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Wouldn't that be an unstable position? Even if the earth was a perfect ball and the cave was a perfect ball exactly in the middle then the gravity everywhere in

by jules 16y ago

Wouldn't that be an unstable position? Even if the earth was a perfect ball and the cave was a perfect ball exactly in the middle then the gravity everywhere inside the cave is zero, so if you gave the black hole a little push it would crash into the earth again.

ars 16y ago
The center of the earth is the position that is "lowest" if you moved away from it gravity would cause it to "fall down" back into the center.
- jules 16y ago
  Not if the black hole carved a spherical cave there. The forces in all directions cancel each other out inside the spherical cave.
  - merraksh 16y ago
    In the perfectly spherical earth hypothesis, being the center of mass in the black hole, wouldn't there be a resulting force towards the center, although very small? [EDIT] Hmm I think I see the point. The resulting force would be proportional to the ratio (black hole mass / earth's mass). Very small indeed.
    - vecter 16y ago
      No, that's irrelevant: http://hyperphysics.phy-astr.gsu.edu/hbase/mechanics/sphshell2.html http://hyperphysics.phy-astr.gsu.edu/hbase/mechanics/sphshel...
      - ars 16y ago
        That's for a hollow shell. For a solid sphere, there is always force toward the center. (And the closer to the center the lower the force, reaching 0 in the middle.)
    - jules 16y ago
      No, the force is EXACTLY zero, not just very small.
      - ars 16y ago
        Inside the cave yes, but not when it's inside the solid mass of the earth. Inside a solid sphere the force is toward the center.
        jules 16y ago
        Yes, but we're talking about the situation where there is a cave?
- vecter 16y ago
  That is completely false. Modelling the inside of the earth as a hollow spherical shell, the force inside at all points due to the gravity of the surrounding shell is 0.
  - ars 16y ago
    But it's not actually a shell. In a solid sphere there is always force, and it always points to, and is lowest, at the center.
    - vecter 16y ago
      I assumed the black hole carved out a spherical hole in the center of the Earth. If it was inside it, then it would be inside a spherical shell (a very thick one at that).
      - ars 16y ago
        But, you said it would be unstable, while actually if it crashed into the wall the resultant forces would put it back somewhere in the middle. Or more accurately oscillating back and forth in the middle, but not touching the wall. If there was any vapor in the middle (which seems likely to me, considering it would be a perfect vacuum at pretty extreme temperatures), then the gas would eventually slow down the oscillations and it would end up exactly in the middle.
        joe_the_user 16y ago
        Well, it would be sucking up the matter on the walls as well.. BTW, Sci fans of yesteryear were disappointed when it was discovered that Dyson Spheres and Ring Worlds gravitationally unstable...
        ars 16y ago
        > it would be sucking up the matter on the walls as well It won't. The first time it touches (or comes near) the wall it will take what it can get, but it will never go farther than that. There is nothing that will "push" it closer to the walls.

by jules 16y ago

ars 16y ago

The center of the earth is the position that is "lowest" if you moved away from it gravity would cause it to "fall down" back into the center.

jules 16y ago
Not if the black hole carved a spherical cave there. The forces in all directions cancel each other out inside the spherical cave.
- merraksh 16y ago
  In the perfectly spherical earth hypothesis, being the center of mass in the black hole, wouldn't there be a resulting force towards the center, although very small? [EDIT] Hmm I think I see the point. The resulting force would be proportional to the ratio (black hole mass / earth's mass). Very small indeed.
  - vecter 16y ago
    No, that's irrelevant: http://hyperphysics.phy-astr.gsu.edu/hbase/mechanics/sphshell2.html http://hyperphysics.phy-astr.gsu.edu/hbase/mechanics/sphshel...
    - ars 16y ago
      That's for a hollow shell. For a solid sphere, there is always force toward the center. (And the closer to the center the lower the force, reaching 0 in the middle.)
  - jules 16y ago
    No, the force is EXACTLY zero, not just very small.
    - ars 16y ago
      Inside the cave yes, but not when it's inside the solid mass of the earth. Inside a solid sphere the force is toward the center.
      - jules 16y ago
        Yes, but we're talking about the situation where there is a cave?
vecter 16y ago
That is completely false. Modelling the inside of the earth as a hollow spherical shell, the force inside at all points due to the gravity of the surrounding shell is 0.
- ars 16y ago
  But it's not actually a shell. In a solid sphere there is always force, and it always points to, and is lowest, at the center.
  - vecter 16y ago
    I assumed the black hole carved out a spherical hole in the center of the Earth. If it was inside it, then it would be inside a spherical shell (a very thick one at that).
    - ars 16y ago
      But, you said it would be unstable, while actually if it crashed into the wall the resultant forces would put it back somewhere in the middle. Or more accurately oscillating back and forth in the middle, but not touching the wall. If there was any vapor in the middle (which seems likely to me, considering it would be a perfect vacuum at pretty extreme temperatures), then the gas would eventually slow down the oscillations and it would end up exactly in the middle.
      - joe_the_user 16y ago
        Well, it would be sucking up the matter on the walls as well.. BTW, Sci fans of yesteryear were disappointed when it was discovered that Dyson Spheres and Ring Worlds gravitationally unstable...
        ars 16y ago
        > it would be sucking up the matter on the walls as well It won't. The first time it touches (or comes near) the wall it will take what it can get, but it will never go farther than that. There is nothing that will "push" it closer to the walls.