Pressure in the depth of the planetary body

[quiet]

Hi. Some questions have been installed in my head.

1. In what is transformed a material subjected to a pressure that overcomes the atomic cohesion?

2. There are tables dedicated to the maximum pressure that each material supports without losing its basic constitution.

3. There are enough data on our planet and other astronomical objects to calculate the pressure as a function of the radial coordinate, inside the body of the object. In the case of our planet, it would be the pressure at a point below the planetary surface.

4. Is there any known material, natural or artificial, capable of withstanding the pressure in points that are deeper than a certain limit? I'm thinking of putting up with the pressure without atomic cohesion being overcome.

5. Could we formulate the pressure according to the radial coordinate?

6. Can there be a region, around the center of the planet, where solid, liquid and gaseous states are impossible, so that the only state able to withstand the pressure is plasma? That is, the area closest to the center is occupied by plasma.

Edited September 4, 2018 by quiet

[mathematic]

A collapsed state won't be a plasma as long as fusion is not taking place.  Neutron stars are the best example of collapsed state materials.

[quiet]

28 minutes ago, mathematic said:

A collapsed state won't be a plasma as long as fusion is not taking place.  Neutron stars are the best example of collapsed state materials.

Hello, thanks for making you present. I will try to explain the idea better. When there is matter enclosed and subjected to a pressure incompatible with the states of aggregation (solid, liquid, gas), one can assume that this enclosed matter goes to the state of hot plasma and that, that hot plasma, is capable of generating a pressure that balance the gravitational pressure of the material that encloses it.

I have tried a rudimentary exploration of the proposal, assuming conditions that simplify the calculation.

1. Planet with uniform density, perfectly spherical.

2. Validity of Newton's gravitational equation within the body of the planet.

3. Validity of the use of continuous variables, to use differentials and integrals.

Think of a spherical shell of infinitesimal thickness, whose volume dV is expressed in the following way.

[math]dV = 4 \ \pi \ r^2 \ dr \ \ \ \ \ \ \ \ \ (01)[/math]

[math]r \ \rightarrow[/math] radius of the infinitesimal shell

Symbolize P to a point on the shell of radius r. We want to calculate the gravitational force at that point.

The point P is inside the finite shell between [math]r[/math] and [math]R_{_T}[/math]. Newton demonstrated that a closed shell of matter, independent of the form, exerts net gravitational force equal to zero in all points of the inner region. A similar theorem exists for the electrostatic force within a closed shell. That means that the force of gravity on P depends only on the sphere between the center of the planet and the radius [math]r[/math].

Now we need to reason something. Think of a radius of the planet, which extends from the center to the planetary surface. That radius contains infinite points. Each one fulfills the conditions of point P, for a determined value of the radius. Think of 3 contiguous points, [math]P_{_1},P_{_2},P_{_3}[/math]. At [math]P_{_1}[/math] there is an infinitesimal force, at [math]P_{_2}[/math] other and [math]P_{_3}[/math] another. In gross language, we can say that [math]P_{_1}[/math] and [math]P_{_2}[/math] are touching. The same [math]P_{_2}[/math] and [math]P_{_3}[/math]. In a little more precise language, we can say that between two contiguous points are the quantum interactions, which are responsible for transmitting and adding, in radial direction, the infinitesimal forces of all points [math]P_i[/math]. What does this mean ? If we have reasoned well, it means that the force at a point P is the sum of the infinitesimal forces of the points between r and [math]R_{_T}[/math], belonging to the same radial segment that contains P. In coarse language, the force at a point P is calculated by adding, in the radial direction, the infinitesimal force of P with all the infinitesimals of the points between P and the planetary surface.

Is there a contradiction between Newton's theorem and the sum of infinitesimals in the radial direction? The theorem corresponds to a closed shell whose interior is empty. The net force is zero at the points of the interior vacuum. The inside of the shell that we are defining on the planet is not empty. Then there is something that transmits force and the infinitesimals add up in a radial direction. The spherical symmetry of Newton's theorem also exists on the planet. For Newton's gravitational formula, the only mass causing net force is the mass contained between the center of the planet and the radius r.

I would like to receive opinions regarding that reasoning. If appropriate, we can advance a little more in the mathematical approach.

Edited September 5, 2018 by quiet

[Country Boy]

 No "planet" is going to have that kind of density.  You appear to be talking about a "neutron star".

[quiet]

16 minutes ago, Country Boy said:

 No "planet" is going to have that kind of density.  You appear to be talking about a "neutron star".

I understand what you say, because it's reasonable. Beyond that, I prefer to try an abstract mathematical approach, even if it is rudimentary, to then take the tables of known natural and artificial materials, find the material that supports the maximum pressure that matter can support in states of aggregation, put in the final equation the data of our planet, calculate the pressure based on the radius and, finally, find out what happens. Could the maximum pressure supported by states of aggregation be overcome before reaching the center of our planet? Without the calculations we will never know.

[studiot]

You will find much of this work already carried out in

 

Thermodynamics of the Earth and Planets

Alberto Douce

Cambridge University Press 2011

 

Your diagram, for instance looks like the one of page 75.

 

He treats equations of solid state in chapter 8 pages 386 to 419

and

Melting in planetary bodies chapter 10 pages 477 to 521

 

Comparative figure for most of the planets are worked out.

 

[beecee]

From memory there does seem to be a size limitation for a terrestrial planet, before it will attract gases to form heavy, dense atmospheres and become actually gaseous giants. Jupiter is thought to have a rocky core. Then there is the scenario of adding more to gaseous planets and adding to their density but little to their size....This then can reach a stage where limited nuclear-ignition is initiated and we have a Brown Dwarf.

I did find this......

https://www.universetoday.com/13757/how-big-do-planets-get/

"The largest known rocky planet is thought to be Gliese 436 c. This is probably a rocky world with about 5 Earth masses and 1.5 times our planet’s radius. Amazingly, this planet is thought to be within its star’s habitable zone".

 

[quiet]

30 minutes ago, studiot said:

Alberto Douce

Cambridge University Press 2011

page 75.

chapter 8 pages 386 to 419

chapter 10 pages 477 to 521

Thanks for the reference. For doubts, I add the link.

https://assets.cambridge.org/97805218/96214/frontmatter/9780521896214_frontmatter.pdf

9 minutes ago, beecee said:

https://www.universetoday.com/13757/how-big-do-planets-get/

Thanks for the reference.

Edited September 5, 2018 by quiet

[quiet]

I have calculated the pressure according to the radial coordinate, in the way explained in my second post. That is, integrating the infinitesimal forces between [math]r [/math] and [math]R_{_T}[/math]. 

I have obtained the following result.

[math]p = \dfrac{\pi}{3} \ G \ \delta^2 \ \left[ \dfrac{R_{_T}^4}{r^2}-r^2 \right][/math]

In the equation we observe the following.

a. For [math]r=R_{_T}[/math] is [math]p=0[/math] . This is logical, because there is no planetary material above the surface of the sphere.

b. Regardless of density, [math]p \rightarrow \infty[/math] for [math]r \rightarrow 0[/math] . This happens because the radial force is finite for all the values of the radius. A finite force on a surface tending to zero produces a pressure tending to infinite.

My second post exposes the essential detail of the reasoning that leads to that equation. I need that this detail be examined and, if appropriate, criticized, because it leads to the integration of force [math]r[/math] and [math]R_{_T}[/math] . In case that reasoning is wrong, the equation will be invalid. And in case of being successful, all the spheres with finite average density meet the following condition.

Between the center and a finite radius [math] r_o [/math] there can be no matter in any of the states of aggregation, solid, liquid or gaseous. That region of radio [math]r_o[/math] it must contain something in another state, which is able to balance the pressure exerted by the rest of the sphere. The most suitable to occupy the central region and balance the pressure of the rest could be a hot plasma.

The obtained equation applies to all physical spheres, regardless of size and average density. Although the hole is microscopic, a billiard ball should have something around the center that meets the required condition. It also applies to the Sun, to all the spherical planets, to the Moon, to all the stars, etc. If the only possible thing were hot plasma in the central region, then, in the case of the Sun, the great pressure of the central plasma could have dug a conduit towards each pole, where the hot plasma bristles and spreads around the body forming the crown . Polar auroras are produced on Earth. That perfectly could be emissions of plasma expelled from the center by a pair of conduits that go from the center to the poles, as in the Sun. Why Earth has no hot crown? Because it has less mass than the Sun, the central plasma is in less violent thermodynamic conditions and large-scale statistical fluctuations are less frequent. In the sun they are incessant and maintain a permanent crown.

The temperature in the center of the Earth is close to 6900 ºC. The plasma of the solar crown has a temperature close to 6000 ºC. Taking into account that one temperature corresponds to the center of the sphere and the other to the region that surrounds the surface, the little difference of the values is an interesting fact.

Whether all this is credible or not depends on the success or failure of the basic reasoning exposed in my second post. That's why I need to examine it.

Edited September 6, 2018 by quiet

[quiet]

Temperature at the Earth's center, auroras, properties of the upper layers of the atmosphere, agree very well with the properties of the plasmas and with what the plasmas are capable of doing. I put a couple of links referring to that.

https://www.sciencedaily.com/releases/2018/06/180619122949.htm

https://vdocuments.mx/documents/plasma-physics.html

[studiot]

15 hours ago, quiet said:

The obtained equation applies to all physical spheres, regardless of size and average density. Although the hole is microscopic, a billiard ball should have something around the center that meets the required condition. It also applies to the Sun, to all the spherical planets, to the Moon, to all the stars, etc. If the only possible thing were hot plasma in the central region, then, in the case of the Sun, the great pressure of the central plasma could have dug a conduit towards each pole, where the hot plasma bristles and spreads around the body forming the crown . Polar auroras are produced on Earth. That perfectly could be emissions of plasma expelled from the center by a pair of conduits that go from the center to the poles, as in the Sun. Why Earth has no hot crown? Because it has less mass than the Sun, the central plasma is in less violent thermodynamic conditions and large-scale statistical fluctuations are less frequent. In the sun they are incessant and maintain a permanent crown.

The temperature in the center of the Earth is close to 6900 ºC. The plasma of the solar crown has a temperature close to 6000 ºC. Taking into account that one temperature corresponds to the center of the sphere and the other to the region that surrounds the surface, the little difference of the values is an interesting fact.

You seem to be moving from fact towards fancy.

 

What evidence do you have for direct conduits from the centre to the poles of the earth (or the Sun for that matter) ?
I think there is lots of evidence against this proposal.

 

The Sun is largely plasma formed of the lightest elements, hydrogen and helium. The Earth's core is made of quite different material that lies around the bottom (or top depending upon which way you orient it) of the packing fraction curve.
Have you considered the temperatures necessary to turn these into plasma?

 

Mentioning the Aurorae I have been reading a new in 2018 book by a lady plasma physicist who has made the study of the aurorae her life's work.

I'm sure you would find source of insight in the technical bits.

Aurora

Melanie Windridge

William Collins 2018

[quiet]

4 hours ago, studiot said:

What evidence do you have for direct conduits from the centre to the poles of the earth (or the Sun for that matter) ?

Hi, studiot. The first thing is to admit that you tell the truth. I have no evidence. I only take some data as indications that invite us to examine the subject of the central hole, with hot plasma and ducts towards the poles. I do not want to discard the model without giving it a chance to be examined.

1. I have assumed Newton's gravitational equation to be valid within the planetary body.

2. I have validated Newton's theorem regarding gravity inside a spherical shell of matter.

3. I have assumed that in the radial direction the infinitesimal forces, corresponding to all the points of the segment where the integral is defined, are added. The discrete analogy of that is a set of coins stacked one on top of the other on the table. The table supports the summation of the weights of all the coins.

With these criteria we arrive at the equation of pressure at a point within the planetary body.

[math]p = \dfrac{\pi}{3} \ G \ \delta^2 \ \left[ \dfrac{R_{_T}^4}{r^2}-r^2 \right][/math]

Although the approach is referred to ideal conditions, such as uniform density and perfect spherical symmetry, the shape of the equation reports that when the point has the center the pressure tends to infinity. This ideal result, well interpreted, informs that no material sphere can contain solid, liquid or gaseous matter between the center and a critical radius [math]r_o[/math], because from the center to that radius the pressure overcomes the cohesion of those states. A hot plasma can perfectly work in the central hole and oppose the pressure of matter at the border [math]r_o[/math]. That's why the only thing I can assume is that, if Newton's gravitational equation, Newton's shell theorem and stacked coins are valid, it would be reasonable to think of a hot plasma that occupies the central hole.

The plasmas are magnetized and acquire rotational movement, as reported by the following links.

https://www.sciencedaily.com/releases/2018/06/180619122949.htm

https://vdocuments.mx/documents/plasma-physics.html
 Magnetization and rotation establish a dynamic axis and an electromagnetic axis, which are not required to be on the same line, but neither do they differ too much. Statistical fluctuations, as reported by these links, produce laser-like effects of short range and with concentrated energy. The electromagnetic axis directs some pulses towards the poles. In that way, by successive pulses, the plasma can dig ducts towards the poles and the pressure fill them with plasma. The temperature of the plasma should decrease towards the poles.

The idea of a molten metal core at 6900 ° C in the center of the planet has never facilitated a fully satisfactory reconciliation between observations and physical laws. The idea of the plasma would make conciliation much easier. And the same model would work for all astronomical objects whose approaches approximate spherical symmetry, such as planets, common stars, neutron stars and others. Perhaps it would even facilitate the explanation of the collapse of a supernova, in case that collapse occurs because at a given moment, the material shell is broken by the pressure of the inner plasma.

Newton's gravitational equation, Newton's shell theorem and stacked coins. I trust that. The molten metal core causes stumbling in my mind.

Edited September 6, 2018 by quiet

[beecee]

Not sure yet where this is leading but the central core of Earth is solid and is surrounded by a molten outer core. The heat at the core is thought to be caused by the left over heat from the accretion of the planet, and radioactive decay.

https://en.wikipedia.org/wiki/Inner_core

[StringJunky]

10 minutes ago, beecee said:

Not sure yet where this is leading but the central core of Earth is solid and is surrounded by a molten outer core. The heat at the core is thought to be caused by the left over heat from the accretion of the planet, and radioactive decay.

https://en.wikipedia.org/wiki/Inner_core

Tidal forces from the Sun and Moon contribute as well, it seems. The Earth is constantly having its shape changed slightly and that causes friction within its structure. I think the radioactive components surround the outer core and the solid centre part is where it is cooler. The inner core is increasing very slightly by mm every year.

[beecee]

25 minutes ago, StringJunky said:

Tidal forces from the Sun and Moon contribute as well, it seems. The Earth is constantly having its shape changed slightly and that causes friction within its structure. I think the radioactive components surround the outer core and the solid centre part is where it is cooler. The inner core is increasing very slightly by mm every year.

Yep, of course. But again, where is all this re plasma leading [I have a horrible feeling!!! ]

[Phi for All]

2 hours ago, quiet said:

Hi, studiot. The first thing is to admit that you tell the truth. I have no evidence.

!

Moderator Note

In the future, if you have nothing to support an idea, perhaps the idea isn't ready for discussion here, especially in a mainstream section.

Also, please don't start with a mainstream question if you're intending to propose a pet theory. We need to keep mainstream science separate from guesswork for the sake of studying students.

Thread moved to Speculations, since it's strayed from the original question.

 

[studiot]

2 hours ago, quiet said:

Magnetization and rotation establish a dynamic axis and an electromagnetic axis, which are not required to be on the same line, but neither do they differ too much. Statistical fluctuations, as reported by these links, produce laser-like effects of short range and with concentrated energy. The electromagnetic axis directs some pulses towards the poles. In that way, by successive pulses, the plasma can dig ducts towards the poles and the pressure fill them with plasma. The temperature of the plasma should decrease towards the poles.

The idea of a molten metal core at 6900 ° C in the center of the planet has never facilitated a fully satisfactory reconciliation between observations and physical laws. The idea of the plasma would make conciliation much easier. And the same model would work for all astronomical objects whose approaches approximate spherical symmetry, such as planets, common stars, neutron stars and others. Perhaps it would even facilitate the explanation of the collapse of a supernova, in case that collapse occurs because at a given moment, the material shell is broken by the pressure of the inner plasma.

 

All of this is stated as fact when indeed it is just speculation, much of which runs counter to the available experimental evidence.
 

In particular the science of seismology which offers over a hundred years of reading by now puts limitations on the nature of the core and has lead to the two part model we have today.

 

That Aurora book I mentioned offers a much more convincing thermo-magnetic generator in the core than any I have seen before.
The Russian member (Fermer) might like to learn that it relies heavily on his pet Coriolis effect.

 

Finally you say that your calculations match those of Newtonian mechanics.

Using Newton, we can deduce a mass for the Earth from its interaction with the rest of the Solar system.
The mantle and crust plus any sort of light plasma do not contain enough mass to meet this requirement.

The core has to be very 'heavy'.

I do not see a response to my request for your estimate of the temperature required for the core material to reach the plasma state.

Gaseous iron is only just getting nicely warm by your temperatures.

[quiet]

3 hours ago, Phi for All said:

!

Moderator Note

In the future, if you have nothing to support an idea, perhaps the idea isn't ready for discussion here

 

Understood. Thanks for moving the thread to this section.

3 hours ago, studiot said:

All of this is stated as fact when indeed it is just speculation, much of which runs counter to the available experimental evidence.

Do we have good reasons to dismiss it? Let's do that without the slightest grief and, in reality, with the advantage of knowing that we have eliminated a serious error. Thanks for what you have contributed.

[swansont]

On 9/5/2018 at 7:55 PM, quiet said:

 

I have obtained the following result.

p=π3 G δ2 [R4Tr2−r2]

In the equation we observe the following.

a. For r=RT is p=0 . This is logical, because there is no planetary material above the surface of the sphere.

b. Regardless of density, p→∞ for r→0 . This happens because the radial force is finite for all the values of the radius. A finite force on a surface tending to zero produces a pressure tending to infinite.

 

Which is obviously wrong, so somewhere in your calculations you have erred, either in math or in application of physics, or you've made a bad assumption.

The pressure is simply due to the weight of the material in a vertical column (We know that works for atmosphere). That's not infinite — neither the mass, not the acceleration from gravity.  And you're integrating over a finite distance, so getting a result that tends to infinity doesn't seem physically reasonable. 

8 hours ago, quiet said:

 Do we have good reasons to dismiss it? Let's do that without the slightest grief and, in reality, with the advantage of knowing that we have eliminated a serious error. Thanks for what you have contributed.

The pressure inside the earth (or any planet or even the sun) does not tend to infinity.

[quiet]

Thank you very much. Best regards.

[studiot]

On 06/09/2018 at 10:54 PM, studiot said:

I do not see a response to my request for your estimate of the temperature required for the core material to reach the plasma state.

Gaseous iron is only just getting nicely warm by your temperatures.

Since you haven't come up with any answers, here are some 2018 facts and figures, quoted from the Aurora book I already mentioned.

The Solar magnetic field permeates from inside the Sun through the photoshpere, the chromosphere and out into the Sun's outer atmosphere, the corona.

Quote

'Aurora',  Windridge 2018

The Solar magnetic field permeates from inside the Sun through the photoshpere, the chromosphere and out into the Sun's outer atmosphere, the corona. The corona is hot highly ionised matter around the Sun. In fact it is intensly hot, mysteriously hot even - almost 2 million degrees Kelvin, rising from a minimum in the photosphere of around 5 thousand degrees Kelvin.

.......

The first inkling that the corona exhibited strange behaviours came from observations of an eclipse in the 1860s. The spectroscope had just been invented and scientists could now analyse light by splitting it into its constituent colours..........

..................

During the solar eclipse of 1869, Harkness and Young were independently examining the Suns's corona. They both saw a strong green line that didn't correspond to any of the colours they recognised, and certainly not one would expect from a temperature of 5000k. They thought it must be a new unknown element. They named it coronium.

........

It wasn't till 1939 that the mysterious green colour was identified as - this spectral line - in the corona  was identified as iron with 13 of its 14 (outer) electrons stripped off.

 

So there you have it - ferrous plasma at 2000,000K.

I bit out of your pay grade, I believe.

 

Edited September 13, 2018 by studiot

[studiot]

On ‎9‎/‎7‎/‎2018 at 12:17 PM, quiet said:

Thank you very much. Best regards.

See my previous post.

[quiet]

5 minutes ago, studiot said:

See my previous post.

Hi, studiot. I had read that post long before this moment. Granted, the accepted explanation of the polar aurora is based on the interaction between the atmosphere and the solar wind. It is a fact that I usually read from many years ago. Why do we want to speculate with some new type of explanation, when there is an accepted explanation? In my case, to exercise curiosity, without the intention of replacing the accepted explanation with another one not accepted.

[studiot]

5 minutes ago, quiet said:

Hi, studiot. I had read that post long before this moment. Granted, the accepted explanation of the polar aurora is based on the interaction between the atmosphere and the solar wind. It is a fact that I usually read from many years ago. Why do we want to speculate with some new type of explanation, when there is an accepted explanation? In my case, to exercise curiosity, without the intention of replacing the accepted explanation with another one not accepted.

Did you?

I only posted it this morning.

 

This was not an explanation of the terrestrial aurora, just a source of data.

This was in response to your suggestion that the material in the Earth's core is compressed into a plasma.

Edited September 13, 2018 by studiot

[quiet]

22 minutes ago, studiot said:

Did you?

The speculation about plasma, commented somewhere in this thread, does not imply that a metal, a solid or whatever is transformed into plasma by pressure. The plasma hypothesis would involve the transformation of a metal or a solid into plasma if we want to accommodate that hypothesis in some link of the theory of accretion. The ideal Newtonian model of a material sphere does not come to propose a model of a process that forms the sphere. I have the impression of incompatibility between the plasma hypothesis and the accretion model.

Did you know that when something hits the lunar surface powerfully the vibration spreads like a wave around the moon? And did you know that the characteristics of the wave do not agree with a totally solid sphere? They agree with a sphere that has solid its shell farthest and has the rest hollow.

Edited September 13, 2018 by quiet