Did you ever dream of digging a hole so deep it came out the other side of the earth? Let’s play that game again, using a little physics.
First we have to imagine that our tunnel is lined with super-heat-resistant material so we can pass through layers of molten rock. Also, the earth’s core is a metal sphere 800 miles wide, but just pretend we’ve bored through it. What would be the result? For one thing, you could then travel to the other side of the world in under one hour. This by far exceeds the best travel times possible in any airplane or train. How? By stepping into the hole. You’d fall all the way through the earth and then step out again at the other side.
But wait! When you fall into a hole you just keep on picking up speed until you reach your maximum velocity or hit bottom. If this hole goes all the way through, wouldn’t you fly out the other end like a cannonball? No. The reason you keep falling in a normal hole is that gravity is continuing to pull you in the direction of the earth’s center. In our imaginary scenario, once you passed the midpoint of the earth, you would then be fighting gravity. All the speed you picked up on the way down would slowly diminish as you rose up the other side.
Assuming there was no air resistance in the tunnel, your fall would send you past the center at roughly 18,000 MPH–almost exactly enough force to get to the top again. The trick comes in the “almost” part. It couldn’t really be the case that you’d pick up exactly as much speed as would be needed to reach the same spot on the other side. Some energy always finds a way to escape. Think of swinging on a swing. If you just push off once and then sit still, the swing doesn’t keep going back and forth forever. Gradually it slows down.
It’s the same situation when you step into that hole. Down you go, and when you come out the other side, your feet will stop at slightly less than ground-level. If you miss your chance to grab onto something, you will fall though the entire planet again. Back at your starting place you rise slightly less than last time, and so on.
See the trouble? It would be a fast way to travel, but miss your step and you will wind up yo-yoing inside the tunnel, each time rising slightly less than the time before. Eventually you will stop moving altogether and be stuck in the middle–with a long climb home.
A Moment of Science®