As thrill-seekers, we like to do a lot of extreme, gravity-defying stunts to push our limits. If base jumping or caving is your thing, how about taking a tumble all the way through the Earth?
How fast could you go? What happens to gravity at the center of the Earth? What would happen when you reached the other side?
Before you take the plunge, we’ll need to learn a little bit about gravity. A gravitational force is simply an interaction between two objects with mass. In this case, the two objects are you and the Earth.
If we drop a feather and a bowling ball, at the same time, outdoors, it’s fairly obvious which one will hit the ground first. But if we repeat this experiment in a vaccuum, strangely, they both accelerate towards the ground at the same rate. This is because they aren’t actually falling, but standing still. With no air resistance, and the force of gravity being constant, it appears as if they are both stationary. As Einstein puts it, if you couldn’t see the background, there would be no way of knowing that they were falling at all.
But what happens to gravity when we reach the middle of the Earth? Let’s assume, in this scenario, we’ve built a smooth-walled vaccuum tunnel through the Earth. And it will protect you from the extreme heat of the planet’s core.
As you begin falling through the hole, there is less mass beneath you and more mass above you. So what exactly happens as you get closer to the center of the Earth?
A skydiver will reach their terminal velocity of about 195 km/h (122 mph) after about 10 seconds. They never speed up past this point, because the forces of air resistance and gravity will have equal magnitudes.
In the vaccuum hole scenario, however, you will continue to accelerate well beyond this terminal velocity. You’ll hit speeds of about 29,000 km/h (18,019 mi/h) as you pass through the center of the Earth. That’s 23 times faster than the speed of sound, or about 250 times faster than your average car on the highway. I hope you only ate a light lunch beforehand.
According to physicist Alexandor Klotz at McGill University, the fall would take only about 38 minutes and 11 seconds. Mind you, this is assuming that the strength of Earth’s graviational pull is constant and that the Earth is a perfect sphere.
In reality, Earth’s gravity only changes about 10% as you fall, and it starts to decrease a little after the first 3,000 km (1,865 miles). At Earth’s center, gravity is at its weakest, so if you somehow managed to stop here, you would feel weightless.
But at the blistering speed you’re falling, you’ll fly straight past the center. And gravity will start increasing, but in the opposite direction. At this point, as you fly upside down towards the other side of the Earth, you will begin to slow down as you get closer to the exit.
Once you reach the end, if you don’t grab on to the ledge at this point, well, I’m sorry, but you’re out of luck. As you fall back down, you’d be stuck in a free fall, going back and forth, oscillating infinitely like a yo-yo.
This is due to Hooke’s law, which basically states that the force of an elastic or spring is proportional to its extension. This is why if two people keep pulling an elastic band, well, eventually, someone’s going to get hurt badly.
In this case, the elastic band is the force of gravity in the Earth, and the further it stretches toward the edge, the stronger its pull is. If you happen to make the jump and there’s air resistance, you’ll only go as fast as 55 m/s (180 ft/s). So kick back, relax, and throw on a podcast or two. You’ll be falling for two and a half days before you reach the other side of the Earth. If you’re hoping to get to Australia, China or wherever you’re aiming for sooner, make yourself as aerodynamic as possible. Tuck in your legs and arms like a diver. If you’d like a slower, more relaxed journey, spread your arms and legs wide to help you balance. And try not to spin, otherwise you might get disoriented and pass out!
- “Fall Is Here! Time To Learn The Physics Of… Falling”. Allain, Rhett. 2018. Wired.
- “How Long Would It Take To Fall Through The Earth?”. Choi, Charles. 2015. livescience.com.
- “New way to calculate how long it would take to fall through a hole in the Earth”. Bob Yirka, 2020. phys.org.
- “How long would it take to fall through the center of the Earth?”. 2020. physicscentral.com.
- “How to mathematically calculate a fall through the Earth”. youtube.com
- “What Is Terminal Velocity? – Universe Today”. 2010. Universe Today.