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And you jumped in.

What would happen when you got to the middle of the earth? Would you gradually slow down, until you got to the middle and once you were in middle would every direction feel like it was up?

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This Stack question is closely related: physics.stackexchange.com/questions/2481/… - does it answer this one? – Roy Simpson Mar 21 '11 at 11:16
@Roy: I don't think so, since the answers to that other question don't address the details of the oscillation that would occur. – David Zaslavsky♦ Mar 21 '11 at 15:59
@David, I agree it doesnt handle oscillation, but the question is another "gravity physics at centre of the Earth" topic, so it is worth pointing that out. – Roy Simpson Mar 21 '11 at 16:03

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I seem to remember Dr Karl on the Triple J radio station (Karl Kruszelnicki) explaining this one. In a zero friction environment, you would oscillate back and forth. It would take about 40 minutes to travel from one side of the earth to the other. An interesting side note was that if you were to dig the hole from any point in the Earth to any other point, it would still take the same amount of time to travel from one side to the other.

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Read the comments from Ted Bunn "below". – Georg Mar 21 '11 at 18:58
up vote 11 down vote

And you jumped in.

No, I'd refuse, You should do that Yourself. :=(

Do You want to "solve" this with or without friction by air?

Without friction, You would fall and reach maximum speed in the center of earth, going on until You reach the antipods, where You would stand still for a fraction of a second, then You would go down again. Very boring indeed and You should take some sandwiches and some drink with You.

With friction You wold accelerate up to a speed around 300 km/h, then fall down with this constant speed, slowing down when approaching the center, and go on some distance, fall down to center again and do that oscillation until all Your potential/kinetic energy is consumed by friction.

Because about a dozen of such holes were drilled here in physics.SE alone, You might find some company at the center of earth.

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smile :). It was one of the first problems I had to solve in mechanics back when. – anna v Mar 21 '11 at 12:27
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Unless the hole goes pole-to-pole, you'll have to worry about effects of Earth's rotation as well as friction. Coriolis forces will press you against one side of the tube most of the time. As long as you're ignoring that friction as well as air resistance, the results are qualitatively the same. – Ted Bunn Mar 21 '11 at 14:15
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One other fun exercise for those who haven't done it: Suppose that instead of going through the center of the Earth, the hole goes from one point to a non-antipodal point along a straight line (i.e., a chord of a circle rather than a diameter). Show that the time to fall from one end to the other is independent of the points chosen. (Ignore Earth's rotation and assume frictionless sliding.) – Ted Bunn Mar 21 '11 at 14:17

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