Cold Core Model of Earth's Structure

[Cold-co]

Modest: Thank you for moving my post, but I'm trying to get Pyrotec's attention and his religion post is the last place he was seen. His analysis of my trigonometric calculations that show another gravitational force resides in earth's layers is essential for further discussion on this site.
HydrogenBond: By the handle you are using, I surmise you may be familiar with Harvard Professor, Isaac F. Silveria's work with hydrogen. I've used his summary of diamond anvil test results to come up with a cold-core model with a core of solid hydrogen, but I'm stumped by the geodesist's insistence that earth's moment of inertia must be small. Pyrotec was to review my calculations. If they stand up to his review then earth's mass can be moved to the mantle. A hydrogen core separated from the mantle by a bath of helium would be able to rotate independently from the primary mass of the mantle. Just as NASA suggests. If you would like to review my calculations, please contact me.

[Pyrotex]

Hi guys. I'm back.
ColdCo, thanks for sending me your disk with your numbers.
The printed text you included was basically the same as the first dozen or so posts you made here, so that didn't have any extra explanation.

I've been into your data on the disk, but it is soooooo hard to interpret. You didn't leave any notes, or assumptions, or even a clear starting point that I have found. Yet. I will keep looking. You seemed to think that looking at your calculations would clear everything up. I'm sorry, but so far, it just confuses me even more.

I may just have to resort to asking you over the phone (or a chat line) individual questions about why you did this or that.

I believe Craig explained the anomalous rotation correctly. The hot molten (mostly iron) core would have eventually rotated at the same rate as the surface of the Earth. Assuming that solid iron is more dense than its molten form, even under pressure, then as the core solidified, it would have contracted. This would have forced the core to spin a little faster, to conserve angular momentum. Given that the core is STILL going faster (though not by a lot), this would indicated that the friction between the solid and molten layers is not very large.

As to demonstrating, with trigonometry, that a residual horizontal force of gravity exists -- I cannot offer you much hope that your calculations will support that. Your use of the word "force" is not the same as the scientifically defined concept of "force". That's gonna hurt.

[martillo]

Moderation note: this post and replies to it were moved to What if the planets and stars are "natural supercomputing systems"? , because they are about a different subject than this thread’s

Forgive me If I distract your (all in this thread) attention for a little but I would like you to consider (just for a little) some very unexpected possibility for Earth's core.

Some times we don't find just what we are not looking for.

I know it would be hard to accept mainly at a first view but became to make sense someway to me since some time ago.

Here it goes:

What if the Universe is much more alive than we curently believe and stars are not just a "ball of fire" and planets and moons are not just "balls of some earth".
What if some kind of what we could call "natural supercomputing system"
...

[modest]

Originally Posted by modest

<snip>

...for linearly increasing density I can find no source so I'll attempt to work out a plot...

<snip>

It plots as:

which I plotted at this website.

While looking up some stuff for the other hydrogen core thread I found the real data of a realistic model (PREM model) which doesn't assume linearly increasing density. It's in table form:

Google book -- Allen's astrophysical quantities

I put it in Excel and plotted it:



File attached.

For what it's worth, this does match ColcCo's gvhot plot:



~modest

[Cold-co]

Pyrotec:
Sorry I didn't catch your post from a week ago. Did you get the book I sent? If you did its appendix explains how the figures were derived and what they signify. If you want to discuss my calculations by phone, you can get my phone number the Phoenix directory.

[Cold-co]

Modest:
Thank you for verification that my calculations match those of the PREM model that was calculated by Professor Adam M. Dziewonski (Harvard) and a grad student named Anderson. Their model shows up in most geophysics textbooks

[modest]

Is that where you got your gvhot data—in a geophysics textbook? Or, did you calculate it by some method which you could make reproducible for us?

~modest

[Cold-co]

Modest:
Applying gravity’s elastic nature to gram masses inside the earth, suggests gravity’s horizontal vectors work in a manner similar to the pull exerted by molecules in the skin of a rubber balloon. It seemed reasonable then that the strength of pull (packing effect) by a gram mass at any depth within an orb would be obtained by rerunning calculations similar to the ones Newton used to prove that an orb’s total mass can be considered to be located at the orb’s center—a very tedious trigonometric calculation.
To analysis the packing vectors at work within the earth, I used three different models—cold-core, hot-core, and uniform density. Each model uses the same eighteen divisions of seismically known shells: crust, lithosphere, asthenosphere, 1st bonded shell, 1st transition (phase change), 2nd bonded shell, 2nd transition, five divisions of the 3rd bonded shell, four divisions of the outer core and two divisions of the inner core. Except for the average model, which has the same density for each of its shells, density is proportional to seismic wave speeds in the cold-core model and, as required above, density is concentrated in the core in the hot-core model. All models have a radius of 6371 km and all have the same total mass.
Just as Newton did, I set up my model’s eighteen separate divisions as individual spherical shells of zero thickness. Ninety annulus-masses for a selected shell-radius rotate around to concentrate at odd (1, 3, 5 ... 177, 179) degree points. After creating spreadsheets for each shell, I used a series of trigonometric functions to solve for horizontal, as well as vertical gravity vectors. By moving the radius at which the gram-mass is located and employing an iterative process, I solved for the vertical and horizontal gravity vectors produced by each individual division. Resultant gravity vectors for the radius selected for the location of the gram mass are shown in a previous post. Values for vertical gravity in my hot-core model match well with values obtained by Dziewonski. This increases my confidence that my trigonometric approach is equivalent to his way of calculating vertical gravity for various levels within the earth.
Pyrotex has been reviewing my trigonometric matrix but has yet to figure our that it takes an itterative process of moving the location of the gram mass to get the final results that I posted earlier.

[modest]

Originally Posted by Cold-co

I used a series of trigonometric functions to solve for horizontal, as well as vertical gravity vectors. By moving the radius at which the gram-mass is located and employing an iterative process, I solved for the vertical and horizontal gravity vectors produced by each individual division...

Values for vertical gravity in my hot-core model match well with values obtained by Dziewonski. This increases my confidence that my trigonometric approach is equivalent to his way of calculating vertical gravity for various levels within the earth.

That sounds very interesting. You have my utmost curiosity in how exactly you got the gvhot results. I'm hoping that you will be able to explain well enough to make the process reproducible. That is to say: I'd like to understand how you got the gvhot plot well enough that I would be able to do it myself.

To simplify things, I've built a toy model which would be much simpler than working with all of earth's shells and densities:

Each change in density happens at an additional radius of 1,000 km and each shell is less dense than the one below it by 1 g/cm³ (this is not meant to represent the earth—only to be a simple example we can work on). Do you think it would be possible to show step by step how you would get vertical acceleration for this mock-up?

Hopefully, when done, your method will give results similar to:

at r = 1000 km, acceleration = 1.4 m/s²
at r = 2000 km, acceleration = 2.31 m/s²
at r = 3000 km, acceleration = 2.80 m/s²
at r = 4000 km, acceleration = 2.87 m/s²

which I get using the normal Newtonian method.

Do you think we could work through this? I realize it will probably take more than one post, but I'm very interested in what you've done and I think seeing it done might be the only way to understand it.

~modest

[Cold-co]

Modest:
The model you lay out is basically correct, but to get it to work you need to individually isolate each shell then slice it across its vertical axis into rings then rotate the total mass of each ring around to a common hemi-circumference. Once you have that for a specific shell you can solve the g forces produced by that shell trigonometrically. I used two degree increments. The odd degrees were the points where mass was located.
I'm working on breaking up my work into segments that I can post where they are available for review. I'll be a while doing it though.