16 November 2010

Round-Trip Journey to the Center of the Earth

Nathan DeHoff today posed several questions of how physics works in the land of Oz and surrounding countries, with the general conclusion that it’s questionable.

One particular matter is the tunnel through the center of the Earth depicted in Tik-Tok of Oz, redundantly called the Hollow Tube. The Nome King tricks all the book’s heroes into falling into one end of the tunnel, and they exit the other end like this:

Tik-Tok popped out into broad daylight and, after making a graceful circle in the air, fell with a splash into a great marble fountain. . . .

Queen Ann sailed up from the Tube, took a ride through the air as high as the treetops, and alighted squarely on top of the Peculiar Person’s head…
Later in the book, Quox the adolescent dragon takes all those heroes on his back and crawls into that end of the tunnel. When Quox comes out,
he shot into the open air a hundred feet or more and sailed so far away from the slanting hole that when he landed it was on the peak of a mountain and just over the entrance to the many underground caverns of the Nome King.
Does that accord with the laws of physics? Martin Gardner addressed that very question in The Annotated Alice, in his discussion of Alice’s fall into the Earth. And the basic answer is: gravity doesn’t work like that.

In a frictionless environment, people would travel exactly as far from the center of the Earth as they traveled down into it. Tik-Tok and his companions fall into the tunnel while hiking through some mountains, so conceivably they’re at a higher altitude, farther from the center of the Earth, than the garden at the other end. That would make it possible for them to pop up to some height on the other side and, with some wind and movement of the Earth, not fall right back down into the Tube.

But there are two problems with that scientific explanation:
  • The return journey wouldn’t work at all. Starting from the garden, Quox wouldn’t fall far enough to reach the other end of the tunnel as he rose, much less fly out the other side.
  • The tunnel is not a frictionless environment. In fact, Quox slows himself down by scraping his claws against the Tube’s inner walls.
In an environment with friction, Gardner wrote, air resistance would slow the travelers enough that they wouldn’t rise as far as they had fallen. They would therefore fall back down into the tunnel, pass the center of the Earth again, and rise not quite as far as where they had started from. Those unfortunate folks would continue to oscillate for many trips of decreasing length until coming to a stop at the gravitational center of the Earth.

So what explanation is there for how the Hollow Tube works? I can only assume that it’s magic. It does, after all, run from one fairyland to another, and the Nome King can even shift the opening around.

When creator Hiergargo the Magician first used the tunnel, according to Polychrome the rainbow fairy, “he tumbled through the Tube so fast that he shot out at the other end and hit a star in the sky, which at once exploded.” That hints that Hiergargo juiced the Tube with magic to make the journey faster, and some residual or revised magic might remain.

L. Frank Baum admired science, deliberately mixed it into his fairy tales, and even wrote a bit of science fiction. Occasionally he got some things remarkably right, but he never worked in the field, and never really treated science as more than a jumping-off point.


Greg R. Fishbone said...

I'd suggest checking into barometric pressure. If there's a high pressure system over one entrance to the tube and a low pressure system over the other, you might get slurped along at a manageable and gravity-defying speed. Then when the weather fronts change, you could get sucked through in the other direction.

ericshanower said...

I think the word "slanting" might provide a clue to how the tunnel works. If it slants in relation to the earth's surface, then it doesn't go directly through the center of the earth. Gardner's explanation would not then apply. And when travelers shoot out one end or the other, the wind and earth's rotation don't matter either, since they've been shot out at an angle.

J. L. Bell said...

Gardner did discuss a perfectly straight tunnel that doesn’t go through the center of the Earth, and is therefore slanted. Lewis Carroll wrote about such a thing in Sylvie and Bruno, offering the excuse.

I agree that a slant would help explain how the travelers don’t fall right back into the tunnel. But it raises another issue: the travelers from the Nome King’s region fall for a long time—perhaps the whole way—without hitting the inside of the Tube.

Gardner also notes that the travel time in a straight, frictionless tunnel through a spherical Earth would be the same whether it went through the center of the planet or at a slant.

How many minutes would that trip take? Most curiously, the answer is 42.