Effects of gravity on planetary core structure

[cusz721]

TL;DR Summary

What are the effects of gravity on the internal structure of a planetary body?

Hello everyone!

I joined this forum to reach out to people much smarter than me. After searching the matter, i realize this subject has been beaten to death for a VERY long time. But, as of yet, I have not stumbled upon a definitive answer to my question.

Flipping through my news feed, I saw an article about how physicists finally found out what flavor cheese the moon's core is made of.

To my understanding, this should be self evident. The effect of gravity on a planet body defines it's inner structure as a function of the planetary body's mass, density, and material properties. At the center of a planet body's mass, the net effect of gravity is zero. That is my starting point. As you move towards the outside, the effect of gravity changes two fold in the direction of travel until all the force of gravity is behind you (-1/+1).

My question is:
Based on the associated pressure, temperature increase of said pressure, and material properties, am i correct to assume this is the reason why the inner core of a planet is solid and the outer core/ mantle is liquid? So, between 1/4 and 1/3 r of the planet structure would be the sweet spot for maximum pressure? Thank you for your time.

 

[berkeman]

Welcome to PF.

TL;DR Summary: What are the effects of gravity on the internal structure of a planetary body?

Flipping through my news feed, I saw an article about how physicists finally found out what flavor cheese the moon's core is made of.

Be sure to put a little smiley face emoji by stuff like that when you first start posting at a discussion forum. Otherwise it might give folks a wrong impression of you...

 

[PeroK]

Welcome to PF. Be sure to put a little smiley face emoji by stuff like that when you first start posting at a discussion forum. Otherwise it might give folks a wrong impression of you...

I thought it was the colour of the cheese that was at issue, rather than the flavour. Apologies for the superfluous letter u's.

 

[Drakkith]

Based on the associated pressure, temperature increase of said pressure, and material properties, am i correct to assume this is the reason why the inner core of a planet is solid and the outer core/ mantle is liquid?

The state of the material (solid or liquid) is a function of composition, temperature, and pressure. The Earth's inner core is solid because it is under the most pressure, even though it is also the hottest part of the Earth. The outer core and mantle are liquid even though they are lower in temperature because of the reduced pressure.

So, between 1/4 and 1/3 r of the planet structure would be the sweet spot for maximum pressure?

No, the center of the inner core should be the spot of maximum pressure. Everything is pressing down on this spot.

 

[berkeman]

@Ken G is more specialized in stellar interiors, but may have some helpful thoughts for this question on planetary interiors as well...

 

[Vanadium 50]

I don't think stars are a good proxy for planets. Stars generate their own energy; planets just cool. Chemistry has a big impact on planetary structure (iron-soluble elements are depleted in the crust for example) and stars don't even have atoms.

 

[Ken G]

Yeah, it's pretty hard for the peak pressure to not be at the center, it requires that something breaks the necessary symmetry. But without such a symmetry, the very concept of "center" becomes ambiguous. It's not required that the peak pressure be exactly at the center of mass, because it's not required that the gravitational acceleration at the center of mass be zero. But since large planets are pretty symmetrical objects, it's hard to imagine how it could be much different from the center of mass. Still, if you define "center" to be a zero of the internal acceleration of the effective gravity (including any centrifugal forces from rotation), then that is going to be the place where the pressure has at least a local peak if the object is rigid (if it has circulating magma currents, well, things get very tricky!). Note this could be more than one place for some weirdly shaped object, but it's getting pretty pathological now.

More interestingly, the reason why something is solid or liquid has nothing to do with pressure, it has to do with net heat loss. The pressure can be high or low, the solid will always be found in the place that has undergone more net heat loss per gram at the relevant temperature. This is because solidness is a question of low entropy, and entropy is spontaneously reduced in only one way: net heat loss, since the entropy change dS is given by dQ/T. So the maximum pressure will generally be at the center, but if you make somewhere else lose more net heat than the center, or the same heat but at lower T, then you will have your solid somewhere else than the center. Certainly the difference will end up being noticeable in the temperature and pressure, so you can still tell if something is solid or liquid based on pressure and temperature as is always stressed, but that's not the reason why it became solid, the reason is "net heat loss at the relevant temperature," the integral of dQ/T per gram. That's how you got it to that temperature and pressure. To the extent that the material is incompressible, pressure doesn't matter at all in being solid or liquid, and to the extent that it is compressible, you will simply have a different temperature as it loses net heat.

 

[Ken G]

Hey! I looked up your question on CK-12 and it gave me this answer!

CK-12 is a generative AI, which are known to often give unreliable answers to science questions. In this case the answer is pretty good, but it will often be just completely wrong so is not allowed here. I just did some standard checks of it and it was worse than most, because it had very little ability to take user feedback when it errs. You will not get good results from that AI.

 

[256bits]

Yeah, it's pretty hard for the peak pressure to not be at the center, it requires that something breaks the necessary symmetry. But without such a symmetry, the very concept of "center" becomes ambiguous. It's not required that the peak pressure be exactly at the center of mass, because it's not required that the gravitational acceleration at the center of mass be zero. But since large planets are pretty symmetrical objects, it's hard to imagine how it could be much different from the center of mass. Still, if you define "center" to be a zero of the internal acceleration of the effective gravity (including any centrifugal forces from rotation), then that is going to be the place where the pressure has at least a local peak if the object is rigid (if it has circulating magma currents, well, things get very tricky!). Note this could be more than one place for some weirdly shaped object, but it's getting pretty pathological now.

More interestingly, the reason why something is solid or liquid has nothing to do with pressure, it has to do with net heat loss. The pressure can be high or low, the solid will always be found in the place that has undergone more net heat loss per gram at the relevant temperature. This is because solidness is a question of low entropy, and entropy is spontaneously reduced in only one way: net heat loss, since the entropy change dS is given by dQ/T. So the maximum pressure will generally be at the center, but if you make somewhere else lose more net heat than the center, or the same heat but at lower T, then you will have your solid somewhere else than the center. Certainly the difference will end up being noticeable in the temperature and pressure, so you can still tell if something is solid or liquid based on pressure and temperature as is always stressed, but that's not the reason why it became solid, the reason is "net heat loss at the relevant temperature," the integral of dQ/T per gram. That's how you got it to that temperature and pressure. To the extent that the material is incompressible, pressure doesn't matter at all in being solid or liquid, and to the extent that it is compressible, you will simply have a different temperature as it loses net heat.

Interesting discussion for a phase change.

Entropy is a state variable. Knowledge of 2 state variables gives the complete state that a quantity of matter would be in.

 

[Ken G]

Right, so it's the temperature, and the heat loss, which then gives entropy and temperature. The only reason you would ever need to consider pressure is if there is compressibility affecting the temperature, the pressure would enter into that. That compressibility should be pretty important, come to think of it, because it may be the reason the center has lost so much heat. Ice cubes in the freezer freeze from the outside in, since the net heat loss is mostly from the outside and the center takes time to catch up. Why is the core of a planet different? It must be the compressibility, which causes work to be done on the core, which requires the core to lose more net heat than the exterior, which causes the core to go solid even though its temperature is the highest. Without compressibility, that would not happen, so pressure would not matter, and planets should go solid only on their outsides like ice cubes.