These days, science fiction writers are starting to move away from magical “grav plating,” something that may be impossible, and grappling with the fact that in space, there’s no gravity.
For the most part, you can put up with zero-g. After all, it’s a book, not a movie–you aren’t going to have to film it by stringing up all your actors on cables and CGI-ing some floating hair. You can simply describe how nice it is to float until you have to go to the bathroom and things get complicated. And YouTube is full of videos from the ISS that will let you visualize how things move in space.
But there are two ways to make artificial gravity in space with technology we already have. The first is thrust: if a ship is accelerating at 10 m/s/s, you’ll feel like there’s about a normal Earth gravity pulling you toward the back of the ship. Of course this will affect spaceship design. The ships in The Expanse are basically office buildings with engines on the bottom. You don’t move around the ship; you’re constantly climbing up and down.
The other way is what I want to write about today: centrifugal force. We know that if you’re in a spinning teacup, you feel like you’re being dragged outwards. So if you’re on a spinning space station shaped like a wheel or a barrel, you can walk around the inside surface of the station, pee into a regular toilet, pour a cup of tea, whatever you want. Which, after months of floating in a ship, would be pretty dang nice.
But understanding exactly how big the station has to be, how fast it’s going to be spinning, and how things would actually work on board are more difficult questions. Sometimes authors get vague about the details, either because they don’t know or because they think we don’t want to get bogged down in pages of explanations. Speaking for myself, I very much do want to know! To write my current work in progress, I took a whole Khan Academy course on rotational motion, because I wanted to get things right.
The first question is how much gravity you want. The “gravity” is caused by the change in velocity of the rim of the station. You see, every piece of that rim wants to keep going at a constant speed and direction, but the spokes or struts of the station are constantly adjusting the direction inward. This is called centripetal acceleration. It’s balanced by the “imaginary” force called centrifugal force–the force you feel pushing you outward. So if the rim is traveling fast enough, that’s a pretty hard force pushing outward against the pulling force inward. Imagine you’re in a car making a sharp turn. As you turn, your body is pulled outward, against the turn. Two things affect that force: how fast you are going, and how sharp the turn is. If you want to be jerked around less, you either slow down to make the turn, or you make a wider turn.
The speed of the rim of the station, measured in meters per second, is the first factor. The larger the station, the faster the rim has to go to keep up with the speed the center is turning. So, imagine a station turning one full time around every minute. If it’s 200 meters across, how fast would the rim be going?
Since 1 rpm means each piece travels the whole circumference in one minute, we can use this:
v = circumference in meters/60 seconds.
v = 200m * 3.14 / 60 s
v = 10.5 m/s
The rim of the station is going 10.5 m/s — about 23 miles per hour. A gentle pace for a car.
But a station that’s 2000 meters across, still making a full turn once per minute, will have a rim going much faster:
v = 2000m * 3.14 / 60 s —> 105 m/s. That’s 235 miles per hour! Suddenly the rim of this station is moving like a bullet train.
But it’s not that simple to figure out the magnitude of the artificial gravity on the station. After all, at gentle car pace, we’re taking a much tighter turn than we are at bullet train speed. Here’s the equation for figuring out centripetal acceleration — a number equal to the gravity we’ll feel:
a = v^2 / r, where a is centripetal acceleration, v is the constant speed of the rim, and r is the radius.
Let’s do our 200m station first. Its radius is 100 m, so we plug it in like this:
a = (10.5 m/s)^2 / 100 m
a = 110.25 m^2/s^2 / 100 m
a = 1.1 m/s^2
So on this small station, we’re only feeling just over a tenth of Earth gravity. I would weigh about as much as a cat litter carton. Enough to keep me from floating off and make the toilets work, but it wouldn’t be so good for long-term living. I’d certainly be losing some bone density there, unless maybe I wore a huge lead vest all the time and worked out a lot.
Now the 2000 m station. Its outside edge is moving like a bullet train, and its radius is 1000 m. Let’s put that in.
a = (105 m/s)^2 / 1000 m
a = 11 m/s^2
It’s a little more than Earth gravity here! We might want to spin it a little slower, if we don’t want people to be uncomfortable.
Once you’ve worked out the desired size of your station, it’s time to think about design. Mine is shaped like a bicycle wheel, because a few kilometers of concourse was really enough. It’s less than 100 meters thick. If you’re planning on a whole floating city, you might want to make it barrel shaped. Your radius is pretty much decided for you by the equations above, so if you want to make it larger, you’ll be expanding its thickness.
Or you could even not make it wheel-shaped! A possible option is two habitats joined by a large cable, so it’s less like a wheel and more like two figure skaters holding hands. They rotate around a point between them, with each feeling the amount of force they’d feel if they were parts of a whole wheel.
Time to think about practicalities. Do we have engines on this thing? A generation ship would need some. Even a station might find navigational thrusters handy. But here a problem appears. The only place for your engines would be right at the axis. Or they could be equally spaced anywhere, but they could only fire together. You can only go parallel to the axis, because any thrust applied in another other direction will change as the ship rotates. One possible solution is to have thrusters on a pivot — either a person or a computer can rotate the pivot so it fires in a constant direction despite the rotation of the ship. But it’s not easy. You’ll probably want most of your travel to go parallel to the axis.
And then there’s the question of docking ships. If you want to dock with a station, you’ll want to be moving tangentially to the rim. The moment you lock on, the gravity will kick in at once, since the station will yank you along its circular path — quite a shock. So it’ll be smart to line up your shuttle so that you’re pulled to the floor, not the back of the shuttle. That means you would want airlocks on the side of the station, not on the rim itself.
And what does the inside of the station look like? The rim is the only place with the comfortable gravity we set up at the beginning. Further in, the gravity gets a lot lower, and you might feel dizzy because your feet are moving significantly faster than your head. If you jump, you’ll move sideways. Once you get to the hub there’s no gravity, and I thought initially that it would be a handy zero-g place to be. Except . . . not. Because you have no convenient way to transfer from the spinning part of the station to the still center. As you pass into the center, you’re still moving laterally. So you let go of the ladder you took up there . . . and drift sideways to crash into the wall. You’d need something extra to fix yourself in place.
But it can’t be some kind of control room or command seat. Because if you had something like that, it would have to be fixed to something, and that means it would spin too. My apologies to Mary Robinette Kowal — you probably could not sit still at the center hub and take readings off the stars, because your chair is rotating and you are rotating and that means the stars won’t stay still in your sextant. Unless the whole hub is somehow on ball bearings, in which case where is there room for doors? Maybe an engineer could figure out some kind of workable solution.
Really, the smartest thing to have at the hub is storage. Why? Well, rotating objects tend to wobble. The more weight is at the hub, the less they wobble. (As a spindle spinner, I’m used to this: the more yarn you pile on the spindle, near the whorl, the steadier a spin you’ll have.) So instead of having a big empty space at the middle to float around in, you’re better off with a giant tank of whatever heavy materials you have to store.
That’s only the beginning of the issues that arise with spinning space stations. Other questions include how to aim weapons fired from the station, how to get them up to speed, and what materials could withstand all the forces involved. This sounds like a hassle, except that every tough engineering problem you solve can also be a cool plot twist later on. Oh, there’s a strong Coriolis effect near the hub? Let’s have a fencing duel there where everyone’s dizzy all the time!
Don’t take spinning space stations for granted, but don’t let them intimidate you either. Let the forces fling you around, and have fun!