Am I stupid for thinking this?

Question

I've been having an ongoing argument with a friend for a few days now. He thinks that if there were a hole from one side of the Earth to the other going straight through the core (bear in mind that we are pretending that it's possible to dig such a tunnel) that you could jump into it and then pop out the other side.

My belief is that since Earth's centre of gravity would be strongest right in the core, you wouldn't pop out the other side, but rather you would become stuck in the middle, at the core. At the core, gravity would act very strongly on you going in either direction towards the end of the tunnel, and thus you would become trapped, unable to move either direction.

So, my question is, am I right? Or is my friend right?

Writer of Truth- see where I put in brackets, "pretending that such a tunnel could exist", or something to that efffect.

Answer 1

In a way you are both right. What would actually happen is you would go straight through the center and almost all the way to the other side. Then you would fall back in the opposite direction toward the center and through in the other direction. This would continue until you finally came to a stop in the center after thousands of trips back and forth, each one traveling further from the surface.

Here's why:
When you jump into the hole you have a potential energy equal to the radius of the earth X your mass X the acceleration due to gravity. As you fall toward the center that potential energy decreases (because your height above the center decreases) and it is converted to kinetic energy.

When you reach the center you will no longer have potential energy but you will have kinetic energy that carries you through the center. As the gravity of the earth tries to pull you back toward the center your kinetic energy is changed back to potential energy again and if there was no air resistance you would end up at exactly the same height (the surface of the earth) on the other side.

However since there is air resistance that eats up part of your engery on the descent and ascent you will return to a position slightly lower on the opposite side. The amount of air resistance you are experiencing will determine how many trips it will take for your energy to be used up, leaving you hovering in the center.

Answer 2

Your friend is right. Remember that the gravity from the part of the planet "above" you will be canceled out by the gravity of the planet "below" you. As such, the net gravitational force at the Earth's core is precisely zero. As you pass the center, Earth's gravity will become more intense until the point where you (just barely) reach the opposite side. Neglecting air resistance, coriolis effects, the fact that such a tunnel would immediately collapse under the immense weight of the Earth, etc. - you could stay in the tunnel for as long as desired, merrily oscillating from one side of Earth to the other, until you decided to grab onto the side and climb out of the hole.

Note that the neglecting air resistance part is not trivial here - terminal velocity is quite slow, and nowhere near the velocity needed to get you to the other side. As such, if you intend to use this fictional tunnel as a transportation mechanism, you absolutely MUST get rid of the air.

Answer 3

If you were to jump into a hole going all the way through the earth, you would "fall" until the center point. Then, since you have been moving, you would have momentum. So, you would rise up out of the other side. At the center point, gravity would start slowing you down, though. You would pop out of the other side just a little less than the height from which you jumped inot the hole originally. If there was no one or nothing there to catch you as you came out, you would then stop and fall down towards the center again. Eventually you would come to rest in the center and have to climb out after acting like a pendulum. You would not bump into the sides if you stayed perfectly straight with your legs together and your arms at your sides. Otherwise you could slip though the air like a skydiver and bounce around off the sides of the hole/tunnel.
You would not just jump in and fall to the center and stop, gravity would have to overcome the momentum you built up during your fall. It would diminish the length of your fall each time just a little. And, no matter where you are in the tunnel, you would still only experience 1 g so when you ended up in the center you would be able to climb out from there providing you could float over to the sides.

Answer 4

You are both right in a sense. If you did the math (had to do it for my differential equations class) what would happen is that you would accelerate towards the center and then you would continue to the other side because you have momentum. However, you would emerge out the other side at exactly the same distance from the center of the earth that you jumped from. This would continue for eternity and you would be oscillating between one side and the other kind of like a weight on a spring. This is all assuming you ignore friction of air.

If you include friction losses, what would happen is you would still oscillate, however the distance from the core with each "bounce" would decrease until finally you are stuck floating in the middle of the earth.

Answer 5

My initial reaction was that you were right. But then I thought of the earth as an MRI. Of course you know an MRI is a big magnet. If you took something magnetic into the room you would expect it to go into the middle and become stuck; right? Not necessarily. Sometimes stuff will build up such speed heading toward the middle of the magnet that the force of the magnet in the middle will not hold onto it, but make it go faster; right through to the wall on the other side of the MRI. BUT, we don't really know for sure what the earth's core is like, so you could still be right.

Answer 6

Assuming you could dig such a hole, if you jumped into the hole, gravity would pull you down into the hole. The momentum would almost carry you through to the other end but you wouldn'y quite make it (friction and gravity fighting you). You would shoot back and forth each time traveling less distance. Think of a free-swinging pendulum. Eventually you would come to rest at the center of the earth where the intensity of the gravity would most likely keep you trapped.

Answer 7

Better model: the Moon. No air for friction, a cold solid core to bore through. Science shows say that once you're below the surface, gravity pulls equally from all sides of the tube, so you're essentially weightless till you reach the other end, so you could fall right back in again unless you started with escape velocity.

Answer 8

Earth's gravity is not in the earth but surrounds it. Gravity is what keeps us rotating and keeps us from flying off the earth. Gravity is why we orbit the sun remember, what you have at the earth's core is magnetic fields, which causes the ocean's tides. So I guess you are both wrong because your question is bizarre in that the earth would then look like a doghnut and would not classify as a planet and would end up the way of Pluto. Oh well.

Answer 9

Neglecting air resistance your friend is right. Your mistake is thinking that gravity is strongest at the center of the Earth: it is actually the weakest there--zero. The force of gravity is directly proportional to the amount of mass that between you and the center of the Earth; therefore, the closer you get to the center of the Earth the weaker gravity will become.

Answer 10

Damn dude!! Yeah ive thought about this for years!!! I never told anyone. Yeah I think you are right and not him. It is stronger at the core, but keep in mind, gravity is pulling opposite on both sides of the world. That could effect you staying in the middle. Gravity isnt denser on one side or the other.