would you stay at the center if you jumped in the hole you dug in the earth?

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If you dug a hole through the center of the earth,and jumped in, would you stay at the center because of gravity?

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@BumbleBeeBoogie,

If you jumped in and fell to the center of the earth, you would be going pretty fast by the time you got to the center and you would shoot right past. Of course once you got past, gravity would pull you back toward the center meaning that you would keep falling back and forth like a yo-yo.

If we placed you at the center (ignoring all of the other reasons why you couldn't really do this like pressure and molten lava) then less, you would stay there at the center since gravity would keep you there.

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A cordless bungee jump.

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@maxdancona,

maxdancona wrote:

you would keep falling back and forth like a yo-yo.

Wouldn't the backs and forths get smaller and smaller and eventually stop, leaving the unfortunate faller at the centre?

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@contrex,

contrex wrote:

maxdancona wrote:

If you jumped in and fell to the center of the earth, you would be going pretty fast by the time you got to the center and you would shoot right past. Of course once you got past, gravity would pull you back toward the center meaning that you would keep falling back and forth like a yo-yo.

Wouldn't the swings get smaller and smaller and eventually stop, leaving the unfortunate faller at the centre?

Yes. You would reach a type of gravitational equilibrium.

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@contrex,

Only if there were energy lost as you were falling (i.e. to friction). If there is no energy lost, then you would keep falling back and forth forever.

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@maxdancona,

maxdancona wrote:

Only if there were energy lost as you were falling (i.e. to friction). If there is no energy lost, then you would keep falling back and forth forever.

Indeed. but I imagine that whether the tunnel through the earth was created all at once (as in a thought experiment) or laboriously dug out, it would fill with air which would introduce friction.

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@contrex,

It certainly wouldn't fill with air. It would fill will molten rock.

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@maxdancona,

maxdancona wrote:

It certainly wouldn't fill with air. It would fill will molten rock.

Yes, of course it would, but then the intrepid traveller would not fly though to the other side of the world, they would burn up like a fly in a deep fryer, and we wouldn't have any back and forth oscillation, would we?

If we imagine for the sake of a hypothetical exercise (the one implied in the original question) that it was possible for a the earth to be a sphere of some non-melting material that would allow a tunnel right through the centre to the other side, then anyone jumping in of their own volition must necessarily be alive at that moment, and breathing air, and surely that air would either have already filled the hole, or be busily doing so?

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@contrex,

Sure, but what would the guy weigh when he did come to equilibrium?

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@BumbleBeeBoogie,

If you had frictionless roller-skates and zero air resistance (etc), you would theoretically oscillate about the centre of any straight tunnel bored from one location to another, or indeed any tunnel of radius of curvature greater than that of the earth.

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@roger,

roger wrote:

Sure, but what would the guy weigh when he did come to equilibrium?

Nothing. He would be weightless, just like someone in orbit.

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@contrex,

Then air pressure would also be zero, with a partial pressure of oxygen also being zero. He would suffocate.

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@roger,

roger wrote:

Then air pressure would also be zero

Talk me through why that would be. Would there a pressure gradient each side of the centre?

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@contrex,

Ah, but air pressure is a function of gravity. No gravity; no air pressure. If the guy is weightless, why would air not also be weightless?

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@contrex,

Quote:

If we imagine for the sake of a hypothetical exercise (the one implied in the original question) that it was possible for a the earth to be a sphere of some non-melting material that would allow a tunnel right through the centre to the other side, then anyone jumping in of their own volition must necessarily be alive at that moment, and breathing air, and surely that air would either have already filled the hole, or be busily doing so?

We could just as easily imagine for the sake of a hypothetical exercise (the one implied in the original question) that is was possible for the hole in the earth to be constructed of some air tight material ...

The original question didn't say whether the jumper jumped in of their own volition, nor did it say there was any care taken to keep them alive (i.e. by providing them with air although we could also give them a tank of oxygen if we really cared).

It seems easiest, and most instructive, to imagine the exercise without air. That is the point of hypothetical exercise. I was merely pointing out that my imagining with no air is no more of a stretch then your imagining with no molten lava.

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@roger,

Quite the contrary roger. Pressure is not a vector quantity (i.e. it doesn't have a direction).

You would have the pressure from one side adding to the pressure from the other side. Assuming air pressure, they wouldn't cancel each other out. They would double.

If I am pushing on you with from the left while Contrex pushes from the right, you are going to feel squished with twice the pressure (even though you don't experience any acceleration).

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@roger,

To clarify, the molecules at that very center would be "weightless". But there would certainly be pressure.

Consider the column of air on one side of this tunnel with the bottom at the center of the earth and the top at the Earth's surface. The air molecules at the top of this column would feel a large pull toward the center. The molecules below them would not only feel their own gravity, they would also have the pressure from the molecules above them. At the center the pressure would be the sum of the weight of all of these air molecules.

Then double that. Allowing for air in our hypothetical lava proof tunnel, the pressure at the center of the Earth would be quite high.

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Unless your tunnel is from pole to pole you would also be dealing with one hell of a large change in your angular momentum that I would assume would cause you to be press again the walls of that tunnel.

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would you stay at the center if you jumped in the hole you dug in the earth?

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