Let's make a few simplifications first; we will deal with some of them later. We assume that the Earth is a perfectly spherical ball, solid all the way through; the temperature does not rise near the core; it doesn't rotate; the object dropped into the hole does not experience friction, and it fits in the hole perfectly, without being able to move sideways.

We can deduce from the rotational symmetry that the gravitational force is still directed toward the center of the earth, even though there is a hole there. Moreover, the gravitational pull decreases as we climb down the hole since the is "less earth" below us and in fact some earth above us which pulls us up. Ultimately at the very center we have no gravity.

When we drop the object into the hole gravity causes it to accelerate, all the way until it reaches the center. After that it continues on its straight path with gravity slowing it down, until it comes to rest right at the exit of the hole at the antipodes. From there it falls back on its path, through the center, and back to its starting point. It follows from energy conservation laws that it reaches exactly the point where we dropped it. Hence it falls back, and thus oscillates between the two ends of the tunnel ad infinitum.

Now if there is friction this oscillation is damped. Thus during each period the object reaches a lower height. It will finally come to rest when the gravitational pull is not enough to overcome the friction. Depending on the amount of friction this will happen somewhere in the hole, probably close to the center. If the friction is sufficiently small it will actually reach the center and come to rest there.

Now if we add rotation (and the hole does not follow the Earth's axis) then the falling object is pushed against the Eastern Wall of the hole since the Earth rotates from West to East. This will add to the friction and dampen the oscillation even more. The size of this effect depends on the distance from the center and on the velocity so it can be neglected as we approach the resting position.

If the Earth is not perfectly spherical, but an ellipsoid, the above reasoning should certainly hold along its axes of symmetry, and very likely along the other lines through the center.

So to answer your question: If the friction is small enough the object will come to rest at the center of the Earth.

so the object would feel weightless as it would in outer space

cool thx

lawlz

Not exactly, at rest isn't weightless. In space, if you have an object then move it, it isn't drawn back to it's original point. If you had an object at the center of this hole in the earth and moved it one way or the other up the shaft, it would be drawn back to the center.

As far as an object can feel... if it rests at the center it feels very close to weightless. It's extremities will be pulled down very slightly, but that would happen in outer space too due to the object's own gravitational force.

It would have mass but not weight. If you put it on a set of scales scales would read zero

instead of capital punishment, they should throw the bad guys into a space suit and give them a little push

How would that not be capital punishment? Those suits don't have an unlimited oxygen supply.

nit

Maybe they should have thought of that before doing something bad enough to get themselves nudged into space.

NASA is such a failure

thoughts?

LOL....didn't say I was against capital punishment....just pointing out that the "space nudging" would still be a form of capital punishment. Heck....it would actually be a much quicker form....a few hours of oxygen vs several years on death row.

FYP

Depends on how sensitive the scale is, since they would both be trying to occupy the same space at the very center of the hole.

Agree... except for every other space program ever.

someone should have set food on mars by now

I think the government could've put their resources to better and more practical uses. I don't see the practical or future benefits of exploring some stars or traveling to Pluto. Basically, NASA is just a big science project to wow the masses and show how big America's dick is to the rest of the world.

NASA funding should be going towards cancer/HIV research, healthcare, or education. But wasteful gov't spending isn't a revelation. it's just fact.

but the gov't created aids

I don't follow the new closely. Is there a story I'm missing?

Also, what is NASA's budget compared to other programs?

Do you want to cede ownership of space to the Chinese? I mean sure, they own the later half of this century but we might want to make them work for it ...

You could cut out missions that go past Mars and focus on earth orbit and moon stuff.

Level?

I'm not very knowledgeable about budget allocation or even most of what NASA does (other than space exploration). However, I'm sure NASA has a significant budget (billions). It takes a lot of money to fund those projects in space and other endeavors that we know don't know about.

I'm just wondering how NASA is helping the citizens of the US. Is a 2 billion+ project worth it just for some good memories of seeing pictures of a worthless planet like Pluto? I think that money could easily go into funding research for disease prevention/cures or fixing our pathetic public school systems.

I honestly could care less if China overtakes us in the Space Race. I don't think pride is that much of a concern to me, especially at the expense of other things.

lol touche AAC. Like I said, I'm not very knowledgeable about the many operations of NASA. I'm sure there are useful things that come out of the research done in those facilities. I just think they could cut out some of the explorations, which seem pointless.

The thing about exploration is we've no idea what we're going to discover. Pure scientific research isn't always trying to come up with the new wonder drug or how to make me not get fat after eating cheetos all day. Sometimes it's just "I wonder what happens when you do X, or why does Z happen?" And the fountain of knowledge that could spring forth from such basic questions is immeasurable. The Electron was discovered in the late 19th Century, and had little practical purpose or application for decades. Now our entire economy and our silly poker messaging board couldn't happen without applying our knowledge of them. Relativity and Time Dilation was developed in the 20's and 30's, to little practical use, but now our GPS systems would break almost as soon as we put the satellites in orbit without taking them into account.

What I'm saying is, demanding immediate gratification and return on your investment from programs like NASA isn't a good way to think about it. It's about the possibility of discovering something during the exploration that peaks our interest. Something new that revolutionizes everything all over again. Super efficient solar cells, or cold fusion. I couldn't begin to tell you what it'll be or whether it'll come from NASA, but it's out there, so let's go find it.

Also, before any Moon Landing Deniers come in, I'd like to conclude with a picture of Buzz Aldrin punching one in the face.

GIFSoup

Isn't healthcare just another big science project to prove to the world how big our dicks are?

NASA - I am fascinated by the projects but when it comes right down to it there is no value what they do. Otherwise it would be getting done in private sector.

Fair enough. NASA has made a lot of great discoveries and space exploration program has brought on some great inventions. I think most NASA endeavors are worthy projects, but I just question some explorations. But I see your point Thallium and certainly agree with your point regarding the usefulness and application of scientific discovery.

UD - dunno man. Our current plan seems that way, but the healthcare situation (including R and D) is the nut low. For example, South Korea has a great healthcare system with a national plan. Their income tax is half of what we shell out to the gov't.

I guess it was unfair to really rant on NASA. I guess it was more of a complaint on the inefficient budget allocation of the gov't. We have to ship a 1/4 of our earnings to these bastards and what have they done other than create useless banter?