all the mass were concentrated at the center. So if you could drill a hole along a diameter of the earth and toss an object down into it, I should expect the object to bob around the center. I expect that if you allowed the hole to fill with atmosphere, the gas would be distributed along the hole according to the usual barometric law; then atmospheric resistance would dampen the bobbing; and (it being about 4000 miles to the center) a reasonably dense and compact object would be heated by friction against the gas and might be expected to burn as meteors do

(and at the center, net force is zero). So it behaves as a "spring" system - force is linear with displacement:

http://en.wikipedia.org/wiki/Harmonic_oscillator

whether position: exterior to the shell, the effective force is as if the mass were concentrated at the center; interior to the shell, there is no effective force. so by decomposing the sphere into infinitesimal spherical shells, we see the effective force at an interior point at distance r from the center is as if the mass of the subsphere of radius r were concentrated at the center. so i guess you're right: with the cubic law for mass and an inverse square law for the force, we probably get a linear variation of force with r at interior points. that probably means i'm wrong about the barometric law, too. i'm too lazy to do the atmospheric calculations right now

They increase as you go in: http://jersey.uoregon.edu/~mstrick/AskGeoMan/geoQuerry57.html

So the variation wouldn't be linear, after all.

It will bob back and forth, with sinusoidal motion (at least, if you drill through the axis of rotation).

Greg Benford actually wrote this into one of his "galactic center" books, where a civilization cored a planet as described, and a human falls through.

to answer the OP's question about whether a dropped object might be crushed

Which, as we all know, is at the center of the Earth.

(the object you threw in) and the heat escaping into the atmosphere would crisp us all.

IF you could drill a hole.. we've made it about 8 miles into the crust so far with modern tech. only 7902.41 miles to go!

they did actually almost reach the lower crust at a site in the Atlantic a few years ago, but I haven't seen the data release.

So far, we can't even make drill bits that don't melt at 12 miles deep..

injects them both into the Earth where they orbit the Earth's core until they meet and annihilate, destroying the planet.

is that what you really want??!

Or any moon, for that matter.

I just never knew. Does it have a molten core like planets do, or did it ever?

The interior of the moon is layered into a hard, outer crust, a rigid outer mantle, a semi-rigid inner mantle, and a core. The interior of the moon is cooler than the interior of the Earth. Since the moon is so small (and so its surface area to volume ratio is large compared to that of the Earth), it loses its heat quickly into space. Since the Earth and the moon formed, the moon has cooled down much more than the Earth.
http://www.enchantedlearning.com/subjects/astronomy/moon/Mooninside.shtml

If it's molten, then the moon is like a grilled cheese sandwich.

Ignoring all other effects (friction, materials, etc.) except gravity...

As it falls down the hole it will accelerate reading maximum velocity at the center of the earth (where incidentally gravitational force is zero). It's momentum continues up the other other side only now the gravitational force is slowing it down until eventually it makes it's appearance at the other end. If no one is there to catch it, it will fall backward and repeat the motion in reverse.

It's a rather classic differential equation and you can see the solution here:

http://www.physicscentral.com/explore/poster-earth.cfm

The period of the system works out to 84 minutes (42 minutes each way) which is also the period of the lowest possible orbit if there was no atmosphere or mountains.

The other fun thing is that any straight hole bored through the earth but not necessarily through the center exhibits the same period. Say a hole from San Fransisco to London. Instead of falling, now you're rolling. You're acceleration is less because of the angle and it works out that it doesn't matter.

The answer is always 42 (minutes).

Well, that is the answer to life, the universe and everything after all.



(my... that's big)

To simplify the math, assume no air friction or wall friction (vacuum tunnel and ice walls).

If the tunnel has the right shape, an object released into the front of the tunnel will be accelerated to escape velocity by the time it reaches the other end of the tunnel.

I could be wrong, but that's my recollection.

A more relevant definition of escape velocity than some number calculated for the surface of a given body is that it's the speed required for the kinetic energy and the gravitational potential energy to add to zero (where we take zero potential energy to correspond to infinite separation between the body and the planet/moon/other massive primary object).

So while one might exceed the number you would find for "escape velocity" from Earth's surface inside such a tunnel, you'd be much deeper in Earth's gravitational potential well. Leaving aside rotation, friction and all the other complicating factors, the best you can ever do is start at Earth's surface at rest and return to the surface elsewhere with zero speed. The sum of KE and PE will always be whatever it was when you started - simple energy conservation - and that sum will always be negative in the situation you describe, no matter where you are on the trajectory.

...You could build the hole in a parabola and pull a gravity assist orbit. Not sure how to work out orbital speeds inside the planet, though.

You'd just come out of the hole with (at best) the same speed you entered (relative to the planet, which is all that matters for escape velocity or even reaching orbit).

Gravity assist is a problem where the planet and spacecraft are in a system dominated by the sun. The kinetic energy gained by the spacecraft (for a big change in speed) is lost by the planet (for a negligible change in speed). By contrast, this is more of a 2-body problem in which Earth is essentially at rest before and after; it has no orbital speed about itself to contribute to the object you're trying to fling into space.

We've got this pesky moon exerting a weak but noticeable pull off to the side. And the side in question is constantly moving...
If you managed to arrange it so the hole passed through the earth/moon barycentre when you dropped, you could possibly get a single complete transit before it went bang.

Incidentally, and ignoring atmosphere, the time it would take to get from one side to the other is 42 minutes.
Somewhere, Douglas Adams is laughing...

Well, if you want to get the video on YouTube.



Besides, every kid knows that all you need is a shovel and an afternoon to dig a hole to China (or wherever you think the other side of the earth is).

so far all the crap that was through in on one side, failed to come out the other side.

The man is a regular black hole.

it took me nearly 2 minutes to find it, the least you can do is watch it

Thanks so much!