Falling through Earth might be a long and fruitless trip

Air resistance and friction would prevent reaching the other side

What would happen if you jumped into a hole through the center of the Earth? You might not reach the other side, a new study contends.

Khlongwangchao/istockphoto

The Earth is largely solid or molten rock that’s hot enough to melt iron. So you could never build a tunnel through its diameter. But let’s play a mind game and imagine that you could burrow from one side of the planet through to the other. Physicists do this all of the time. And falling down a hole through the center of the Earth would be rough, they note. Indeed, some now conclude, it might be downright impossible. (And yes, for reasons other than the magma-hot rock or dense metal core.)

As you fell, you would be propelled by the force of gravity. You’d fall and fall and fall an immensely long way. The planned distance would span more than 12,000 kilometers (7,500 miles). There’s also friction to consider. The drag of air resistance and the friction of the tunnel walls would serve to slow your fall.

A new study calculates how these factors would affect an intrepid traveler who jumped down that imaginary tunnel through the center of the Earth. In so doing, it tackles what has become a classic problem for physics students: imagining a hole through the middle of the Earth.

If you could jump into such a hole — or, say, could ride through it on a futuristic transit system — gravity would initially accelerate you downward. It would quickly increase your velocity, or speed. Once you passed Earth’s center, you’d keep going. Now you’d actually be moving upward toward the other side’s surface. Gravity’s inward pull would gradually slow that rise. Your momentum, though, would carry you to the other side. There, you might be able to clamber out of the hole. And all of this, physicists have estimated, could take less than an hour.

Or maybe not.

“There’s a number of assumptions that you have to make to solve this problem,” says Alex Klotz. He is a physicist at the Massachusetts Institute of Technology in Cambridge. He was not involved in the new study. To simplify the calculations, scientists have had to make many unrealistic assumptions. They assume that Earth is a sphere of uniform density (it isn’t). They assume the planet is not rotating (it is). And they assume that there is no drag from friction or air in the tunnel (there would be).

The new study added drag from air resistance and friction from tunnel walls into its calculations. As such, this is “a step forward,” Klotz says.

With those factors, it could be well more than a year before you even reach Earth’s center. And you’d never make it to the other side. Scientists report this in a paper published online June 3 at arXiv.org.

The quandary is fun to think about, say the authors. Thomas Concannon and Gerardo Giordano are both physicists. They work at King’s College in Wilkes-Barre, Pa.

To calculate the drag caused by air in the tunnel, the pair assumed that you would travel in a vehicle with a shape similar to that of a large airplane. They calculated that it would take a whopping 1.8 years to get to Earth’s center under such conditions. But you might not even make it there. That’s because the air deep down would be so highly pressurized that it would behave more like a solid than a gas. The scientists concluded that the tunnel would have to be emptied of all air in order to function as intended.

Yet even in an airless tunnel, there would be friction from contact with the walls or the rails that would direct the underground shuttle. In such a scenario, the scientists determined it would take roughly 19 minutes to get to the center. But energy is lost due to friction. That loss means you wouldn’t be able to overcome the pull of gravity to make it to the other side. Instead, you would fall back down before reaching the far side’s surface. And the process would repeat itself. That would cause you to oscillate back and forth through Earth’s core until finally you slowed to a stop at the center.

“Neither of us think this technology is going to be available” anytime soon, says Giordano. The technical challenges of building such a tunnel would be insurmountable. Instead, the problem is a thought experiment and a tool for instructing physics students. And their new result may further satisfy eager science enthusiasts.

In a 2015 paper in the American Journal of Physics, Klotz attempted to solve the problem too. He used a realistic model of Earth’s density. No one had done that before. But he didn’t account for friction. When his result was covered in online news outlets, Klotz says commenters complained: “This idiot didn’t even take friction into account — this sucks!” It seems there are always critics. Even for mind games.

Physics writer Emily Conover studied physics at the University of Chicago. She loves physics for its ability to reveal the secret rules about how stuff works, from tiny atoms to the vast cosmos.

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