Fellow Science Lovers,
Game update: Nothing to report this month. I’m still engrossed with Scribes Emerge edits.
Metal Donuts?
In Terrific Tomorrows, which has my short story called A Cartoon Saves the Universe, we see this line: “A million people live on this station, which looks like two halves of a metal donut connected by a long cable. I don’t feel it spin, but the stars sneak across my view through the broad windows.”
Would this setup really create artificial gravity? Let’s look at some physics to find out.
Gas Pedal or Steering Wheel
Gravity makes objects accelerate downward. Most commonly, downward means toward the Earth, but in space, that could be toward whatever massive object that happens to be nearby. Conversely, acceleration creates what we call “artificial gravity” on an object. As a kid, I’m sure you windmilled a bucket of water without spilling. (Until you had to slow down the bucket–then some sloshed out.)
This centrifugal force simulates gravity because any object that’s changing directions is, by definition, accelerating. To be more rigorous about it:
Velocity is the speed of an object in a given direction.
Acceleration is the rate of change of velocity.
We tend to think of acceleration as going faster, like pressing a gas pedal. But changing an object’s direction also counts. You feel this when turning a steering wheel. Without changing speed, your body gets thrown to one side. Hopefully without spilling the drinks and pizzas you’ve been bringing home from Domino’s. Yes, that’s a confession. Okay, lava cakes and cheesy bread, too.
Go faster or spin. As it happens, these are the two ways you can give a space station artificial gravity. Either fly it faster and faster in a straight line or just make it spin. Of those options, spinning is much easier. One, you only need to burn a little fuel to get things moving, then it’ll keep spinning on its own. Two, your station can remain, well, stationary. Instead of zooming away from the solar system into empty expanses where space pirates could be waiting to steal your cats and your mobile phones where you store your cat photos.
Anyways… here’s the formula to calculate acceleration:
a = ω2 x R, where
a is acceleration
ω is angular velocity measured in radians per second.
R is the radius of the spinning object
So to make 1 earth gravity of acceleration, which is 9.8 m/s2, you can use a small radius with a very fast rotation, which is a great way to make everyone sick. Or, better yet, you can use a very big radius and a slow rotation. Most stomachs can handle around 1rpm. So to build a space station that makes 1g while spinning only 1rpm, how big would its radius need to be? Let’s rearrange our formula to solve for R.
Trigger warning: we’re about to do algebra. If you post “I haven’t had to do algebra in X years,” on social media, you’ll have to reset that counter. And you can blame me. I’ll be your algebra fairy.
R = a/ω2
Let’s plug in values:
R = 9.8m/s2 / 0.104719717675642
(1rpm = 0.10471971767564 radians per second)
R = 893.65m
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-rotating space station numbers calculator, from https://www.tomlechner.com/outerspace/
Now remember, this is the radius. The diameter will be double, or 1,787m. That’s over 1 mile long (or 16 football fields laid end-to-end!) If you’re a football fan, that’s great news. If you’re the person paying for the space station, that’s bad news. If you’re a football fan who’s paying for the space station, the news hopefully cancels out into a meh.
Have your Donut and Spin it, too
But… there is a way to keep your space station small. Just connect two small stations with a very long cable and use thrusters to spin the whole structure. A cable is much cheaper to build than the same length of living space, and you still get the gravitational benefits. If you make a t-shirt that says “Friends with Gravitational Benefits,” cut me in on the royalties.
So that’s the design of the station in A Cartoon Saves the Solar System. But what about the donut part? I figured that because gravity would push everything into the walls, away from the center of rotation, those walls may as well be roundish. I imagine it would look like this:
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Coriolis Effect
A very long diameter solves another problem: differential gravity. Weird things happen when the space station’s diameter is quite short (say 10m or so). Your feet would feel much more gravity than your head would, because your head is closer to the center of rotation. But when the station’s diameter is over a mile long, the gravity difference becomes too small to notice.
A long diameter solves this problem. Here’s another picture:
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Because person 2 is on a “lower” deck of the space station than person 1, he’ll move faster to make the same rotation because he travels farther in the same amount of time. If person 2 throws a ball up to person 1, it’ll curve because it’ll be moving too fast for the new, smaller radius. This extra speed exerts what we call the Coriolis Force.
Why does this matter? When a person stands, his head will get pushed forward or backward or sideways, depending on which way he’s facing. This could make it hard to keep balance and to hit the target when using the bathroom. This can be your excuse, guys. “The house started spinning, and Coriolis forces pushed my pee sideways!”
These forces are quite strong when the station is spinning fast. But if you use a long cable and slow the rotation, you won’t notice those extra forces. And your excuses fly out the airlock.
A Balancing Act
This design needs a balanced load. Put more weight on one side, and the center of rotation will shift toward it. That side would experience lower gravity since it would rotate slower, and the lighter side would experience more since it would rotate faster. Again, having a longer cable means this imbalance isn’t as severe.
But what if you need to dock a spacecraft on one side? Do you have to dock another spacecraft of equal weight on the other side at the same time? Well, you could use a ballast system: attach a weight on a motorized pulley that rides the cable. When you dock a heavy craft on one side, just transfer the weight toward the other. This approach isn’t perfect, though. Docking a spacecraft adds instant weight while shifting ballast down the cable is more of a gradual change. It would be tricky to time things to avoid too much imbalance.
It’s better to dock large craft on modules near the station that don’t spin. Then use very small craft to shuttle cargo from there to the spinning station. Small additions shouldn’t disrupt the balance, especially when they’re alternated to one side and then the other.
Want more complications? I’ve got ’em. This setup requires cables strong enough to support all the forces, including transient forces caused by load shifting and passing asteroids. And if all the elephants in your space zoo all decide to stampede to the same side of their enclosure. You also have to deal with the occasional slack in the cable, unless you replace that cable with a solid bar.
But all these issues are a matter of engineering. A spinning space station should be scientifically possible, though tricky and expensive to get it right. But hey, living in space is like playing a game on hard mode.
References:
https://www.wired.com/story/the-problem-with-spinning…
https://www.quora.com/Hypothetically-2-modules-separated-in-…
https://en.wikipedia.org/wiki/Space_tether_missions
Want more Christian sci-fi? Check out Red Rain by Rachel Newhouse! This is book 1 of a big series I’ve really enjoyed:
Writing update: I’ve finished the big rewrite for Scribes Emerge, Scribes Series book 3. I’ve already made it to chapter 11 on my next editorial pass and have received great feedback on Scribophile.com. While you’re waiting for this, check out my new short story in Terrific Tomorrows! I may also have even more short stories coming in another anthology in the next month or so. 
See you next month,
Dylan West
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