What if there were a hole from pole to pole?

Question

The age old question, I know & cliche, but what would happen? I told my friends that the gravity from all points would center on one location and crush anything there. is this true? What would happen?

Answer 1

If you drop something into the hole, it will keep oscillating from one pole to another just coming out exactly to the height above the surface from which it was dropped forever.

This is because when it goes to the center of the Earth, g is pulling it towards the center of the Earth. The acceleration will keep on decreasing as it goes closer to the core but its velocity will keep on increasing. At the core, acceleration would be 0 but it will travel further due to inertia. Now the acceleration due to gravity will act as deceleration. The magnitude will remain th same but the direction will be opposite. So after covering exactly the same distance, its velocity will become 0. Now it will go towards the center again due to g. This continues forever.

Hope this helps.

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Answer 2

cpc26ca, excellent!

How about some more details...

What would happen if we dropped a ball down the tunnel from the northh pole? Mark and RainHater are basically correct that the ball would come to rest at (or at least pretty darn close to) the center of the earth, ASSUMING that the tunnel is is filled with air and thus would slow the ball down.

It doesn't take very long at for a dropped baseball to reach its terminal velocity (the speed at which deceleration due to wind resistance exactly balances acceleration due gravity). In fact, tthe air would be densest at the middle of the tunnel and thus slow the ball down more than at either end. I haven't done the calculations, but I wouldn't be surprised if the ball never makes it past the halfway point. But, I can hear you asking, won't gravity pull the ball through even the densest air. Yeah, but...

The force of gravity inside the earth is directly proportional to the distance from the center of the earth. It's kinda like a spring pulling an object through air. If the spring is strong enough compared to the weight of the object and the density of air, the spring will pull the object PAST the spring's rest position and start pushing it back in the opposite direction. If the spring is relatively weak, it will continually pull the object assymtotically closer and closer to but never quite at its rest position. Same thing with our ball and gravity -- depending on the drag of the ball through the air and the gravitational pull, maybe the ball will pass the center of the earth, maybe not. A lead ball might, while a styrofoam one wouldn't.

BUT...
What if all the air was sucked out of the tunnel so that there was no wind resistance on the ball? As I mentioned before, gravity is directly proportional to the distance from the center of the earth. Mathematically speaking, the second derivitive of the position is directly proportional to the position (with a negative sign). d^2x/dt^2 = c1 x (with c1<0). This is an easy one. x = c2 sin(t) This means that path of the ball describes a sine wave. Drop the ball at the north pole, it just barely makes it to the surface at the south pole and then reverses direction.

As for objects being crushed at the center of the earth... No. The gravity pulling you one way is exactly cancelled out by the gravity pulling the opposite direction. This balanced sum is acting on every atom in the ball (or your body, or whatever). In order for something to be crushed, you'd need something forcing your top down while something else forces your bottom up. As it is, all the gravitational forces would balance out and you'd end up just floating weightlessly at the center of the earth.

Am I positive that the gravity in the tunnel is directly proportional to the distance from the center of the earth? Yes. If you REALLY need to see it, I can find or make a web page that works out the double integral to prove it. You could probably google it.

Answer 3

Although there are so many flaws with this question because it would be absolutely impossible for a tunnel or hole from pole to pole. I think the ball would drop and the momentum would carry it until it almost reaches the other pole and then it would come back and keep passing the center of the core, back and forth, until it came to rest.
My question is, what would it be like to be in the center of the earth? The exact center, assuming you could hollow it out. Would you be weightless?

Answer 4

Well,

Gravity is coming from the core, so if for example you dropped a baseball into that hole, i think the following would happen:

It would fall toward the core, and it's momentum would carry it past the core until gravity started pulling it back to the core. This would go back and forth until it ultimately settled exactly at the center.

Answer 5

techincally, i agree w/ mark...but if I were Galactus, from the start, I would have the Silver Surfer make that hole for me, so then I can put the earth on a spit and roast it with the sun before eating it, maybe make a earth s'more.

Answer 6

pole to pole? then that hole would be filled with snow!