I Effect of time on density distribution+shape of uniformly dense sphere

[madchemist]

You are expecting the material to become more dense proportional to pressure? I thought that we were talking about a solid, not an ideal gas.

We're talking about a solid of initial uniform density but not necessarily the same type of matter. The matter per unit volume could be a mixture of iron, nickel, uranium or whatever. It starts out with a uniform density regardless of how long it stays that way. The question is in what arrangement does it end?

 

[jbriggs444]

We're talking about a solid of initial uniform density but not necessarily the same type of matter. The matter per unit volume could be a mixture of iron, nickel, uranium or whatever. It starts out with a uniform density regardless of how long it stays that way. The question is in what arrangement does it end?

Both theoretically and experimentally: a non-hollow sphere at hydrostatic equilibrium. If it is fluid enough to convect, it is fluid enough not to be stable as a hollow shell.

 

[madchemist]

Both theoretically and experimentally: a sphere at hydrostatic equilibrium.

I'm talking about before that while the shell is still a shell and the hollow is still a hollow.

 

[jbriggs444]

I'm talking about before that while the shell is still a shell and the hollow is still a hollow.

If it is fluid enough to convect, it is fluid enough not to be stable as a shell.

 

[madchemist]

If it is fluid enough to convect, it is fluid enough not to be stable as a shell.

In other words, at the moment before the shell collapses, would you expect to find heavy tightly-compacted stuff comprising the inner side of the shell and lighter less-compacted stuff comprising the outer side?

 

[jbriggs444]

In other words, at the moment before the shell collapses, would you expect to find heavy tightly-compacted stuff comprising the inner side of the shell and lighter less-compacted stuff comprising the outer side?

I would expect that the shell will collapse before any significant stratification has occurred and before any pressure gradient sufficient to produce a density gradient has occurred. In addition, I would never expect a shell to form in the first place.

 

[madchemist]

I would expect that the shell will collapse before any significant stratification has occurred and before any pressure gradient sufficient to produce a density gradient has occurred.

Even if the volume of the hollow of the shell is infinitesimal?

 

[Baluncore]

Even if the volume of the hollow of the shell is infinitesimal?

An infinitesimal hollow will be filled instantly as a result of the hydrostatic pressure.

 

[Baluncore]

Consider a sphere of water, the size of a planet. You sit in your boat on the surface, and lower a pressure gauge over the side. The measured hydrostatic pressure rises as you lower the gauge deeper.

I can understand how the pressure can stabilise to a maximum approaching the centre, but how might the pressure fall with increasing depth? Any reduction in pressure with depth would result in an instant implosion toward the centre that would correct the imbalance.

The water molecule at the centre would be attracting every other molecule towards it, resulting in a maximum hydrostatic pressure. At the same time, the molecule in the centre is being attracted equally in all directions at the same time, so the net gravitational force is totally canceled on the molecule at the centre.


Systems tend to move towards a point of minimum energy. For a viscous sphere subjected to self gravity, a central cavity cannot be part of a minimum energy solution. A minimum energy solution will have the highest density, and the highest pressure, at the centre.

No physicist is going to trash the fundamentals of their science to agree with an unrealistic hollow sphere model. Your belief system appears to be incompatible with the science of gravity and hydrostatics. You must either study and accept the physics, or walk away from science.