Which way would you fall?

If there were a small hollowed area in the exact center of the earth, and I were to stand inside, which way would I “fall”? Would the gravitational forces around me cancel each other out and have me float as if there were no gravity, or would I feel like I was being pulled outwards from myself?

If the “small hollowed out area” is at the center of mass of the earth, you would just float there just as if you were in orbit around the earth.

Cecil addressed this

By definition one always falls “down”.

Everywhere inside a hollow symmetric shell, no matter how thick, the gravitational effect of the shell self-cancels, and objects inside the shell would be weightless.

Not perfectly weightless though, would they? I mean, wouldn’t there be some miniscule gravitational pull from objects on the earth and objects beyond the earth? If one half of the earth’s land had a greater total mass (due to large man made objects, buildings and what not), wouldn’t the person in the cavern float towards that side (even if at a miniscule rate)?

I am no scientist, but maybe one of you can answer these?

Actually, I don’t buy Cecil’s thoughts here.

If you were transported to a hollow cave at the centre of the Earth, wouldn’t you smack rather quickly into one side of this chamber, since the Earth is moving pretty quickly around the sun, and thus possesses momentum that you would not?

Or, assumming that you somehow started off with exactly the right momentum in the right direction so that you are stationary relative to the Earth, this will eventually be out of kilter since the Earth is not moving in a straight line - thus you will drift relative to the cave (although you are still technically weightless, I guess).

I don’t know how you would get to the center of the earth without sharing its velocity. Mass cancels out of the equations calculating orbital forces so the sun would should hold you in the same orbit as the earth if you start out with the same relative velocity. The effect of the moon might create some differences but that is nitpicking pretty far from the real question being asked.

The earth is actually quite lumpy at mean sea level due to variations in density and elevation so your point makes sense. On the other hand the only reasonable definition of the center of the earth would be the center of gravity where all forces are cancelled out.

I would think that you would feel quite weightless, but you would “fall” extremely slowly toward the side of the earth that has slightly more mass. You wouldn’t even notice you were falling (It would be that slow).

If we’re positing an XB-7 MK2 matter transmitter that will beam you into the center of the Earth, it seems reasonable to posit purchasing the “momentum-matcher” upgrade.

Well, this is a germane point, actually, although not in the way you meant it. Consider: if you were an object in space, located somewhere along the Earth’s orbit, with a velocity that matched that of the Earth, what would happen? You’d orbit the sun, of course. So, even though you’re physically located in a cavity at the center of the Earth, you’re still orbiting the Sun, right along with the rest of the Earth.

What makes that interesting is that it sorta answers the OP: right along with the Earth, you’d be “falling” toward the Sun, in the same sense that satellites (or the Moon) “fall” toward the Earth.

Although, if we’re talking about the gravitational pull of the Sun, seems as though the gravitational pull of the Moon would be pretty substantial (does anyone remember where the CG of the Earth-Moon pair lies? It’s within the shell of the Earth proper, but I thought it was several hundred miles off from the CG of just the Earth.). So really, I suppose, you’d be falling toward the Moon.

You were moving with the same velocity as the earth before you were banished to that “hollowed out area” at the center of mass and you would retain that velocity.

Even at the center of mass you would still orbit the sun because of the sun’s gravitation. And since you and the earth’s center of mass are at the same orbit, the two of you would move together.

Because you would in free-fall around the sun, you would also feel no “weight” because of the sun’s gravity.

You know, come to think of it, you might rattle around a little before settling down. Your velocity wouldn’t be the same as the earths if you started from the surface because of the added velocity you have from the earth’s rotation.

No, because of the ocean and the principle of isostasy (the continents are “floating” and are depth compensated), the center of figure and the center of mass are the same place–but of course that depends upon how you define center of figure. It’s true of the usual definition. The center of figure of an equipotential surface is the same as its center of mass.

You’d float similar to the way astronauts float on the shuttle, in orbit around the Earth.