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?
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...
I agree.
And the density distribution in such a three-layered shell under a long time scale would be (working from the exterior of the shell to the interior of the shell) dense, very dense and not very dense OR dense, very dense and extremely dense?
Doc Al: Thank you for your patience. I think I get it now. Here is what I've learned (I think) so far about our model compressible solid uniform-density sphere in empty space with no external forces acting on it and capable of density redistribution.
1. The net gravitational field varies...
I agree except that I think even if the single unit core is one particle, it is still subject to endless rounds of division, but that's a different story.
I assume you mean an outer layer exerts no gravitational force on anything at any position within it. If that's true, then why would the gravitational field vary linearly from 0 at the center to its full value at the surface (as I thought we already agreed)?
I agree, but only when the "tiny...
To clarify, I think the components of the inner-most layer are being pulled in the direction of the outer-most layer, not the layer as a unit because the layer as a unit is in gravitational equilibrium.
How do we harmonize this with Newton's Third Law?
I've heard this as well, but have also heard the exact opposite... "Note that the stuff within the shell exerts gravitational forces on the shell" [post #26]. What would happen to a bowling ball whose position is so off-center that it is almost touching the inner-side of the shell?
I think the inner-most layer (which is a layer and therefore not the center/core) is being pulled in the direction of the outer-most layer because the force of gravity in that direction is greater (albeit slightly) that the force of gravity in the other (i.e., the other direction is the one from...
I agree. That is why I think things will settle at approx. r/2. Specifically, the outer-most layer is being pulled in the direction of the core while the inner-most layer is being pulled in the direction of the outer-most layer. Everything between those layers is compacted with the layer at...