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[LARD]

Here is a question my younger brother and his friend came up with and it has been bugging me. Hypothetically, if we were to drill a tunnel through the center of the earth, right from one side to the other, and it was a vacuum. There's no air or particles of any kind in it. you drop an object from one side and it goes straight down through the hole. (this is assuming completely perfect circumstances) Would the object come to a rest in the center of the earth because of gravity, or would the lack of air resistance mean that it would oscillate endlessly? Think about it.

I don't know the answer, so I hope that some of you who know more about physics can help me out.

[Jerick]

It'll lose a bit of energy every oscillation so it'll eventualy come to rest.

[LARD]

from what?

[Bauglir]

Assuming no loss of energy of any kind, that the Earth is a perfect sphere and its gravitational field is perfectly uniform, etc, it'll oscillate eternally. It will convert potential energy into kinetic energy until it passes the center, and then kinetic energy back into potential energy until it runs out of kinetic energy - at which point it falls back again.

EDIT: Also assuming that the Earth is immovable. I think that might be important.

[kaijyuu]

If there's no friction, it will oscillate endlessly. In reality, there's pretty much always friction, even in outer space (though a comparatively tiny amount to what's in a gas filled environment like Earth's surface), so it'll come to rest eventually.

[Graknorke]

Pretty sure it'd just oscillate forever, ignoring the potential for the Earth to accelerate unexpectedly in rotation or speed, in which case it'd bounce against the walls until it came to a stop in the centre.

[LARD]

The real question is, will the object that was dropped reach the same distance on the other side of the gravitational center as where it started.

[Graknorke]

The real question is, will the object that was dropped reach the same distance on the other side of the gravitational center as where it started.

So long as the gravitational field is perfectly uniform, yes.

[Bauglir]

Yes. Such is the nature of the conservation of energy.

[ChairmanPoo]

I'm leaning on it stabilizing over time, friction or not. The gravitational pulls would result in it losing momentum over time.

[Jerick]

I was going to say particles but;

or particles of any kind in it.

Reading comprehension fail.

But any loss of speed no matter how small will eventualy stop it.
If any particles or pieces come away from the object then you have something in the tunnel that could impact the object and slow it down.

[TheBronzePickle]

Assuming perfect conditions (perfect vacuum, perfect gravitation, no acceleration to either object other than that of gravity) there would be no way for the system to stabilize. Of course, there's no way to get perfect conditions like that in the real world.

[Ricky]

somewhat relevant link

[zombie urist]

Assuming a Earth is a perfect sphere and there being no friction, the item would oscillate between the ends of the hole with a period of IIRC slightly more that an hour.

You can calculate this by using Newton's law of gravitation.

[Lectorog]

I read a book with this in it. It would oscillate endlessly, reaching the same point on both sides.
I think you have to make the Earth uniformly dense, as well.

And the book was on 4-dimensional spacetime, so it got more interesting once that was established.