[Admiral_Stones]

Hello people.

This question was bugging me for a while now:

Okay. We are assuming that the Earth was just a rock, no magma/lava and other potentially damaging substances included.
So, one would would dig a hole 20m in diameter exactly from the north pole to the south pole.
Now, somebody falls into it. I think that he would reach his end speed, fly past the middle point, continue some meters and then the gravity would reverse, and he would fly in the other direction. O.C. he would get ever slower and eventually rest in the middle.

Correct?

[achtung]

I'm pretty sure the pressure would kill you long before you reached the center.

Of course, I'm only guessing.

[Herra Tohtori]

Drat, too sl0w... well, I'll post it anyhows.

Hello people.

This question was bugging me for a while now:

Okay. We are assuming that the Earth was just a rock, no magma/lava and other potentially damaging substances included.
So, one would would dig a hole 20m in diameter exactly from the north pole to the south pole.
Now, somebody falls into it. I think that he would reach his end speed, fly past the middle point, continue some meters and then the gravity would reverse, and he would fly in the other direction. O.C. he would get ever slower and eventually rest in the middle.

Correct?

Well. There's two possibilities. Either you ignore atmospheric friction (and the pressure related problems), or you don't.

In reality, air would rush into the hole and fill it. This would result in the air in the centerpoint having hydrostatic pressure of A LOT, I won't be calculating it here because the variable gravitational acceleration is a bit problematic at this kind of scenario and I can't bother to start integrating like a madman at this point of the evening... suffice to say, the atmosphere is about 100 km thick and results in one atmosphere pressure at the sealevel. You would not want a 6356 km high atmosphere on top of you. Really, you wouldn't. It's possible it couldn't even be called air any more in that situation, it might liquify under the immense pressure. Along with you.

Ignoring that, an object falling into this kind of pit of doom would pretty much accelerate to terminal velocity, which would be decreasing towards the center of the tunnel as the pressure and density of the air would increase. It's even possible that at some point the falling object would start to float, and at any case it's behaviour would more and more resemble that of a sinking stone than that of a falling object.

Anyway, the end result would be that if the object were denser than the atmosphere in the center of the tunnel, it would end up there. If it's density was smaller than the air's at the centerpoint of the tunnel, it would end up "floating" at the point where it's density matches the surrounding air's density.

On the other hand, if you ignore the air friction, you would end up with a harmonic oscillator - the velocity of the fallign object would increase until at the centerpoint of the tunnel, then it would reduce it's velocity, falling upwards towards the other end of the hole. It would reach the same altitude on the other side as it did on the other side. And without hitting anything, it would keep falling from one end to other forever.

[Admiral_Stones]

But... doesen't that equal to a perpetuum mobile?

[castor]

No more than the rest of the solar system etc.

[Herra Tohtori]

But... doesen't that equal to a perpetuum mobile?

No. Perpetual motion device is generally perceived as a device that either has bigger energy output than input, OR converts thermal energy continuously and spontaneously to mechanical work.

An oscillator you have described does neither. It just goes on and on without outside resistance - not unlike planets, moons and stars guided by the same force of nature, gravity.

In fact, the falling object actually is on an "orbit". The orbit just is inside the radius of the bigger body of the system. And most orbital terms like apogeum and perigeum don't really apply either....

[Admiral_Stones]

Cool. Now, let's see what happens when you throw some touch-sensitive explosives along 

[Dark RevenantX]

Hmm.  In a spacesuit with enough oxygen, one could literally traverse the entire rock and grab hold of the ledge at the end.  That, indeed, would be trippy.