# Weighing in on the Gravity Tunnel

By Ralph Birch

It would take about 42 minutes to fall through the Earth. Actually, it’s more like 38 minutes. But wait, assuming you could drill a hole from one side of the planet straight through to the other, would it even be possible to fall through the Earth at all?

Physics teachers have been posing this question to students for years, but coming up with the “right” answer to this theoretical problem has been the subject of debate for some time. The so-called gravity tunnel problem does make some incorrect assumptions that have a significant impact on the outcome of this fantasy fall.

First, it’s unrealistic to assume for the sake of mathematical calculation that the Earth is the same density all the way through. It is widely accepted that the outer layers of the planet are less dense and that the composition of the planet becomes denser the closer you get to the center.

Even if you assume that the Earth, like a bowling or billiard ball, is the same density throughout, it is necessary to calculate the changes in the force of gravity as an object — in this case a person — falls through the tunnel. The strength of the gravitational force pulling toward the center of the Earth is going to vary depending on the distance of an object from that center point. The farther away an object is, the weaker the force of gravity. But as an object gets closer to the center, the pull of gravity strengthens. (In physics, this is known as the shell theorem, originally posited by Isaac Newton.) Additionally, the calculation would have to take into account the friction and wind resistance within the tunnel that would serve to slow down the falling object.

Because of the inconsistencies associated with this particular calculation, Alexander Klotz, a graduate student at McGill University in Montreal, Canada, began searching for ways to more realistically represent the mass distribution of the Earth. Klotz used seismic data to more accurately depict the density changes from the surface to the center and back out to the surface on the other side. His new way of thinking is what shaved four minutes off the time of the fall.

While physics professors around the world will still present the gravity tunnel problem to their students, they’ll be able to add Klotz’s recent findings to their lectures.

“With the right idea it's still possible to make, not a monumental discovery, but an incremental one," Klotz said.

### CLASSROOM DISCUSSION

• Can you think of any other calculations like the gravity tunnel problem that might be challenging for physicists to figure out?
• Name some everyday activities that are affected by friction and wind resistance.

VOCABULARY

• Gravity
• Density
• Seismic