strain to oppose the pressure; this strain is a negative force per unit area. When the pressure + strain = zero, the balloon is in equilibrium, neither shrinking nor expanding. At that point, the balloon's membrane (surface) feels no force outward or inward -- but the membrane is still under STRAIN in the plane tangential to the surface of the balloon.

 

Strain is the geometrical measure of deformation representing the relative displacement between particles in the material body, i.e. a measure of how much a given displacement differs locally from a rigid-body displacement.

 

The article (click the blue word "strain" above) goes on to explain that "elastic" is a property of the material (the rubber in this case) not the stressal forces themselves.

 

As with stresses, strains may also be classified as 'normal strain' and 'shear strain' (i.e. acting perpendicular to or along the face of an element respectively). For an isotropic material that obeys Hooke's law, a normal stress will cause a normal strain. Strains are relative displacements - they are the actual displacement divided by the length before the strain was applied. Rigid body motions don't produce strains. Normal strains produce dilations, however they merely stretch the body along the axis of application...

 

The rest of the articles on normal strain and compression are beyond my current math comfort levels without several days of study and I don't have the time. But I will say, that your attempt to derive the "horizontal gravity" sounds so close to deriving the "normal strain" in a balloon-like shell of the Earth's interior from the surrounding mass, that it's damn near spot-on. :naughty:

 

Because real forces actually do "cancel" at a point, if they all balance out. But strains do not "cancel". They behave exactly like you described in earlier posts when you discussed "bidirectional forces". Stresses and strains (including compression) match exactly with what you describe as a "bidirectional force"; by definition, they do not act at a "point", they act over an arbitrarily small "region" and cause the region to deform.

 

So, it isn't gravity that is a "bidirectional force", it's the gravitationally induced "stress" that is bidirectional. Actually, within the plane of the stress, there are an infinite number of infinitesimal forces in all directions within that plane. All the gravity forces from all the "gram masses" to all sides pulling outward on that point, and deforming the "region" around that point. The amount of stress is a direct measure NOT of "forces", but of the actual amount of deformation.

 

The residual "bidirectional force" that you are attempting to calculate at each point inside the Earth is actually one or more of the following: the inward compression strain, the outward normal strain from the Earth's spin, the outward normal strain from elements of the Earth's mass in a plane through that point and perpendicular to the axis.

[Cold-co]

Pyrotex:

You are absolutely correct, strain is what horizontal gravity produces. For the earth to bulge she must overcome the force of vertical gravity as well as the strain inherent in her surface layer. There is no way to see or measure the strain in the surface layer but a good analogy can be obtained by filling a grid marked rubber balloon with water and then rotating it. Using a strobe light syncronized with the rate of rotation, you will see the distortion of the grid just as seen in bulge tests used to study the ductility of elastic materials.

Moontainman:

In a cold-core model the bulk of earth's mass moves up into the mantle. Since the volume of the mantle is so much greater than that of the core the density of the mantle only needs to be about 7.5 g/cc, which is about equivalent to the speed of S-waves seen in the mantle.

Modest:

You are still stuck using directional vectors in explaining horizontal gravity's effect. Pyrotex is on the right track with strain, because in an elastic world, strain works in a 360 degree plane.

[Pyrotex]

...strain is what horizontal gravity produces. For the earth to bulge she must overcome the force of vertical gravity as well as the strain inherent in her surface layer. ...You are still stuck using directional vectors in explaining horizontal gravity's effect. Pyrotex is on the right track with strain, because in an elastic world, strain works in a 360 degree plane.

Strain may indeed be produced by your "horizontal gravity" -- that is, the ordinary horizontal components of gravity, but we still have to explain why your actual values for HG are hundreds and probably thousands of times greater than makes any sense.

 

For the Earth to bulge, it is enough that the Earth is spinning. The centripetal force is strongest at the equator, because the equator is farther from the axis than all other areas of the planet.

 

All vectors are, by definition, directional. A vector's "value" is: (1) a magnitude, and (2) a direction.

 

Strain can work in ALL directions for ALL 3 dimensions. It is not bound to just a "360 degree plane".

 

Your work goes to great lengths to calculate the outward strain on a tiny mass within the Earth from the horizontal components of gravity. BUT, what about the in inward strain (compression) from the great pressures within the Earth. Compressive strain DOES CANCEL outward strain. And what about the strain from the Earth's spin? Your work is not finished. You have to calculate ALL strains within the Earth's interior and add them up.

 

Finally, we need to see the equations for how you add up all the "horizontal gravity" on a tiny mass inside the Earth. This would give us a clue why your values are 1000's of times too big.

[Cold-co]

Pyrotex etal:

I have offered to send you a CD of my method of calculations. The offer still stands.

[Turtle]

Pyrotex etal:

I have offered to send you a CD of my method of calculations. The offer still stands.

 

Hey Mr. C. :confused: Et Al here; but you can call me Roger. :shrug: So yeah; no. :) In this day and age of religious whackos going out & hunting down & killing folks that disagree with them on secular grounds, you have no business asking, let alone pushing, anyone to send you their home address. You're on the internet now and it has its own protocols.

 

Given that you are the one(s) making the claim(s) that virtually turn(s) all physics, geology, cosmology, and a few other -ologies on their heads, the onus is on you to provide your evidence in the appropriate form for the venue. After all, such a proof as you claim is gonna make you famous and the calculations will end up on the web and in textbooks sooner or later anyway, right?

 

Suck it up & just do it Mr. C. We've got nothin' but time, or to quote a vulgar phrase, we've got 'til hell freezes over. :confused:

[Moontanman]

Moontainman:

In a cold-core model the bulk of earth's mass moves up into the mantle. Since the volume of the mantle is so much greater than that of the core the density of the mantle only needs to be about 7.5 g/cc, which is about equivalent to the speed of S-waves seen in the mantle.

 

No Coldco, you cannot just make such a claim with out some sort of back up. If the mantle has a density of 7.5 g/cc it would have to be almost pure iron. We know this is not true, if it were, iron would displace the Ices and metallic hydrogen due to being more dense they would migrate to the core displacing the much less dense "hydrogen" :) There is also the problem of there not being enough pressure inside the Earth to keep the hydrogen as a metallic solid. You are really going to have to do better than this. :confused:

[Boerseun]

I rarely quote myself, but:

We've danced and parlayed around this topic, but the one question asked which remains to be answered, is simply how do you propose your model to explain the Earth's measurable and demonstrable density?

[modest]

Strain can work in ALL directions for ALL 3 dimensions. It is not bound to just a "360 degree plane".

 

Yes.

 

Cold-co, when stress is equal on all sides then it is no longer a tensor with direction, but a scalar. That scalar is called pressure. As a direct result of Newton's first law: a static fluid undergoes static ("geostatic", "hydrostatic", "isotropic") pressure. A fluid cannot support shear stress. While this is demanded for a fluid, it is also a good approximation for layers of rock strata near earth's surface:

 

There is a sense, however, in which one may speak of a "geostatic" pressure analogous to a hydrostatic pressure. At sufficiently large depths of burial (or in sufficiently weak rocks, such as ice or salt) under conditions of large compressive normal stress ("confining pressure") and at sufficiently high temperatures, rocks deform easily in response to relatively low shear stresses, provided that the stresses are maintained for long periods of time. Under these conditions, therefore, shear stresses will tend to be reduced to low values and the three principal normal stresses will tend to become almost equal. Even though such rocks still behave as solids in response to stresses imposed over short time periods (e.g., seismic waves) they respond as fluids to stresses of long duration. Thus, averaged over long periods of time (and over large volumes of rock) shear stresses disappear and the magnitude of the three principal stresses becomes equal to the pressure exerted by a column of rock extending to the surface.

 

Mechanics in the earth and ... - Google Books

 

Cold-co, can you tell us what units stress, stain, and pressure have? Can you relate that to the units of acceleration in your data? Can you explain how your data is a measure of stress, strain, or pressure?

 

It is, by the bye, possible to verify that the pressure deep in the earth is isotropic by looking at crystals that formed down there (like diamonds). They are isotropic.

 

~modest

[Cold-co]

Moontainman:

You asked about pressures. Here is how I have calculated them. See attachments.

[Pyrotex]

Nice drawing on that first page, Cold-co.

So, that is how you calculated pressure inside the Earth?

 

Hmmmmm...

 

Did you find that technique somewhere?

Because I've never seen that approach to calculating pressure inside the Earth?

And I've got to tell you that I'm sceptical that that technique gives a correct answer.

You calculate only the gravitational pull between two halves of a shell.

What about the shells of matter "above" that?

Your technique would conclude that if we took equal-thickness shells down to the core,

then the Earth's internal pressure actually decreases as you approach the core.

That can't be right.

Or is there something here that I'm not seeing?

 

PS: you do neat work. That doesn't mean I agree with you. :confused:

[Moontanman]

Ok coldco, can you give me a model of the Earth with a hydrogen core? How big is the hydrogen core and how thick are the ice layers covering it and what temps do these layers have? So far experiments have shown that at pressures near what is expected at the very center of the earth metallic hydrogen can form at 100K to 300K . Temps at the center of the Earth are much higher and so no metallic hydrogen could form or exist at those pressures. Take away the iron core and you get less pressure and even less likely hood of metallic hydrogen. So far you have failed to show how the mass of the earth could be accounted for by your model or how a metallic hydrogen core could form to start with or it could be at the center of the earth to start with or how it could stay in the metallic state once formed. Please show how your metalic hydrogen core could form to begin with before you postulate it is at the center of the earth.

[Cold-co]

Moontanman:

CharlieO posted a site where my cold-core model is explained both verbally and graphically. I recommend you go back to his post and sit through my powerpoint on the subject. Therein you will see how a planetary body condenses from a 9 Kelvin molecular cloud composed of 75% hydrogen, 23% helium and 2% dirty ice coated dust. At 9 Kelvin all other materials are in a dry dust form save for hydrogen and helium.

[Cold-co]

Pyrotex:

Yesterday I made a post in response to your query "Did you find that technique somewhere?

Because I've never seen that approach to calculating pressure inside the Earth?"

In my response I stated I am a cookbook engineer I've used my engineering handbook to derive the method I used. My method produces pressures that match in part the pressures reported in The Cambridge Encycolopedia of Earth Sciences. Note the pressures are for individual shell lips and highest pressure shows up in the lower mantle. Hence the pressures below the lower mantle in the core are in effect meaningless, because the lower mantle dictates the pressure that can be tolerated in the core before structural failure will occur. Lower mantle pressure matches the pressures used in diamond anvil devices to demonstrate the physical characteristics of hydrogen, helium and ice.

[stereologist]

CharlieO posted a site

 

The link is what? Did not see the posting.

[Pyrotex]

Pyrotex:

...My method produces pressures that match in part the pressures reported in The Cambridge Encyclopedia of Earth Sciences. Note the pressures are for individual shell lips and highest pressure shows up in the lower mantle. Hence the pressures below the lower mantle in the core are in effect meaningless, because the lower mantle dictates the pressure that can be tolerated in the core before structural failure will occur. ...

Yes, I agree that the pressures you calculate for the shells below the mantle are meaningless. However, there is no such thing as "structural failure" of the core. There is no "structure" in the core to fail. the core is solid matter under tremendous pressure and temperature. Unless you apply pressures similar to those in neutron stars, the Earth's core cannot collapse or suffer any form of structural failure.

 

If your technique for calculating pressure is at all valid, then it must come within, oh say, plus or minus 20% of all pressures in The Cambridge Encyclopedia of ES. If your technique produces "meaningless values" then it would appear your technique is meaningless.

[Turtle]

According to the gang of C's, this business of shells is presupposed on layer sorting caused by Earth's rotation. (Note we have already seen that this is a physical impossibility.) Nonetheless, as Janus pointed out to Charlie a couple years ago in one of the other threads on this topic, if this were true, then Earth would have a cross-sectional profile like that of a tree's rings, not a cross-section of an onion.

[Pyrotex]

According to the gang of C's, this business of shells is presupposed on layer sorting caused by Earth's rotation. (Note we have already seen that this is a physical impossibility.) ...

Correct.

It's trivially easy to show that the Earth's gravity, at any depth, totally dominates the teensy outward centripetal force caused by Earth's rotation.

 

What CharlieO seems to be missing is the concept of "integration" -- as in Integral Calculus. It may be valid to calculate pressure caused by a shell of matter, as he has done. BUT, pressure is a scalar, not a vector, and it adds just like real numbers add. The pressure near the core would be the pressure caused by the innermost shell PLUS the pressure of the next outer shell PLUS the pressure of the shell just outside of that one PLUS ... PLUS the pressure caused by the final outside shell.

 

CharlieO? did you read that last paragraph? Pressure doesn't come from just ONE shell. It comes from that shell PLUS ALL the shells above that shell. Whether you have a hot core or a cold core--an iron core or a hydrogen core--the pressure as you go down towards the core will always increase. Maximum pressure will always be at the center of the planet. Structure or chemical makeup will not change this.

 

Any comments?