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Imagine a hollow 100 metre diameter (for example) sphere made of incredible dense material (ie neutron star dust etc) but is self supporting (ie the central cavity).

Assuming that the sphere skin is reletively thick so that the whole object is exceptionally heavy (eg the mass of planet earth.

What would someone who was stationed dead center of the sphere feel? IE would they be crushed by the potential gravity or ripped apart and smeared on the inside other sphere cavity (due to the gravity of the surrounding material?

Jake Harman
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2 Answers2

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Gravity is gravity is gravity. Whether treated using Newtonian gravity or GR, the result is the same. An observer anywhere within the hollow of the sphere feels no force. This result is independent of the density of the hollow sphere (assuming only that the density is the same on every "shell" of distance $r$ and the sphere isn't rotating) - it's a result of symmetry.

To elaborate:

(1) Using Newtonian gravity, this can easily be seen via the "Newton's shell theorem". The observer inside the hollow experiences no gravitational force.

(2) Using GR, this can easily be seen via "Birkhoff's theorem". The observer inside the hollow is in flat (Minkowski) space-time - there is no curvature and therefore experiences no "gravitational force".

Will
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The answer is that the person in the hollow shell would feel no gravity at all (assuming the shell is the only significant source of gravity). The person can be anywhere inside the shell, and this will still be true. This can be understood as a consequence of Gauss's law for gravity.

$$ \oint \mathbf{g} \cdot d \mathbf{A} = -4\pi GM $$

where the integral is a surface integral over gravity, $G$ is the gravitational constant, and $M$ is the mass enclosed by the surface.

It's difficult to explain why this in a mathematical way, unless you're familiar with vector fields and flux.

An easier to understand explanation is that all the gravity cancels out. If the person inside the sphere is really close to one side (left side for example), then the mass on the left side pulls more strongly because it's closer. But if the person is on the left side, then there's far more mass pulling from the right side, even if each amount of mass pulls more weakly. The gravity from both sides cancels out perfectly, regardless of where you are in the sphere. The result is that the person inside feels nothing.

David
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