Scientific opinion discussion -- What would happen if??

[mjr]

First, assume spherical <whatever> in a vacuum...

I kid.

But seriously...

Let's say you had a sphere about the size of a bowling ball. And let's say that sphere was nearly indestructable, in that it would resist low/high temperatures and pressures.

And let's say we had the ability to drill a 2 meter diameter hole all the way through the earth, in a straight line.

So now, you have a sphere, and a 2 meter diameter hole through the entire earth. If you dropped the sphere into the hole, what would happen?

My hypothesis is this:

The sphere would gain speed until it reached terminal velocity. Once it passes where the center of the earth would be, it then would be headed on an "upward" trajectory, until it lost enough kinetic energy. Then with maximum potential energy, the sphere would fall back through the earth again.

I think eventually the sphere would "stop" at the spot in the hole where the "center" of the earth would be.

Anybody else got opinions on this??

[Jay 2K Winger]

I think eventually the sphere would "stop" at the spot in the hole where the "center" of the earth would be.

Anybody else got opinions on this??

This is exactly what would happen. The sphere might pick up enough velocity on its trip through the earth to go up in the sky on the other side, but gravity would pull it back down through, but I think over time and numerous trips, it would lose momentum and eventually just stop by the center of the earth.

[Yfandes]

but if it shot out of the hole on the other side a fair distance, wouldnt the rotation of the earth, winds, Coriolis force... make it probable that it would not come back down exacty into the hole?

[mjr]

but if it shot out of the hole on the other side a fair distance, wouldnt the rotation of the earth, winds, Coriolis force... make it probable that it would not come back down exacty into the hole?

I think Terminal Velocity would probably keep that from happening. Especially if there were air friction in the hole.

[lordlundar]

I doubt it would even get through the hole.

First off, the Earth is not a solid mass, so once the hole got to the liquid portion of the core it would likely be whisked away.

Second, even if it got through bot ends of the liquid portion, the crust essentially floats on the liquid portion so the hole wouldn't line up.

Finally, assuming it was a solid mass all the way through, unless you drop the orb through the pivot of rotation of the planet, the orb would hit the walls of the hole and lose a lot of kinetic energy, preventing it from popping up at the other end.

[Ironclad Alibi]

The sphere would gain speed until it reached terminal velocity. Once it passes where the center of the earth would be, it then would be headed on an "upward" trajectory, until it lost enough kinetic energy. Then with maximum potential energy, the sphere would fall back through the earth again.

I think eventually the sphere would "stop" at the spot in the hole where the "center" of the earth would be.

I agree.

For extra points, what is the weight of that bowling ball once it comes to rest at the center of the earth? Why?

[wolfie]

Zero, because gravity is acting on it equally in all directions.

[Buzzard]

Also, your ball would be bouncing off the wall of the hole/tunnel pretty much the whole time. Rotational speed at the surface is higher than down below. As the ball drops, this gets rather noticeable.
Yes, ignoring the oozing fluids and such in the hole. Since we're putting in that big a hole, it should have a nice casing.

[mjr]

What if the hole was "pole to pole", so then there's only axial tilt to deal with? You'd still have rotation, but it would be around an axis at that point.

[lordlundar]

I could have sworn I covered all of these issues already...

[mjr]

I could have sworn I covered all of these issues already...

Indeed you did.

I was more interested in the "end result", which was also covered.

[ComputerNecromancer]

first off, this is an *old* physics problem. Well worked out for teaching students.

Assuming we can ignore rotation and air friction, and that earth was a perfect sphere of either uniform density, or density that changed with depth (ie a series of nested spheres of whatever density) the ball will fall thru the center and go up to the exact altitude it was dropped from, on the other side.

It will then fall back down to the other side and return to the exact point it was dropped from.

Repeat indefinitely.

It starts at distance X from the center of the earth and kinetic energy of 0. As it drops, distance decreases, and kinetic energy increases.

Kinetic energy reaches a maximum at the center of the earth, where the distance is zero. Since exactly the same forces will be *decelerating it as it passes the center of the earth, it will hit distance X on the other side and once again have
KE of 0.

The velocity (and thus KE) varies oddly. That's because the gravity inside a hollow sphere of constant density is zero. Not just at the center, but at all points inside. It requires calculus to prove it, but it's a fairly simple proof.

So, that means that as the ball falls, all of earth that is farther from the center than the ball is, counts as such a hollow sphere. So the sphere is only affected by the attraction of the parts *closer* to the center than it is.

If you work this out, it means that the gravity in your hole varies *linearly* from 1 g at the surface to 0 g at the center. So 1/4 of the way in, you've got 0.75 g, halfway in you've got 0.5 g, 3/4s of the way in you've got 0.25 g, etc.

This makes calculating velocity at any point a bit of a pain.

Anyway, I went thru that because it has a big effect on things if you do have air in the hole.

The air is going to get denser and denser the deeper you go. Which will cause more and more resistance to the ball. Heck. by the time you reach the center, the air (under 4000 *miles* of pressure) is likely denser than the ball. In which case it'll only go a bit past the point where its density matches that of the air, and then float back up. it'd oscillate around that level a few times before coming to rest.

[Ironclad Alibi]

Zero, because gravity is acting on it equally in all directions.

We have a winner!