Throwback Thursday: The science of bottomless pits
What would happen if you dove into a hole straight through the Earth?
“Where you used to be, there is a hole in the world, which I find myself constantly walking around in the daytime, and falling in at night.” –Edna St. Vincent Millay
I’m sure you’ve thought about it before: what would happen if you dropped something into a bottomless pit?
No, not one of those fake bottomless pits that you find in various Mystery Spots off the beaten trail. Those are a dime a dozen, and may claim to be bottomless, but usually they go down only a few tens of meters, and no more than that.
Whether you hear about the “well to Hell” or other astounding claims, they all turn out to be nothing more than urban legends upon closer investigation.
The ones that actually exist? Those may be deep, but they’re definitely not bottomless. And I want something truly bottomless. To get that, we’d have to use our imagination, and pretend there were somehow a cylindrical shaft that extended all the way down, past the Earth’s crust, mantle, and inner and outer cores, all the way to the center of the Earth, and then that continued back out to the other side, most probably into the ocean if you live on a continent. (These are known as antipodal points.)
This requires a lot of imagination, because the temperatures and pressures are so spectacularly large they would literally melt, boil or sublimate any known materials! Yet, despite the pressure and temperature gradients all the way down, despite having a liquid, molten outer core and a radioactive nickel-iron-cobalt inner core at over 4000 °F, let’s assume you’ve gone and physically created created something that will stabilize your cylindrical shaft going right through the Earth’s center. If you can do that, you will have created a true bottomless pit.
(Maybe a graphene cylinder of sufficient thickness that’s cooled by a layer of liquid helium pumped through it would do the trick?)
So, now we’re good, right? We’ve got a bottomless pit that starts at one point on the Earth, goes all the way through the center, and back out the other side.
Are you ready to dive in? Let’s do it, and see what happens!
Here goes your master plan to make the world’s longest skydive look like a paltry coin-toss. While Felix Baumgartner may have journeyed 36 kilometers, your plan is to go more than 12,000 km, all the way from one side of the Earth to the other, through a truly bottomless pit!
Well, it turns out your brilliant plan wouldn’t get you very far. Here, near the surface of the Earth, the atmosphere is moving along with you and the Earth’s surface as the planet rotates, at a clip of about 1000 kilometers-per-hour, with variations depending on your latitude.
This isn’t a big deal for most normal applications, but as you start moving away from the surface of the Earth’s crust and deep into the interior, you’ll find that, horizontally, you’re moving too quickly.
The Earth rotates at a constant angular speed, meaning — like a record — that the outer parts, where we are, rotate at a faster linear speed than the inner parts. At the core, in fact, the speed is zero in the tangential direction, meaning that you’d smack into the walls of the shaft you built in short order. It’s only a matter of time (and, surprisingly, a few dozen kilometers) before you find that you’ve smashed into the wall of your cylindrical tube, since the Earth is still rotating — with the interior rotating more slowly than the surface — after you jump!
There’s a workaround, however, if you’re clever.
Build your shaft directly along the Earth’s rotation axis, from the North Pole through the center of the Earth all the way out at the South Pole. Now, there will be no effects from differential rotation, no coriolis forces, and — so long as your cylindrical tube holds — nothing keeping you from having a true-to-life bottomless pit!
So do it — jump into the bottomless pit — and what happens?
Now, the fun begins! You start accelerating downwards as the air rushes by. Pretty quickly — after about 7 seconds — you hit terminal velocity, which is about 140-to-210 miles-per-hour, depending on how your arms and legs are positioned. This speed actually increases marginally for a while as you continue down the shaft, as the inner layers of the Earth are denser than the outer layers.
But then the gravity (paradoxically) gets weaker, and the density of air filling the shaft gets larger, meaning that you slow down tremendously. The fall (and the slow speeds thanks to air resistance) will take a long time: it will take you somewhere around 20-to-24 hours to reach the Earth’s center. This is a long journey of around 4,000 miles (or 6,400 km). When you do, you’ll be moving at a paltry speed of only around 30 miles-per-hour (or 48 km/hr; your actual number will vary dependent on air density in the core of the shaft), and you’ll only overshoot the true gravitational center by less than a single mile.
In other words, in fairly short order, you’ll be trapped in the gravitational center of the Earth, a crummy fate for anyone or anything tossed into your bottomless pit.
So be smart about it! Don’t toss something into an air-filled shaft through the Earth’s poles, toss it into a vacuum! Your cylindrical shaft, reinforced and cooled, will extend continuously from the North Pole to the South Pole, and you’ll have removed all the air from it!
Now, the fun begins. You toss an object into the bottomless pit, and what happens?
It never reaches terminal velocity! On the contrary, it just keeps on accelerating, reaching a maximum speed at the very center-of-Earth of over 11,000 meters-per-second, which is around 40,000 km/hr or 25,000 mph! Your journey to the center of the Earth only takes about 22 minutes, with some uncertainties in there based on the densities of different layers, but because there’s no air resistance, no energy is lost, and that’s where the fun begins!
“I wonder if I shall fall right through the Earth!” –Alice, from Lewis Carroll’s Alice In Wonderland
You’d now slow down as you progressively moved away from the Earth’s core and through the various outer layers; your acceleration would change as you moved as well, dependent on the total mass enclosed by a sphere of your current distance from the Earth’s center, as well as that distance (squared) itself. And a total of 45 minutes or so after you were dropped into the shaft from by the North Pole, you’d emerge from the South Pole.
Only, because the South Pole is at an elevation of around 2,800 meters (over 9,000 feet), you’d barely be able to see daylight overhead before you came to a halt, and then had the identical journey back from whence you came.
And so you’d make a round-trip, back through all the various layers of mantle, outer core, and inner core, to the center of the Earth, and back once again through the northern layers. About an hour-and-a-half from when you first were dropped in at the North Pole, you’d re-emerge at the same exact position you started at.
A round-trip journey, from the North Pole to just shy of the South Pole and back to the North Pole again, all through the Earth’s center, in just a whisker under 90 minutes.
Under ideal conditions:
- creating a vacuum,
- straight through the Earth’s rotational axis,
- starting with no tangential velocity,
- devoid of any type of resistance and subject only to gravitational forces,
you’d wind up right back where you started, no worse for the wear so long as you insulated yourself from the radioactivity and temperature changes along the Earth’s interior. And that’s the physics of a bottomless pit!
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