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There are many assumptions in this question. So let's say we have a vacuum tube that traverses from the north to south axes, and you (in a spacesuit) are dropped from one end-- You would accelerate until you got to the center, then decelerate until you got to the other end. Assuming no drag from air, this would continue forever. You could figure out how long it would take, but I will spare you some effort. One cycle up-and-down would take about 88 minutes. Exactly the same time a grazing satellite orbit would take! Cool.

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Q: What happens if you could actually fall through the centre of the earth?
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