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# Density Of Earths Inner Core = 232.3 G/cm3

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density of earth = 5.515 g/cm3

density of ultramafic rock = 3.3 g/cm3

Radius of earth = 6370 km

Radius of core = 6370 - 2890 = 3480 km

Average density of entire core = (5.515-3.3)*(6370^3/3480^3)+3.3 = 16.9 g/cm3

https://www.wolframalpha.com/input/?i=%285.515-3.3%29*%286370%5E3%2F3480%5E3%29%2B3.3

Radius of inner core = 1220 km

Density of outer core = density of liquid iron = 7.2 g/cm3

Density of inner core = (16.9-7.2)*(3480^3/1220^3)+7.2 = 232.3 g/cm3

https://www.wolframalpha.com/input/?i=%2816.9-7.2%29*%283480%5E3%2F1220%5E3%29%2B7.2

Density of iron = 7.87 g/cm3 (bcc) or 8.6 g/cm3 (fcc/close packing)

Density of inner core = 232.3 g/cm3 = 27 * 8.6 g/cm3

Exactly 27 times denser!

﻿This means that the iron atoms in the inner core are exactly three times smaller

This is the expected result if electron shells are evenly spaced﻿.

(Except it isn't clear why the iron atoms go from 3rd to 1st electron shell rather than 3rd to 2﻿nd)

Iron has 4 electron shells but the 4th is already degenerate (which is why its a metal and a conductor)

Gravity at the top of the inner core = (232.3/5.515)*(1220/6370) = 8.067 g﻿'s

3/5 of earth gravity is due to density 3.3

Gravity = (0.6 g's * r/6370 km) + (0.4 g's * (6370 km)^2/r^2) for r=3480 to 6370 km﻿

Gravity = 1.668 g's at r=3480 km﻿

1.668*7.2/16.9 = 0.71 g's of that is due to density 7.2

Gravity = ( 0.71 g's * r/3480 km) + (0.958 g's * (3480 km)^2/r^2) for r=1220 to 3480 km﻿

Gravity = 8.04 g's at r=1220 km ﻿

integral of [ (0.6 * r/6370) + (0.4 * (6370)^2/r^2)] for r=3480 to 6370 = 3456 g's * km

integral of [( 0.71 * r/3480) + (0.958 * (3480)^2/r^2)] for r=1220 to 3480 = 7260 g's * km

3456 g's * 1 km * 3.3 g/cm3 = 1.13 * 10^6 bar

7260 g's * 1 km * 7.2 g/cm3 = 5.13 * 10^6 bar

Pressure at top of inner core = 1.13 + 5.13 = 6.26 million bar﻿

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Gravity at the top of the inner core = (232.3/5.515)*(1220/6370) = 8.067 g﻿'s

The force of gravity at any point distance r from the centre of Earth is the force caused by the mass of Earth below it, i.e. a (almost) sphere of radius r, NOT the total mass of the Earth). So the gravity at the top of the inner core is going to be less than on the surface.

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The force of gravity at any point distance r from the centre of Earth is the force caused by the mass of Earth below it, i.e. a (almost) sphere of radius r, NOT the total mass of the Earth). So the gravity at the top of the inner core is going to be less than on the surface.

Yes, isn't this called Newton's Shell Theorem, or something?

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Yes, isn't this called Newton's Shell Theorem, or something?

I don't know, but I remember in school doing the integration to prove this. I don't think I could do it now without a lot of swotting up.

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The force of gravity at any point distance r from the centre of Earth is the force caused by the mass of Earth below it, i.e. a (almost) sphere of radius r, NOT the total mass of the Earth). So the gravity at the top of the inner core is going to be less than on the surface.

You are assuming constant density. Because gravity follows an inverse Square law and because the core is much denser the gravity there is actually stronger than at the surface.

To see what I mean just imagine that the density of the mantle was zero

Edited by granpa
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You are assuming constant density. Because gravity follows an inverse Square law and because the core is much denser the gravity there is actually stronger than at the surface.

To see what I mean just imagine that the density of the mantle was zero

That is true, up to a point, but most certainly not what you calculated!

The g at the top of the outer core is about 10.67 m/s^2 only slightly higher than at the earth’s surface and decreases towards zero as you go deeper. At the top of the inner core it is about 4.63 m/s^2.

I think your error starts where you calculate the density of the inner core. It averages about 13,000 kg/m^3 or 13 g/cm^3 and not the extremely high number you came up with of 232.2 g/cm^3!

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That is what they say. I am saying something different

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The density distribution does not matter.

Do you know what would happen to the moon if earth was instantly replaced by a black hole  of 1 earth mass with the same gravitational center than earth?

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Sanctus, are you making a joke? The internal structure of the earth may not matter in the very limited sense of the gravitational attraction between the earth and the moon, but I am sure you agree it matters a great deal in most other ways. If the earth was just a black hole, none of us would be here to discuss the internal structure and density. In fact, the internal structure and density variation is critical to all life on Earth. Without the liquid iron outer core, there would be no magnetic field to shield lifeforms from the cosmic rays and the solar wind. And of course, the structure of the mantle and crust allows for the formation of oceans and continents.

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That is what they say. I am saying something different

Yes but you seem to be wrong, as a result of using a method of calculation that does not work. Ocean Breeze's figure for the density of the inner core is the one that appears in any internet search. I think you would be better off to start with the mass of the Earth, work out the mass due to the crust and mantle, then the remaining mass due to the core. Given its dimensions, you will get a density figure from that.

There are some of the numbers required here: http://www.madsci.org/posts/archives/1999-11/943288749.Es.r.html

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Density of earth = 5.515 g/cm3
Density of ocean = 1.0 g/cm3
Density of continental crust = 2.7 g/cm3 (granite)
2*10^22 kg / (2.7 g/cm3) = 7.4 * 10^9 km3 = 0.34 * volume of moon = 0.25 volume of d'' layer
Density of upper 600 km of mantle = 3.0 g/cm3 (basalt/gabbro)
Upper 600 km = 0.3068 * volume of mantle
Density of lower mantle = 3.4 g/cm3 (olivine)
Average density of mantle = 3.27756
(5.515*6370^3-(17)*(3480^3))/(6370^3-3480^3) = 3.27756
Density of outer core = density of liquid iron = 7.2 g/cm3

Radius of earth = 6370 km
Average density below 600 km = (5.515-3.0)*(6370^3/5770^3)+3.0 = 6.384 g/cm3
https://www.wolframalpha.com/input/?i=%285.515-3.0%29*%286370%5E3%2F5770%5E3%29%2B3.0

Radius of core = 6370 - 2890 = 3480 km
Average density of entire core = (6.384-3.4)*(5770^3/3480^3)+3.4 = 17.00 g/cm3
https://www.wolframalpha.com/input/?i=%286.384-3.4%29*%285770%5E3%2F3480%5E3%29%2B3.4

Radius of inner core = 1220 km
Density of inner core = (17.00-7.2)*(3480^3/1220^3)+7.2 = 234.65 g/cm3
https://www.wolframalpha.com/input/?i=%2817-7.2%29*%283480%5E3%2F1220%5E3%29%2B7.2

Density of nickle =8.90 g/cm3 (fcc)
Density of iron = 7.87 g/cm3 (bcc) or 8.6 g/cm3 (fcc/close packing)
Density of inner core = 234.65 g/cm3 = 27 * 8.69 g/cm3
Exactly 27 times denser!

﻿This means that the iron atoms in the inner core are exactly three times smaller
Iron has 4 electron shells but the 4th is already degenerate (which is why its a metal and a conductor)
Radius of iron atom in core = ((232/(1.2*0.125))*(4/56))^0.3333 = 1/4.79757 helium radii.
And iron atom in the ground electron state would be expected to be 1/13 helium nuclii.
It would appear from this that each electron shell is three times larger than the previous shell

It would appear that all rocky bodies differentiate into an dense core overlaid with a lighter material consisting of whatever is left over after the core has finished settling out.
Earth differentiated into Basalt and Olivine.
I think Theia (and our moon) differentiated into Granite and something even denser than Olivine (Pyrope/Silicate perovskite?).
When Theia struck the Earth the granite became the continental crust and the denser material sank to the core and became the d'' layer.
Volume of d'' layer = 4 * pi * (3480 km)^2 * 200 km = 3.0 * 10^10 km3
Volume of moon = 2.2 * 10^10 km3
Density of d'' layer = 3.5 g/cm3
If, like Ceres, Theia had a large amount of water ice on its surface then that could also explain where our ocean came from.
volume of ocean / moon surface area = 35 km

Gravity at the top of the inner core = (234.65/5.515)*(1220/6370) = 8.1488 g﻿'s

3/5.515 of earth gravity is due to density 3.0
solve [ ((3/5.515)  * r/6370 ) + ((2.515/5.515) * (6370 )^2/r^2) ] for r=5770 to 6370 km﻿

Gravity = 1.04854 g's at 5770 km
3.4/6.384 of that is due to density 3.4
solve [ ((3.4/6.384) *1.04854 * r/5770 ) + ((2.984/6.384) * 1.04854 * (5770 )^2/r^2)] for r=3480 to 5770 km﻿

Gravity = 1.68416 g's at r=3480 km﻿
7.2/17 = 0.71 g's of that is due to density 7.2
solve [ ((7.2/17)*1.68416 * r/3480) + ((9.8/17)*1.68416 * (3480)^2/r^2)] for r=1220 to 3480 km﻿
Gravity = 8.15 g's at r=1220 km ﻿

integral of [ ((3/5.515)  * r/6370 ) + ((2.515/5.515) * (6370 )^2/r^2) ] for r=5770 to 6370 = 613
integral of [ ((3.4/6.384) *1.04854 * r/5770 ) + ((2.984/6.384) * 1.04854 * (5770 )^2/r^2)] for r=3480 to 5770 = 2886
integral of [ ((7.2/17)*1.68416 * r/3480) + ((9.8/17)*1.68416 * (3480)^2/r^2)] for r=1220 to 3480 = 7347

613 g's * 1 km * 3.0 g/cm3 in bar = 180,000 bar
2886 g's * 1 km * 3.4 g/cm3 in bar = 962,000 bar
7347 g's * 1 km * 7.2 g/cm3 in bar = 5,190,000 bar

Pressure at 600 km = 180,000 bar
Pressure at top of outer core = 1,142,000 bar
Pressure at top of inner core = 6,332,000 bar﻿

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Each electron shell is three times larger than the previous shell

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Each electron shell is three times larger than the previous shell

That diagram bears no relation to modern physics.

It is better represented thus: http://www.chem1.com/acad/webtext/atoms/atpt-images/s-orb_shells.png

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density of earth = 5.515 g/cm3

density of ultramafic rock = 3.3 g/cm3

Radius of earth = 6370 km

Radius of core = 6370 - 2890 = 3480 km

Average density of entire core = (5.515-3.3)*(6370^3/3480^3)+3.3 = 16.9 g/cm3

https://www.wolframalpha.com/input/?i=%285.515-3.3%29*%286370%5E3%2F3480%5E3%29%2B3.3

Radius of inner core = 1220 km

Density of outer core = density of liquid iron = 7.2 g/cm3

Density of inner core = (16.9-7.2)*(3480^3/1220^3)+7.2 = 232.3 g/cm3

https://www.wolframalpha.com/input/?i=%2816.9-7.2%29*%283480%5E3%2F1220%5E3%29%2B7.2

Density of iron = 7.87 g/cm3 (bcc) or 8.6 g/cm3 (fcc/close packing)

Density of inner core = 232.3 g/cm3 = 27 * 8.6 g/cm3

Exactly 27 times denser!

﻿This means that the iron atoms in the inner core are exactly three times smaller

This is the expected result if electron shells are evenly spaced﻿.

(Except it isn't clear why the iron atoms go from 3rd to 1st electron shell rather than 3rd to 2﻿nd)

Iron has 4 electron shells but the 4th is already degenerate (which is why its a metal and a conductor)

Gravity at the top of the inner core = (232.3/5.515)*(1220/6370) = 8.067 g﻿'s

3/5 of earth gravity is due to density 3.3

Gravity = (0.6 g's * r/6370 km) + (0.4 g's * (6370 km)^2/r^2) for r=3480 to 6370 km﻿

Gravity = 1.668 g's at r=3480 km﻿

1.668*7.2/16.9 = 0.71 g's of that is due to density 7.2

Gravity = ( 0.71 g's * r/3480 km) + (0.958 g's * (3480 km)^2/r^2) for r=1220 to 3480 km﻿

Gravity = 8.04 g's at r=1220 km ﻿

integral of [ (0.6 * r/6370) + (0.4 * (6370)^2/r^2)] for r=3480 to 6370 = 3456 g's * km

integral of [( 0.71 * r/3480) + (0.958 * (3480)^2/r^2)] for r=1220 to 3480 = 7260 g's * km

3456 g's * 1 km * 3.3 g/cm3 = 1.13 * 10^6 bar

7260 g's * 1 km * 7.2 g/cm3 = 5.13 * 10^6 bar

Pressure at top of inner core = 1.13 + 5.13 = 6.26 million bar﻿

What is the point of repeating wrong figures? You can look the density up in numerous geophysical sources and they all say the inner core has a density of approx 13,000kg/m3. Do you really think you are right and everyone else is wrong? Is that likely? Or are you a Trump voter?

Edited by exchemist
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Sanctus, are you making a joke? The internal structure of the earth may not matter in the very limited sense of the gravitational attraction between the earth and the moon, but I am sure you agree it matters a great deal in most other ways. If the earth was just a black hole, none of us would be here to discuss the internal structure and density. In fact, the internal structure and density variation is critical to all life on Earth. Without the liquid iron outer core, there would be no magnetic field to shield lifeforms from the cosmic rays and the solar wind. And of course, the structure of the mantle and crust allows for the formation of oceans and continents.

No, no joke. The moon would just keep the same orbit, why should it change? (The honors of thinking about it go to the creator of this forum: see post #38 here last paragraph: http://www.scienceforums.com/topic/9462-origin-of-the-universe/page-3?hl=%2Bearth+%2Bblack+%2Bhole+%2Bmoon&do=findComment&comment=153811)

Gravitational attraction depends only on the masses involved right? So if you replace earth with a black hole of same mass, tell me why that should change the moons orbit? Ok, maybe the oceans being liquid have a tiny effect (since we have tides) which disappears but otherwise I see no reason why there should be any effect on the moons orbit.

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No, no joke. The moon would just keep the same orbit, why should it change? (The honors of thinking about it go to the creator of this forum: see post #38 here last paragraph: http://www.scienceforums.com/topic/9462-origin-of-the-universe/page-3?hl=%2Bearth+%2Bblack+%2Bhole+%2Bmoon&do=findComment&comment=153811)

Gravitational attraction depends only on the masses involved right? So if you replace earth with a black hole of same mass, tell me why that should change the moons orbit? Ok, maybe the oceans being liquid have a tiny effect (since we have tides) which disappears but otherwise I see no reason why there should be any effect on the moons orbit.

Yes that's obviously true, but what has it got to do with the OP's bonkers assertions about the density of the inner core of the Earth?

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