Hollow earth physics

[CurtC]

@Canadjun

I’ll let someone else provide the mathematics to show it works out evenly, but keep in mind that if you are on the outside of a hollow sphere then the whole sphere is pulling you more or less down (either directly down or down at an angle, but no part pulls up). On the inside you are pulled in both directions, and it turns out the pulls balance.

This is the best answer to the OP - a correct and intuitive explanation that he was looking for.

[ZenBeam]

@AargleZymurgy

So which “hollow earth” article is correct?

How much would I have to hollow out the earth to make the days longer? - The Straight Dope

What if you fell into a tube through the earth? - The Straight Dope

hmm?

Both.

I’m guessing the confusion is that in the Tube Through the Earth case, you’re only weightless in the center, while in the Hollow Earth case, you’re weightless everywhere inside. The difference is that in the first case, almost all of the Earth is still present, pulling you towards its center. In the second, all of the Earth’s interior has been removed and placed on the surface.

[Irishman]

Agreed.

[SCSimmons]

The conditions of the math in question are that the mass distribution is radially symmetrical. That is, the density at a given point can be determined entirely from your distance from the center of mass. This is obviously not true in the case of a hole bored through the planet, but will be true (at least to a close approximation) when the planet has been fully hollowed out.

[Kurt_N]

@SCSimmons

The conditions of the math in question are that the mass distribution is radially symmetrical. That is, the density at a given point can be determined entirely from your distance from the center of mass. This is obviously not true in the case of a hole bored through the planet, but will be true (at least to a close approximation) when the planet has been fully hollowed out.

It will also be true to a close approximation with the hole through the planet. The hole is narrow and the missing mass doesn’t make much difference to the gravity field.

[Andy_L]

@ZenBeam

Both.

I’m guessing the confusion is that in the Tube Through the Earth case, you’re only weightless in the center, while in the Hollow Earth case, you’re weightless everywhere inside. The difference is that in the first case, almost all of the Earth is still present, pulling you towards its center. In the second, all of the Earth’s interior has been removed and placed on the surface.

Yes.

[SCSimmons]

@Kurt_N

It will also be true to a close approximation with the hole through the planet. The hole is narrow and the missing mass doesn’t make much difference to the gravity field.

Well, yes–the point is, you won’t be weightless everywhere inside the hole. Gravity will slowly decrease as you get closer to the center of the planet, as the mass outside the narrow hole will continue to exert gravitational force on you.

[Kurt_N]

^ Right. I’m just saying that radial symmetry isn’t the point of difference. The key difference is the amount of mass that’s closer to the Earth’s center than you are. For the hollow Earth scenario that amount is zero. For the tunnel case it’s nonzero.