Falling through the Earth would be a drag

Falling down a hole through the center of the Earth would be rough — especially if there’s friction involved. A new study reveals what would happen to an intrepid traveler who jumped through a hypothetical tunnel through Earth, propelled by the force of gravity but impeded by the drag of air resistance and the friction of the tunnel walls.

Physicists have estimated that, if you jumped into a tunnel without such drag, you would be able to reach the other side in less than an hour. But include drag and it could be well over a year before you even reach Earth’s center — and you’d never make it to the other side — scientists report in a paper published online June 3 at arXiv.org.

“There’s a number of assumptions that you have to make to solve this problem,” says physicist Alex Klotz of MIT, who was not involved in the new study. To simplify the calculations, scientists have had to make unrealistic assumptions: that the Earth is a sphere of uniform density, that the Earth is not rotating and that there is no drag from friction or air in the tunnel.Including drag, Klotz says, is “a step forward.”

If you jumped into such a hole — or, say, rode through it on a futuristic subterranean transit system — gravity would accelerate you downward, quickly increasing your velocity. Once you passed the Earth’s center, you’d keep going, shooting upward. Gravity’s inward pull would gradually slow your rise to the opposite surface. Neglecting air resistance and friction, your momentum would carry you to the other side, where you might be able to clamber out of the hole. Adding drag to the mix complicates the problem, but the details haven’t been carefully analyzed until now.

The quandary is fun to think about, say the authors of the study, Thomas Concannon and Gerardo Giordano from King’s College in Wilkes-Barre, Pa. But, says Giordano, “neither of us think this technology is going to be available” anytime soon. 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.

To calculate the drag forces caused by air resistance in the tunnel, the researchers assumed that you would travel in a vehicle with a profile similar to that of a large airplane. The scientists calculated that it would take you a whopping 1.8 years to get to Earth’s center under such conditions. But you might not even make it there, 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.

Even in an airless tunnel, you would feel friction from contact with the walls or 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 thanks to the energy lost due to friction, 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 surface and the process would repeat, causing you to oscillate around Earth’s core until you slowed to a stop at the center.

The new result may further satisfy eager physics enthusiasts. In a 2015 paper in American Journal of Physics, Klotz solved the problem using a realistic model of Earth’s density for the first time, but he didn’t account for friction. When the result was covered in online news outlets, Klotz says commenters complained, “‘This idiot didn’t even take friction into account — this sucks!’”