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What would happen if you fell into a shaft through the earth?

If a shaft was possible from the surface of the Earth, through the centre, and re-emerged on the other side (heat etc notwithstanding) what would happen if you fell down it?
Simon Wright from South Yorkshire (Age: 35-44)


One Response

  1. Actually, as long as you don’t melt (and if air resistance is negligible) what would happen is that you’d oscillate back and forth from one side of the earth to the other ad infinitum. This is a rather unusual example of “simple harmonic motion”, the underlying principle behind many types of oscillations in the physical world, such as a pendulum.

    The reason is as follows. At the “top” of the earth, gravity will accelerate you downwards. Your speed will increase, until you reach the centre of the earth. At the centre of the earth, you’ll feel gravity equally above and below you, so acceleration on you will be zero. However, you don’t stop. All the potential energy you had at the top of the earth has been converted to kinetic energy, and you’re travelling downwards at a significant velocity! Newton’s second law dictates that because gravity is zero exactly at the centre, your speed won’t change, and you’ll keep on going!

    As you carry on going, and you get closer to the “bottom” of the earth, there is more earth above you than below you, and in balance, the gravity will begin pulling you back up to the top again, making you decelerate and slow down. Without air resistance, you’ll find that exactly at the point that you come out the other side, you come to an instantaneous standstill, and then get pulled back into the shaft again.

    And how do we know that you’ll stop exactly as you emerge from the other side of the earth? Well, that’s easy if you consider energy conservation. All your energy at the top of the earth is in potential energy, and by the time you’re at the centre of the earth, it’s been entirely converted to kinetic energy. You know the Earth is symmetric, so that means you’ve got exactly enough energy to carry on and reach the bottom of the Earth before gravity wins and you get pulled back again. You don’t lose any energy though, and when you’re at the bottom of the earth, you’re in the same situation as you were at the top of the earth. This means that you keep on bouncing back and forth for ever!

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