A tunnel from San Diego to other side of the earth

Friction and earth's spin considered

I do like the idea of somebody halfway around the world suddenly getting whapped in the face with a #2 combination plate from Roberto’s.
  • I do like the idea of somebody halfway around the world suddenly getting whapped in the face with a #2 combination plate from Roberto’s.
  • Image by Rick Geary

Hey, Matt... Suppose for a moment Earth’s core isn’t composed of molten lava. Now suppose that a tunnel was bored straight through, beginning here in San Diego, and out the other side of the planet. If an object were dropped into this hole, how would gravitational force affect its trajectory? Would it fall “up” and out the other side, be swung from the core out of the original side, or float somewhere in the center? Please...I have to know! — Koenig, San Diego

Working up a scheme to save on parcel post rates to the other side of the globe? A budget vacation trip to Tasmania, perhaps. Ah, well, here’s another case where the story behind the question is undoubtedly more interesting than its answer.

But I do like the idea of somebody halfway around the world peeking quizzically into your mysterious tunnel and suddenly getting whapped in the face with a #2 combination plate from Roberto’s. The only way this will happen is if we eliminate friction while we’re dispensing with Earth’s fiery core. In that event, anything dropped into the hole would accelerate like crazy until it passed Earth’s midpoint, then the greater mass of the globe behind it would begin to slow it down. By the time it had reached the other end of the tunnel, it would have slowed to a stop, then it would begin falling back the other way, accelerating once again. With no intervention, our object would continue to boomerang, trapped forever by gravity and momentum.

Add friction to the mix and we’ll have to cope with “terminal velocity.” That’s not the speed you’re going when you crash your car into a tree, it’s the maximurn speed our dropped object can reach before the resistance of the air (friction) balances out the force of gravity and our object can fall no faster. In this case, whatever you fling down the hole will have Jess momentum for gravity to overcome, so it will reach some unknown point past Earth’s core, head back the other way for a while, and feebly ping-pong awhile until it’s finally suspended forever at mid-globe, where all gravitational forces are roughly equal (roughly, because Earth’s not a perfect sphere).

Hope this information fits neatly with your grand plans. Though I should warn you that the point on the globe directly opposite San Diego is a couple of hundred miles off the coast of Antarctica, way south in the Indian Ocean. When you break on through to the other side, make sure you’ve got nose clips and a towel.

April 27 update

Time to catch up on correspondence from people who have more answers than questions. Today’s comes from Peter Danes, who takes theoretical issue with my theoretical answer to a theoretical question posed by someone I can only assume is an actual person. The question had to do with what happens if you drop your car keys or a beer can or something through a hole dug straight through the globe. In part, Mr. Danes says we’d have to consider Earth’s spin (our old friend the Coriolis effect) and the resulting velocity of the sides of the tunnel, which will vary with depth, from full speed at the surface to zero at Earth’s core. “When you drop something into your tunnel, it will keep its sideways velocity, but travel toward the core will carry it into sections of the tunnel that are moving progressively slower. [Therefore,] your dropped object will continually drift against the side of the tunnel....” Because of gradually decreasing gravitation and increasing air friction from the denser air near the core, the object “would probably drift very slowly to the center and stop. The exact shape of the tunnel is beyond my capability to compute, but a straight line would definitely not do [because of Coriolis, decreasing gravitation, and increasing air friction].” Another theoretical public service for the bewildered millions.

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