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Q & A: Hole Through the Earth

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Most recent answer: 02/15/2013
Q:
If I were to bore a hole straight through the Earth to the other side and somehow insulate it so the heat wasn't an issue, effectively turning planet Earth into a massive bead what would happen if I jumped in - how far would I fall? Would I hover in the middle when one side of the earth's gravity met the other?
- James (age 28)
Aldeburgh, Suffolk, UK.
A:
To answer your question we need to think in terms of your GPE, gravitational potential energy (the energy you have based on your position in the Earth's gravitational field), and KE, kinetic energy (the energy you have due to your motion), and how they change as you fall down this hole through the Earth. You start out on the Earth's surface and as you fall down the hole, your GPE decreases and is converted into KE (in this hypothetical case we will assume that energy is not dissipated through sound waves, heat, etc.).  Also, the Earth is rotating and you would hit the sides of the hole as you fall, so we should also assume that the walls of the hole are frictionless in our hypothetical scenario. When you reach the center of the Earth your GPE is the lowest it can be and you have the most KE you can get. Since you have KE at the center you will still be moving so you will not get stuck there and float around.

Instead, you will keep on moving past the center toward the other side of the hole and your KE will be converted completely back into GPE. So if you fall into the hole on one side you will keep on moving until you come to a stop exactly at the other side (assuming that the hole on the other side is the same distance away from the center as your initial position). Also, you would repeatedly fall from one end of the hole to the other as your gravitational potential energy is converted into kinetic energy and vice versa in the same way that a pendulum or a spring would oscillate forever between two points. This is true of any path that you can make through the Earth from one point on the surface to another and you do not even have to go through the center of the Earth.

Additionally, since the force of gravity is the only force acting on you no matter what path you take and since your initial and final positions are the same distance away from the center, the time it takes for you to get from one end to the other is always the same! This time has been calculated to be around 42 minutes. So falling through a hole from your home to any other point on the Earth surface's always takes about 42 minutes.

Shalin

(published on 02/15/2013)

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