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Old 06-29-2017, 01:04 PM
 
2,225 posts, read 1,096,292 times
Reputation: 239

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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/?...0%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/?...0%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

 
Old 06-30-2017, 05:01 AM
Yac
 
5,515 posts, read 5,775,231 times
Have you considered starting a blog ? I don't see this as a basis for a discussion, as that's what forums are for, but it could be a great blog post And we have blog platform right here on c-d
Yac.
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Old 06-30-2017, 08:45 AM
 
Location: Tampa, FL
25,653 posts, read 21,539,680 times
Reputation: 11920
Quote:
Originally Posted by granpa View Post
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/?...0%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/?...0%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
Curious how these numbers are obtained - powers of deduction because as far as I know, we've never been able to explore past a few miles into the upper mantle. But it is very interesting and spooky to think about the core and the possibilities for how the earth will appear in another billion years.....
 
Old 07-15-2017, 07:02 PM
 
2,225 posts, read 1,096,292 times
Reputation: 239
 
Old 07-17-2017, 08:19 AM
Yac
 
5,515 posts, read 5,775,231 times
I was trying to be nice before, but I feel I have to be blunt: OP, if you simply want to post whatever, you can start a blog. This is a discussion forum, which requires at least some attempt at discussion.
Closed.
Yac.
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