Does internal pressure always increase inwards with size

[curiouschris]

I was reading about states of planetary ice in the following article. http://www.sciencedaily.com/releases/2015/06/150622182455.htm when it struck me that perhaps we should not assume that pressure increases as we descend into a large object.

Like a cathedral ceiling a large cave does not exert pressure on the cavity within. This is because of the lateral forces supporting the structure.

Do we assume this does not happen inside large rocky objects? Clearly in a large liquid object this would occur but in a cool or frozen object could not the lateral forces negate the vertical forces meaning a ice planet does not experience the extremes of pressure discussed in the article?

 

[Simon Bridge]

Pressure increases as you descent assuming that variatons from homogeniety as you descent are small compared with the overall size.
Sure - there could be a hollow Moon someplace but how likely is that?
How would the hollow space within form without balancing the inwards pressure from the upper surfaces?
(Cathedrals need scaffolding to hold them up while they form.)

 

[curiouschris]

Although I used a hollow object as in a cathedral or a cave. it was only to get across the idea of a self supporting structure.

My point is at some point the entire structure assuming it is not plastic will actually have layers of self supporting material which prevents or reduces the transmission of pressure to the lower layers.

Combine that with a decrease in gravity as you progress towards the centre and while I don't see hollow moons I certainly see objects where the density is greatly over estimated.

 

[A.T.]

Like a cathedral ceiling a large cave does not exert pressure on the cavity within. This is because of the lateral forces supporting the structure.

In a solid sphere under its own gravity, there is a layer near the surface that will be stretched radially (PROBLEM 3):
https://books.google.de/books?id=tpY-VkwCkAIC&lpg=PP1&hl=de&pg=PA19#v=onepage&q&f=false

 

[curiouschris]

In a solid sphere under its own gravity, there is a layer near the surface that will be stretched radially (PROBLEM 3):
https://books.google.de/books?id=tpY-VkwCkAIC&lpg=PP1&hl=de&pg=PA19#v=onepage&q&f=false

Yes. that problem makes the assumption I am talking about.

Lets assume that we are talking about heavenly bodies. Planets form over million and billions of years. if the formation is rapid the planet will not have enough time to cool, thus it will remain plastic and all the formulas will be approximately correct.

But bodies forming more slowly which radiate their heat and thus cool to a solid state will support new material added (and stretched radially) until it too cools and hardens enough to support new material added to its surface. Thus the cycle continues.

In this process you would end up with concentric layers of self supporting material which transfers little of its own weight to underlying layers. thus creating lower density objects than one would assume.

Clearly the Earth with its molten centre is not a sphere that fits this description. I am just saying the Earth may not be prototypical.

 

[Simon Bridge]

You are thinking of, say, concentric shells of material that do not touch with vacuum between them?
The addition of more concentric spheres outside would not contribute to the load on the lower spheres?
Likewise, a ball inside a house does not need to support the weight of the house.

 

[A.T.]

Yes. that problem makes the assumption I am talking about.

They assume uniform material properties and elastic deformation. I doubt this applies to planet formation, which is more plastic.

 

[curiouschris]

You are thinking of, say, concentric shells of material that do not touch with vacuum between them?

No need for a vacuum although if the inner shell contracted for some reason a vacuum could form or gases or liquids leak in from other levels.

All I am saying is that once a shell is self supporting it no longer adds to the internal pressure. Therefore an assumption of internal pressures and hence density based on the size of an object may be incorrect.

It was just a thought.

 

[russ_watters]

A planet is far too massive to be self-supporting even it it were rigid, which it isn't (it is plastic). Indeed, that's part of the definition of "planet".

Moreover, since we'sent probes to all of the planets in the solar system, we've confirmed their mass by sensing their gravitational pull.