Naked Science Forum

Non Life Sciences => Physics, Astronomy & Cosmology => Topic started by: Alan McDougall on 01/06/2016 15:13:53

Title: How would gravity behave inside a hollow Earth?
Post by: Alan McDougall on 01/06/2016 15:13:53
If you hollowed out the earth and left a 2,000 kilometre-thick "shell", how would an entity living inside get around?

Would he be able to walk on the inside of the shell, or would he just float somewhere near the centre?

How would gravity behave inside a hollow sphere like this?

What do you think?

Alan
Title: Re: If you hollowed out the earth and left a shell, how would an entity get around
Post by: impyre on 01/06/2016 15:27:46
I imagine it depends on the thickness of the shell. If it's thick enough then you'd get some light gravity pulling you toward the shell itself (be it the inside or outside makes no difference). Of course an internal "orbit" would be impossible inside the sphere since inertia and gravity would both be pulling you back to the surface. In the center of the sphere there would be a LaGrange point similar to an L1 point, which means it would likely not be a stable point and you'd end up falling or floating back toward the surface in some direction or another. If the shell was exceptionally thin, little local gravity would be produced though... so you'd need some form of propulsion to move around, much the same as with a small satellite.
Title: Re: If you hollowed out the earth and left a shell, how would an entity get around
Post by: Alan McDougall on 01/06/2016 16:44:21
I imagine it depends on the thickness of the shell. If it's thick enough then you'd get some light gravity pulling you toward the shell itself (be it the inside or outside makes no difference). Of course an internal "orbit" would be impossible inside the sphere since inertia and gravity would both be pulling you back to the surface. In the center of the sphere there would be a LaGrange point similar to an L1 point, which means it would likely not be a stable point and you'd end up falling or floating back toward the surface in some direction or another. If the shell was exceptionally thin, little local gravity would be produced though... so you'd need some form of propulsion to move around, much the same as with a small satellite.

I did say the shell was 2,000 kilometers thick?
Title: Re: If you hollowed out the earth and left a shell, how would an entity get around
Post by: impyre on 01/06/2016 16:52:35
I can see where that would be implied to mean thickness, though it wasn't specified as such. :p
Yeah, that'd definitely give you some gravity, but it'd be weird gravity for sure. I might try to draw up a 2d model.
Title: Re: If you hollowed out the earth and left a shell, how would an entity get around
Post by: evan_au on 02/06/2016 22:39:33
Quote from: impyre
I imagine it depends on the thickness of the shell. If it's thick enough then you'd get some light gravity pulling you toward the shell itself
This calculation was done my first-year physics class at university.

As I recall, the gravitational attraction towards the center of a spherical object is determined by the amount of mass between you and the center, and is not affected by the amount of mass at a greater radius than the observer.

So in this example, the entire volume inside the sphere would experience microgravity.

You would not be pulled towards the nearby shell, because it is exactly counterbalanced by the pull of the larger amount of the shell which is on the other side of you (but farther away).

Apparently, Isaac Newton deduced this result - but then he had to invent new physics (universal law of gravitation) and a whole new branch of mathematics (differential equations) to do the calculations. A bright cookie.

Quote from: Alan McDougall
I did say the shell was 2,000 kilometers thick?
The result is independent of the thickness of the shell.
Title: Re: If you hollowed out the earth and left a shell, how would an entity get around
Post by: Alan McDougall on 03/06/2016 05:04:19
Quote from: impyre
I imagine it depends on the thickness of the shell. If it's thick enough then you'd get some light gravity pulling you toward the shell itself
This calculation was done my first-year physics class at university.

As I recall, the gravitational attraction towards the center of a spherical object is determined by the amount of mass between you and the center, and is not affected by the amount of mass at a greater radius than the observer.

So in this example, the entire volume inside the sphere would experience microgravity.

You would not be pulled towards the nearby shell, because it is exactly counterbalanced by the pull of the larger amount of the shell which is on the other side of you (but farther away).

Apparently, Isaac Newton deduced this result - but then he had to invent new physics (universal law of gravitation) and a whole new branch of mathematics (differential equations) to do the calculations. A bright cookie.

Quote from: Alan McDougall
I did say the shell was 2,000 kilometers thick?
The result is independent of the thickness of the shell.

Thus if you were unlucky to be one of its citizens, then to get around you would basically have to float from point to point?
Title: Re: How would gravity behave inside a hollow Earth?
Post by: JohnDuffield on 03/06/2016 13:35:46
If you hollowed out the earth and left a 2,000 kilometre-thick "shell", how would an entity living inside get around? Would he be able to walk on the inside of the shell, or would he just float somewhere near the centre? How would gravity behave inside a hollow sphere like this? What do you think?
Like evan said, there's no gravity to speak of. So assuming the void is filled with air, the entity would "fly" or "swim" or otherwise propel itself through the air. The situation would be akin to the ocean, where fish are largely unaffected by gravity.
Title: Re: How would gravity behave inside a hollow Earth?
Post by: chris on 03/06/2016 17:17:37
You would not be pulled towards the nearby shell, because it is exactly counterbalanced by the pull of the larger amount of the shell which is on the other side of you (but farther away).

I think the same maths and conclusion is true of the gravitational field within a "chord" cut through a sphere...