Science Forums

# Density Of Earths Inner Core = 232.3 G/cm3

## Recommended Posts

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?

Exactly. Sanctus is raising an entirely different issue that nobody else is talking about.

When he wrote "The density distribution does not matter" I really thought he was making some kind of joke.

Of course it doesn't matter in the limited case that he is talking about, but it definitely does matter in general, and in the context that the OP was talking about.

• Replies 51
• Created

#### Popular Days

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

https://en.wikipedia.org/wiki/Theia_%28planet%29

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

All you need to do, to prove yourself wrong, is calculate the mass of the inner core using your figure of 232 gram/ cm^3 and see how much mass is left for the rest of the earth. You will find that a liquid iron outer core will be an impossibility if the inner core is as dense as you say, and the mantle would need to be made out of thin air!

##### Share on other sites

All you need to do, to prove yourself wrong, is calculate the mass of the inner core using your figure of 232 gram/ cm^3 and see how much mass is left for the rest of the earth. You will find that a liquid iron outer core will be an impossibility if the inner core is as dense as you say, and the mantle would need to be made out of thin air!

0.3 earth masses. That leaves 0.7 earth masses for everything else. Seems like you could have figured that out yourself

http://wolframalpha.com/input/?i=4*pi*%281220+km%29%5E3%2F3+*+232+g%2Fcm3+in+earth+masses&x=0&y=0

Edited by granpa
##### Share on other sites

Simple, he was saying gravity changes depending on the  mass distribution inside of earth core, in reply to which the shell theorem was brought up. And I just made a more hardcore example of the shell theorem: if the shell´s radius is center of earth to moon distance, it does not matter whether all mass is concentrated in 1 very dense "point" (BH) or whether on a  planet.

##### Share on other sites

Simple, he was saying gravity changes depending on the  mass distribution inside of earth core, in reply to which the shell theorem was brought up. And I just made a more hardcore example of the shell theorem: if the shell´s radius is center of earth to moon distance, it does not matter whether all mass is concentrated in 1 very dense "point" (BH) or whether on a  planet.

Except he was talking about the gravity force/acceleration internal to the Earth's surface.

##### Share on other sites

0.3 earth masses. That leaves 0.7 earth masses for everything else. Seems like you could have figured that out yourself

http://wolframalpha.com/input/?i=4*pi*%281220+km%29%5E3%2F3+*+232+g%2Fcm3+in+earth+masses&x=0&y=0

So, now calculate the volume of the outer core and tell us how much mass it will have if it consists of liquid iron. Is it more or less than 0.7 earth masses? And if less, how much mass is left for the mantle?

##### Share on other sites

Except he was talking about the gravity force/acceleration internal to the Earth's surface.

Yeah but the reply to that was the shell thoerem no?

##### Share on other sites

Yeah but the reply to that was the shell thoerem no?

Right, and then we subsequently determined that the shell theorem only holds true if the Earth was a sphere of uniform density. As you know, that isn’t the case, therefore the gravitational attraction at different depths does depend to a large extent on the different densities at different depths.

The gravitational acceleration at the surface of the Earth is about 9.8 m/s^2 and I calculated the g at the top of the outer core is about 10.67 m/s^2, and at the top of the inner core it is about 4.63 m/s^2 to show that variable density does matter.

Do you agree with that or not? I suppose that I could be misunderstanding you, as I am not even sure what your point is?

##### Share on other sites

Right, and then we subsequently determined that the shell theorem only holds true if the Earth was a sphere of uniform density. As you know, that isn’t the case, therefore the gravitational attraction at different depths does depend to a large extent on the different densities at different depths.

The gravitational acceleration at the surface of the Earth is about 9.8 m/s^2 and I calculated the g at the top of the outer core is about 10.67 m/s^2, and at the top of the inner core it is about 4.63 m/s^2 to show that variable density does matter.

Do you agree with that or not? I suppose that I could be misunderstanding you, as I am not even sure what your point is?

Erm, I'd have thought that, since the shell theorem says there will be no net force of gravity inside a uniform spherical shell, then the fact that the density varies radially would not invalidate it, because you can always treat a shell whose density varies radially as a series of concentric uniform shells.  So all we have to do, which I presume is what you did, is to consider the gravity due to the remaining portion at lower depth than the point of interest. Is that what you did?

Edited by exchemist
##### Share on other sites

Erm, I'd have thought that, since the shell theorem says there will be no net force of gravity inside a uniform spherical shell, then the fact that the density varies radially would not invalidate it, because you can always treat a shell whose density varies radially as a series of concentric uniform shells.  So all we have to do, which I presume is what you did, is to consider the gravity due to the remaining portion at lower depth than the point of interest. Is that what you did?

It doesn't invalidate it entirely but it certainly does change the calculated values between a sphere of uniform density and one of variable density, such as the Earth.

In a sphere of uniform density, the gravity force would decrease steadily with depth, as you go beneath the surface. But, the variable density of the Earth actually causes g to increase with depth until the outer core is reached, then it decreases to zero at the center.

I didn't bother to post my calculations because I thought this was something that was well established.

##### Share on other sites

Missed that part (about requiring uniform density). The shell theorem though does not require uniform density, it requires spherically symmetric distributed mass.

Was reading up a bit on it now. What surprises me most is that it actually increases (like you  posted), but agree with
>>> outer_core_m=5.972e24*30/100
>>> G=6.67408e-11
10.343669314878895
I get something similar.

And the shell theorem still holds btw, as long as the  approximation same density at same distance from center holds, which I think holds for a long time.
But now I stop, since somehow  it seems we are not talking about the same thing :-).

##### Share on other sites

Ok suddenly am no more out of topic :-)

##### Share on other sites

It doesn't invalidate it entirely but it certainly does change the calculated values between a sphere of uniform density and one of variable density, such as the Earth.

In a sphere of uniform density, the gravity force would decrease steadily with depth, as you go beneath the surface. But, the variable density of the Earth actually causes g to increase with depth until the outer core is reached, then it decreases to zero at the center.

I didn't bother to post my calculations because I thought this was something that was well established.

Yes indeed, that of course I understand and agree with. As I understand it, the shell theorem does not actually say how gravity should vary with depth within the Earth, just that one can ignore whatever mass lies at less depth than the point of interest.

Re Granpa, I see you are following the path of getting him to work out the mass contributions. Good idea: he was trying to go too fast with density differences and got silly numbers.

##### Share on other sites

Missed that part (about requiring uniform density). The shell theorem though does not require uniform density, it requires spherically symmetric distributed mass.

Was reading up a bit on it now. What surprises me most is that it actually increases (like you  posted), but agree with

>>> outer_core_m=5.972e24*30/100

>>> G=6.67408e-11

10.343669314878895

I get something similar.

And the shell theorem still holds btw, as long as the  approximation same density at same distance from center holds, which I think holds for a long time.

But now I stop, since somehow  it seems we are not talking about the same thing :-).

Great. We are in agreement then. My calculation was probably based on slightly different average density and radius, but our results are close enough.

I mis-spoke when I said the shell theorem does not hold with variable density; only that the results are not what you would expect with uniform density.

##### Share on other sites

Yes indeed, that of course I understand and agree with. As I understand it, the shell theorem does not actually say how gravity should vary with depth within the Earth, just that one can ignore whatever mass lies at less depth than the point of interest.

Re Granpa, I see you are following the path of getting him to work out the mass contributions. Good idea: he was trying to go too fast with density differences and got silly numbers.

Yes, we are also in agreement.

I think if Granpa works it out the way I asked, he will find there is not enough mass left to accommodate the mantle.

The mantle actually accounts for the greatest part of the Earth's mass, about 69%, followed by the outer core at 29% and the inner core at only 2%, roughly speaking. His calculation of 30% for the inner core is way off, as you know.

##### Share on other sites

So, now calculate the volume of the outer core and tell us how much mass it will have if it consists of liquid iron. Is it more or less than 0.7 earth masses? And if less, how much mass is left for the mantle?

0.2 earth masses of liquid iron

http://m.wolframalpha.com/input/?i=7.2+g%2Fcm3+*+4+*+pi+*+%283480+km%29%5E3+%2F+3+in+earth+masses&x=0&y=0

## Join the conversation

You can post now and register later. If you have an account, sign in now to post with your account.

×   Pasted as rich text.   Paste as plain text instead

Only 75 emoji are allowed.

×   Your previous content has been restored.   Clear editor

×   You cannot paste images directly. Upload or insert images from URL.