Newton's shell theorem & Nuclear Fusion

[willoughby]

I have a problem reconciling something. According to Newton's shell theorem, at any point within a solid sphere, for the purposes of calculating the gravitational force exerted on you, the mass that is outside your own radius to the center can be ignored since it cancels out, and the net force from any mass outside your radius is zero. I understand this theorem, and it makes complete sense. What I have a problem with is if this is the case, then what is causing the enormous amount of pressure that causes the Earth's core to remain solid? What causes the pressure in the sun's core that allows fusion to occur? Can someone please reconcile these two concepts for me. It seems to me, that the farther you get to the center, the LESS force there is from gravity. In other words, if the mass OUTSIDE your radius exerts a net force of ZERO, then WHAT is pushing DOWN on you in the core? What is compressing the core?

I hope this isn't a dumb question. First time posting in this forum. That would be a rough start!

 

[A.T.]

if the mass OUTSIDE your radius exerts a net force of ZERO, then WHAT is pushing DOWN on you in the core?

The mass outside your radius exerts a GRAVITATIONAL net force of zero. What is pushing down is ELECTROMAGNETIC repulsion.

 

[Nugatory]

I have a problem reconciling something. According to Newton's shell theorem, at any point within a solid sphere, for the purposes of calculating the gravitational force exerted on you, the mass that is outside your own radius to the center can be ignored since it cancels out, and the net force from any mass outside your radius is zero. I understand this theorem, and it makes complete sense. What I have a problem with is if this is the case, then what is causing the enormous amount of pressure that causes the Earth's core to remain solid? What causes the pressure in the sun's core that allows fusion to occur? Can someone please reconcile these two concepts for me. It seems to me, that the farther you get to the center, the LESS force there is from gravity. In other words, if the mass OUTSIDE your radius exerts a net force of ZERO, then WHAT is pushing DOWN on you in the core? What is compressing the core?

The gravitational pull of the shell on anything inside the shell is indeed zero. But the shell still has weight - left to its own devices it would fall inwards, and that's where the crushing force comes from.

The easiest way to see this might be to calculate the gravitational force (from the shell itself) experienced by a point ON the shell, as opposed to inside it. That force is non-zero and inwards-directed everywhere on the shell.

 

[A.T.]

The easiest way to see this might be to calculate...

Or even simpler: Consider two identical massive spheres in space, touching each other. If you are placed right between them, the net gravitational force on you is zero, because their attraction ON YOU cancels. But they are still attracting EACH OTHER, so they will squeeze you.

 

[willoughby]

Or even simpler: Consider two identical massive spheres in space, touching each other. If you are placed right between them, the net gravitational force on you is zero, because their attraction ON YOU cancels. But they are still attracting EACH OTHER, so they will squeeze you.

This is what lit the light bulb for me. This is a perfect explanation. I completely understand. Thanks a lot!