If a hole was drilled down to the centre of the earth and out the other side - what wld happen if I jumped in?

Question

What effect would gravity have? Would I end up at the centre?

Answer 1

If you ignore the fact that the inside of the earth is searing hot, and you make the assumption that the earth has a uniform density and you encounter no friction as you fall through the earth, you will move in a simple harmonic motion and it takes about 42 minutes for you to reach the other side of the earth, no matter where and how you drill as long as the tunnel is a straight line.

So you can get from Washington to Paris (or any two cities for that matter) in 42 minutes by drilling a tunnel between the two cities, using the above assumptions.

When you throw the object its initial velocity will be zero but it starts increasing and kept on increasing until it reaches the center of earth.

The body will not stop due to its inertia. It will pass the center move towards the bottom surface. But now its velocity will be decreased gradually and will become zero on reaching the surface. At this moment, it will start moving back. This motion will continue forever if there is no friction and collissions.

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I have put in my working below in case you are interested. You will need basic physics and high-school math.

Below are the data that I use for earth. I got this from Britannica.
Radius = 6378140 m
Mass = 5.976 * 10^24 kg
Density = 5498.44 kg/m^3

If we were to assume that the earth is a perfect sphere with uniform density and the person falling through the earth encounters no air resistance, an interesting result is observed. Let us first consider the simplest case whereby the person falls through the diameter of the earth.

g = G M / r^2
M = 4/3 * Pi * r^3 * rho, where r is the distance of that person falling from the centre of the earth. (Now, M is not the mass of the total mass of earth! If a person is at distance r from the centre of the earth, the gravitational effect of the earth will behave as if it originates a point mass with mass as given by the formula. This is in accordance to Newton's Shell Theory.)

Hence g = 4/3 * G * Pi * rho * r, i.e. g is directly proportional to r, which means that the person will move with simple harmonic motion. (ignoring friction, etc) Simple physics will tell you that omega^2 = 4/3 * G * Pi * rho, where omega is equal to 2Pi / T with T being the period of the simple harmonic motion.

Solve[ (2Pi /T)^2  4/3 Pi density (6.67 * 10^-11), T]

T -> 5069.36 seconds, which is about 84 minutes
But 84 minutes is the time for the person to fall to the other side and back, so divide by half and you get 42 minutes. The effect is that the person will move with simple harmonic motion with the centre of the earth as the equilibrium position, with period of 5096 seconds.

It takes me some time to prove that T must still be 84 minutes for any chord. Try working it out. Hint: resolve the forces.

Answer 2

The question can be answered if we make the following assumptions: (1) The earth is not spinning. (2) The earth is of uniform density throughout. (3) The hole forms a diameter of the earth (i.e., it passes through the earth's center). The hole must be through the center; otherwise, the gravity from the earth would pull you into the side of the hole eventually; your motion would not exist along a straight line for the same reason that a bullet shot straight forward falls toward the surface. (4) There's no air resistance. The gravitational force vector will always point toward the center of the earth along the direction of the hole no matter what direction you're moving in and its magnitude will be proportional to your distance from the earth's center. In symbols, the force will be of the form k(c - v), where v is your position vector and c is the position vector of the earth's center. This will cause you to execute harmonic motion--you'll oscillate back and forth. You would reach the opposite end of the hole at which point you'd temporarily stop and then start falling in the opposite direction. You would proceed to go back and forth between the ends of the hole maintaining a constant total mechanical energy.

Answer 3

In theory, neglecting air friction, contact with the sides of the hole, high temperatures &c you would arrive at the other end of the hole about 45 minutes later. If you failed to get out you would get back to your starting point after another 45 minutes. Oddly enough if a straight frictionless tunnel was bored between any two points on the earth's surface the same transit time would be observed.

Answer 4

By theory, you would execute simple harmonic motion about the center of the earth as the middle point. The gravity on the earth's surface is maximum and reduces as you go deeper into the earth. It is zero at the core. There won't be high pressure at the core, considering there is no gravity.

This would also be possible if you dug any chord on the earth, which does not pass through the center.

Answer 5

Here is an article on a similar idea called the gravity train which doesn't go throught the centre of the earth but a bit to the side of it!

http://www.damninteresting.com/?p=696#more-696

And while on the subject of holes here is the deepest manmade hole on earth:

http://www.damninteresting.com/?p=567#more-567

Answer 6

You will continue to do Simple Harmonic Motion from one end to the other. When u enter from one end you will be pulled by g towards centre & you will gain velocity. With this velocity u will cross the centre then g will pull u which will make your velocity to zero & then u will start coming back to centre due to g. This will happen other side also. Therefore, u will perform SHM around centre of the earth.

Answer 7

people r far too cynical on this. HYPOTHETICALLY youd go into simple harmonic motion till eventually youd come to a stop in the middle where you would normally be crushed. and contrary to everyones belief here the japanese are drilling a hole to the "centre" of the earth. theyre drilling deep in the ocean so theres less earth to go through. a probe has already been designed to go down. it works alot like dropping a ball into treacle. more info on the web somewhere.

Answer 8

You would fall and yo yo back and forth or up and down around the centre where there is no gravity assuming that the molten core of the earth is not a problem.

Answer 9

In theory you would accelerate towards the centre and then you would have enough speed to get to the other side to reach the surface again. Of course if there was any air you would experience a great deal of drag and you wouldn't get very far past the centre.

It would be a great challenge to line the tunnel to resist a molten iron core at about 5000K temperature.

Answer 10

U will oscillate for some time around the centre of the earth .. in simple harmonic motion as said in a post above .. but due to air resistance you will finally come to a stop in the centre of the earth and remain suspended ...
BTW .. u can't possibly build something that can drill 6400km .. . that something that can withstand the heat in the core .. atleast not with materials on earth ...