If you dug a hole right through the earth and then fell in. Would you come out the other side?

Question

Considering the effect of gravity does that mean you would stop in the middle?

Answer 1

The Earth would need to be solid (obviously) and preferably not rotating. If the Earth was rotating, your mine shaft would need to be exactly along the Earth's axis of rotation, otherwise you'd bang against the walls of your mine shaft as you fell. It would help if there was no air inside the mine shaft, otherwise air resistance would be a problem. So you'd better wear a space suit.

Assuming you've fulfilled all these conditions, then if you dived down the mine shaft, you'd accelerate down towards the centre of the Earth. As you descended, your weight and acceleration would both decrease, both becoming zero at the centre of the Earth, where your speed would be at its maximum. You'd keep on going (due to your momentum) in a straight line, but now you'd be going up, so you'd be decelerating and your weight would gradually be increasing (throughout the whole journey from one side of the Earth to the other, though, you'd be in freefall, so you'd always "feel weightless"). When you reached the surface, you'd stop, but you'd need to hold onto something, otherwise, you'd fall back down again and, after a while, return to your starting point (where you would stop momentarily and then start falling back again, beginning another oscillation).

As you fell, the force on your body would be GMm/(r squared), where G is the universal gravitational constant, M is the mass of the material of the Earth beneath you (the material of the Earth above you exerts no force on you - the inside of a spherical shell is a weightless environment), m is your mass, and r is the distance between you and the centre of the Earth (as you fall further, M decreases, becoming zero at the centre of the Earth). Your acceleration would be GM/(r squared).

If you dived down the mine shaft head down, once you had reached the other side of the Earth you would be standing upright.

I once read that in this situation - assuming uniform density of the material of the Earth - the falling man would oscillate according to "simple harmonic motion" - i.e. the acceleration of the man would be proportional to the distance of the man from the centre of the Earth. A mass bouncing up and down on the end of a spring is another example of simple harmonic motion (SHM).

We can show that this situation is SHM, because M = (4/3) x Pi x (r cubed) x density, and if we substitute this equation into the acceleration equation above, we find that acceleration is proportional to r. The defining formula of SHM is a = - kx, where a = acceleration, k is a constant and x is displacement.

Assuming the Earth has a uniform density of 5464 kg/(m cubed), your maximum speed (at the centre of the Earth) would be 7.9 kilometres per second, and your journey from one side of the Earth to the other would take 42 minutes. (I worked this out using the standard SHM equations a = - (omega squared) times displacement; maximum speed = omega times maximum displacement; period of one complete oscillation = (2 times pi) / omega).

As long as you didn't touch the walls of the mine shaft, you'd be quite safe, but watching the walls rush past at a few kilometres per second might be scary. Maybe, to be on the safe side, the mine shaft should be a few miles wide and your spacesuit should have position-correcting mini-rockets.

The biggest practical problem with this would be the mine shaft, which would have to withstand pressures much higher than those that crush diamond! It would have to be a very high-tech mineshaft, using technology that doesn't exist at the moment (assuming such technology is possible). Constructing a mine shaft right through the Moon might be possible, though, and drilling a mine shaft right through a 50-mile-diameter asteroid would be fairly easy.

Answer 2

Basically, no. First, if the hole were filled with air, the air resistance would slow you down so that you would never reach the surface on the other side. However, even if the hole contained a perfect vacuum, you would still slam into the sides of the hole because of your momentum at the surface.

When sitting on the surface of the earth, you are moving relative to the core due to the rotation of the planet. Each part of the hole through the earth would be moving slower and slower relative to the center of the planet as you approached the center, therefore you would be moving sideways relative to the hole, and would hit the side. Multiple times. This would slow your descent so you would not make it to the other side. You would bounce off the walls, through the center but not all the way to the opposite surface, then return towards the center bouncing the entire way. Eventually, you would stop in the middle. And probably get very warm.

Now suppose you had a carefully-crafted, curving hole with a perfect vacuum in it. The hole is designed such that your trajectory matches the profile of the hole, that is, you do not hit the sides. Then probably yes, you would come out onto the surface, but not directly opposite from where you entered the hole. And don't even think about jumping back in, because the hole would not work in reverse! Bump, bump, bang, bang. Ouch.

Answer 3

Forgetting about air resistance and the incinerating heat at the Earth's core, if you fell into a hole that went all the way through the Earth to the other side, you would never stop falling, literally (unless you take a jumping start). Your acceleration would be oscillating along with your velocity. In other words, you would fall in, reach the other side of the hole, and then immediately start to fall backwards toward where you started.

But, there would be air resistance in real life so you never really make it all the way to the other side (once again, this is disregarding the extreme heat in the core). You would yo-yo back and forth a long while and eventually get caught in the center.

Edit: Note to jay and pheonix, you guys aren't considering that when you've reached the center, you've already attained a certain initial velocity, and due to inertia, you would continue through the hole. This a Simple Harmonic Motion situation.

Answer 4

It's just like a pendulum. You would go down, getting faster and faster until the middle. Then you would slow down on the way up the other side. If the hole were evacuated so there was no air resistance, and you started at sea level here, you'd come to rest at sea level on the other side. Time of travel: 44 minutes. You would feel weightless the whole time.
If there is air resistance in the hole, then, again like a pendulum, you oscillate until you finally lose all your speed in the centre.

Answer 5

If you jumped through the tunnel you would oscillate from one side of the earth to the other, like a pendulum (assuming no air resistance). If friction were present, in this scenario, you would finally end up in the centre of the earth.

Answer 6

i hope it would be like a sea-saw, but only for few seconds. as matter can achieve a certain max speed while moving through air and after that speed doesn't increase.

also the acc. due to gravity decreases as we go down the sea level. so one would stop at the centre at last feeling no gravity but one more thing.



what would u do with magma.

Answer 7

Yes to the second question. At the centre of the Earth you'd be weightless and therefore kind of stuck. Your problem would be short-lived, though, as you'd be pretty much instantly vaporised by the heat. So, no, you wouldn't come out the other side.

Answer 8

Gravity would pull you to the center of the Earth.

There you would remain until someone or something hoisted you back to the surface.

Of course the temperature and pressure would kill you long before you actually reached the center of the Earth.

Answer 9

no you wouldn't because the earths core is the centre of its gravity so you would just get stuck there forever
and plus the earths core is so hot you wouldn't live to see the other side

Answer 10

you cant dig through as the centre is liquid an rather hot so the hole would fill its self in as well as a few blisters take a damp cloth