4 ms·

I don’t think this is correct. I think the shell theorem says that the gravitational forces cancel if you are on the inside of a hollow sphere and all mass is

I don’t think this is correct. I think the shell theorem says that the gravitational forces cancel if you are on the inside of a hollow sphere and all mass is on the surface. A perfect sphere of uniform density would not meet the shell theorem assumptions.

srtjstjsj 6y ago
Yes, it would. A solid ball (filled sphere) is just a union of many shells (hollow spheres), so the theorem still applies. en.wikipedia.org/wiki/Shell_theorem
- deleted 6y ago
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pdonis 6y ago
> I think the shell theorem says that the gravitational forces cancel if you are on the inside of a hollow sphere and all mass is on the surface. No, it's stronger than that. It says that any spherically symmetric distribution of matter outside a certain radius exerts no "gravitational force" on anything inside that radius, whether there is matter inside that radius or not.
- willis936 6y ago
  What if my distance to one point on the shell was zero? Would I not feel infinite acceleration towards the massive point on the shell that I was infinitely close to?
  - pdonis 6y ago
    > What if my distance to one point on the shell was zero? Then you are not inside the shell, you are on it. The shell theorem only applies if you are inside the shell. > Would I not feel infinite acceleration towards the massive point on the shell that I was infinitely close to? In General Relativity, matter is not viewed as point particles. It is viewed as a continuum, described by the stress-energy tensor. This is one of those cases where the difference shows up.
  - tim333 6y ago
    I think how gravity works at really short distances like 10^(-50)m is still a mystery as we don't have a consistent quantum theory of gravity that works there. But as you get close to stuff, say two atoms, the electrostatic and other forces are far greater than the gravitational ones.
  - d_tr 6y ago
    Any point on the shell, whether the shell has zero thickness or not, has zero mass, but a finite mass density is assigned to it. Any finite mass is spread out, so you cannot have zero distance to enough of its points to feel infinite force.
d_tr 6y ago
You and pdonis are correct but you are saying different things. Inside a perfect solid sphere, you would of course feel force everywhere except at the center, but this force would only be due to the mass that is nearer to the center than you.

srtjstjsj 6y ago

Yes, it would. A solid ball (filled sphere) is just a union of many shells (hollow spheres), so the theorem still applies. en.wikipedia.org/wiki/Shell_theorem

deleted 6y ago
[deleted]

pdonis 6y ago

> I think the shell theorem says that the gravitational forces cancel if you are on the inside of a hollow sphere and all mass is on the surface. No, it's stronger than that. It says that any spherically symmetric distribution of matter outside a certain radius exerts no "gravitational force" on anything inside that radius, whether there is matter inside that radius or not.

willis936 6y ago
What if my distance to one point on the shell was zero? Would I not feel infinite acceleration towards the massive point on the shell that I was infinitely close to?
- pdonis 6y ago
  > What if my distance to one point on the shell was zero? Then you are not inside the shell, you are on it. The shell theorem only applies if you are inside the shell. > Would I not feel infinite acceleration towards the massive point on the shell that I was infinitely close to? In General Relativity, matter is not viewed as point particles. It is viewed as a continuum, described by the stress-energy tensor. This is one of those cases where the difference shows up.
- tim333 6y ago
  I think how gravity works at really short distances like 10^(-50)m is still a mystery as we don't have a consistent quantum theory of gravity that works there. But as you get close to stuff, say two atoms, the electrostatic and other forces are far greater than the gravitational ones.
- d_tr 6y ago
  Any point on the shell, whether the shell has zero thickness or not, has zero mass, but a finite mass density is assigned to it. Any finite mass is spread out, so you cannot have zero distance to enough of its points to feel infinite force.

d_tr 6y ago

You and pdonis are correct but you are saying different things. Inside a perfect solid sphere, you would of course feel force everywhere except at the center, but this force would only be due to the mass that is nearer to the center than you.