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Why do the gravitational forces within a hollow (Newtonian)shell planet ,not tear a body apart?

The gravitational force within a hollow shell like planet are mathematically zero -- yet presumably, a body inside the planet would feel equal forces acting on it from all sides ?.These undoubtedly "cancel out", but only in the sense that the body as a whole ,would not experience any net motion ?.

But doesn't the body still feel "hydrostatic " forces pulling it apart ?

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  • neb
    Lv 7
    9 months ago
    Favourite answer

    Hydrostatic forces are probably the wrong word to use. I don’t think you are asking whether there is gravitational force on a point body (which is easily shown to be zero), but why aren’t there tensions across an extended body within the shell?

    It’s sometimes useful to drop back and think of forces as being derived from some form of potential, gravitational potential in this case. The forces are derived from a change in potential, e,g. F=-∇U. So, if the gravitational potential, U, is constant within the hollow sphere, then there are no forces F across even an extended body. This the case with the hollow sphere. The gravitational potential is constant over the entire interior so no forces are exerted across extended bodies.

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    • neb
      Lv 7
      8 months agoReport

      It’s nice to answer question for somebody who reads and studies answers, and asks follow on questions. It’s the way this forum should work, but rarely does.

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  • Who
    Lv 7
    8 months ago

    "The gravitational force within a hollow shell like planet are mathematically zero"

    no it aint -

    I would advise ANYBODY who thinks it is study einstein's theory on gravity

    the planet itself does not create gravity

    Its the effect its mass has on space/time that creates it

    the mass creates a distortion in space/time - its that distortion that creates the effect of "gravity"

    and THAT distortion does not change whether you are inside or outside the planet (hollow or not)

    The MAXIMUM gravity is at the centre of that distortion - which is the centre of the planet (hollow or not)

    (I would go and sue wherever you were taught to get your money back "carolOklanola" cos this is wrong

    "The gravitational forces cancel out only at the center"

    cos this could ONLY occur if gravity was PULLING equally in all directions - but gravity is NOT the effect of something "pulling" - but of something (that distortion in space/time) PUSHING

    and something "pushing" on you from all directions will maximise the effect of that distortion)

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  • 9 months ago

    Newtonian physics don't quite work that way. While it is true that anything with mass has gravity, a hollow shell would behave much like the gas giants such as Jupiter and Saturn. This is because the center space must have a gas (and therefore an attributable mass) otherwise the object would collapse upon itself in the vacuum of space and form a solid core, due to the fact that the walls would have equal gravitational attraction to each other.

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  • 9 months ago

    A real shell the size of a planet can't exist. It would crumble and collapse. This shell concept is just a thought experiment to study how gravity works. There would be no gravity inside the shell, IF such a shell were possible.

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  • cosmo
    Lv 7
    9 months ago

    The absolute magnitude of the gravitational potential energy inside the shell is larger than outside the shell, but it is uniform inside the shell so there's no gravitational force.

    Newton calculated this. Pick a point anywhere inside the shell (your location). Chose any line that goes through that point as the axis of a cone, and construct the whole cone, a "double cone" with both nappes. In general the intersection of one nappe with the shell will be smaller than the other, and so will cut off a smaller piece of the shell, but the distance to the vertex point will also be smaller. The gravitational force from the two cut-off pieces of the shell will be equal, because the size of the cut-off piece is proportional to the square of the distance to the vertex, and the strength of the gravitational force varies as the inverse square of the distance. The small piece is nearer to the vertex by an amount that exactly compensates for the smaller size of the cut-off piece of shell, so the gravitational force from the two nappes cancels.

    Since the net force is zero for every part of your body, there is no tidal "spaghettification" force like there is inside a black hole.

    BTW, this generalizes to the force inside a shell that is bounded by two tri-axial ellipsoids.

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  • Dixon
    Lv 7
    9 months ago

    The forces cancel each other to zero. It's like you have two guys equally pulling either end of one rope and you grasp the rope. There is no force from the rope acting on you because the two guys cancel each other out. Its not like being pulled apart by two ropes, you can't insert yourself between the two forces, they cancel out and the net result operates on you.

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  • 9 months ago

    "hydrostatic " forces ?? no such thing.

    the gravitational forces inside a shell are zero everywhere.

    You are perhaps, thinking of forces on an object closely orbiting a massive body. if the body is, for example, a thin rod oriented perpendicular to the orbital motion, the two ends of the rod experience forces tending to pull the rod apart. This is due to the facts that the ends of the rod want to be in different orbits due to their different distances from the central body.

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  • 9 months ago

    Because any Tidal Forces would be equal and stable

    As well as the pressure

    Source(s): What a silly Question.... signed. Arthur Limb Bimb Wimb, Bimb, F'tang Ftang Ole Big Biscuit Barrel I have changed my name to Vincent Wong, which is a bit less silly... Penguins don't have nipples, don't they ??
    • Ronald 7
      Lv 7
      9 months agoReport

      I cant stand all these lies !

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  • 9 months ago

    You are ignoring solid body tides that Earth DOES experience, up to a foot or more. Earth is NOT hollow. The gravitational forces cancel out only at the center where the force of pressure is greatest and make the inner core solid. Pressure IS a force like gravity, an opposite force. Earth's crust dies fracture where the stresses and strain limits are exceeded because of solid earth tides and tectonic forces . The result is major earthquakes and tsunamis. Europa's crust of ice is fractured because if gravitational stresses and strains from an elliptical orbit around Jupiter resonant with Io, which is the most volcanically active body in the Solar System, and Ganymede.

    Source(s): B.S. geology, M.S. ABT geophysics, B.S. physical geography, M.S. geology
    • hoarseman
      Lv 7
      9 months agoReport

      I accept that unequal gravitational forces -- tidal forces-- can "stress" a body

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  • 9 months ago

    What would these hydrostatic forces be? And where do they come from? The gravitational forces inside a hollow shell planet are zero, it's just as if the shell was not there at all.

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    • neb
      Lv 7
      9 months agoReport

      Hoarseman- that is why it is better to use gravitational potentials as fundamental and force as a derived quantity. The gravitational potential can be non-zero and at the same time the force can be zero.

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