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hole through the earth, what would happen?

Crash
in Classical Physics

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If there was a hole straight through the earth and (neglecting all other effects that would prohibit doing this) and someone jumped into it, would you after passing through the centre point start to bungy back and forth untill coming to a rest right at the centre due to gravity?

What would happen?

My guess would be you would keep traveling up and down eventually settling in the middle where you would float.

 

But IRL you would die from running into the side of the tunnel because the earth's density is not uniform. Plus the moon might have enough pull on you to eventually drag you to one side of the tunnel.

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