But what if you did dig a hole through the Earth and jump in? What would happen?
Well, you’d die… But if you had some magic material coating the walls of your 13,000 km deep well, you’d have quite a trip. You’d accelerate all the way down to the center, taking about 20 minutes to get there. Then, when you passed the center, you’d start falling up for another 20 minutes, slowing the whole way. You’d just reach the surface, then you’d fall again. Assuming you evacuated the air and compensated for Coriolis forces, you’d repeat the trip over and over again, much to your enjoyment and/or terror. Actually, this would go on forever, with you bouncing up and down. I hope you remember to pack a lunch.
As you pass the centre, you’ll be doing about 5 miles per second (18,000 mph or Mach 23).
Beats the hell out of Chessington World of Adventures.
There’s one practical problem, though (“one”?): you need to make sure that when you dig your hole, you won’t come out in the sea at the other end. About 70% of the Earth’s surface is water and 30% land; and because most land is in the northern hemisphere, very little of it has antipodean land.
But if you don’t fancy the yo-yo effect, then my understanding is that you could be gently lowered down to the centre and then released, where the equal gravity from both directions will keep you floating where you are. Just watch out for anyone doing the jump.