# Circular space station - what's the rotational speed to achieve earth-like gravity?

Imagine there is a space station shaped like a cylinder. The cylinder spins on its axis, in order to create artificial gravity through centripetal force.

My question: How fast would the space station need to spin to have the gravity be the same as on Earth?

I realize I probably can't get any exact speed without details on size and mass, so I'm looking more for a range (if it is possible to get an exact speed without knowing the details [like through a formula or something] that would be great too). The space station would be big. I'm thinking it would be made up out of 'wheels,' and then each wheel attaches on its axis to form the cylinder. Each wheel would be about the size of a small city. The space station would also have an extremely large population (think evacuation of Earth), so its mass would likely be gigantic. The space station is drifting - it is not orbiting anything.

I realize it isn't much to go on. Unfortunately, those are about all the details I have at the moment.

• This really belongs in the physics or space-exploration stack exchange. Apr 28 '16 at 13:35
• @iAdjunct, the question is too old to migrate. I suggest the OP create a new question there. Apr 28 '16 at 15:41
• At the time of posting this OP, I did not know that Space Exploration SE existed. So I'm sorry about that. But since this question already has an answer, I don't really see any cause to post it again on another SE. Unless there's something I'm overlooking? Apr 28 '16 at 16:12
• @TommyMyron if you're satisfied with the answers you've gotten here, there's no need to do anything. The question isn't in danger of going away, after all. Apr 28 '16 at 22:40
• Nominating for re-opening because it is similar to a variety of accepted, well answered, and well voted questions on this site. Knowing how to make a space station work can be an integral part of worldbuilding. Jan 25 '17 at 18:49

Not only does this calculator give you the values based on what you know about your design, but it also gives you nice graphical indicators for how comfortable it will be (e.g. it'll tell you whether your feet will feel significantly more gravity than your head).

• Thanks for the link! However, this looks like it measures surface gravity - that is, the gravity on the surface of the station. The people would be living inside the station, from just beneath the surface for at least about 100-200 meters or so. Would gravity differ depending how far inside the station you were - that is, how close to the center? Feb 21 '15 at 5:57
• It would; the closer in you get, the less gravity you'd feel. The rotation rate would stay the same though, so you can use this calculator to gauge the effect by keeping the rate the same and decreasing the radius. Feb 21 '15 at 5:59
• If I were farther in, would the rim speed need to change too? Feb 21 '15 at 18:06
• The rim speed would change. Only two of the four variables can be independent (i.e. controlled by you) at a time, and in this case they would be the angular velocity and the radius. Feb 21 '15 at 20:35
• @TommyMyron Check out Robert Heinlein's 'The Cat Who Walked Through Walls' for some great prose on stations with differing gravity on different levels. Do note that some of this can be solved by rotating each level at different speeds, though traveling between levels becomes difficult. Feb 22 '15 at 0:44

The speed of the spin is entirely based upon the diameter of the cylinder. The larger the diameter the slower it needs to go. If the diameter is 2 small, the speed needed to make the gravity will affect humans, like riding on a carnival ride. So bigger is better. I think I've read 1 mile is a pretty good starting diameter.

Because of this if you want multiple levels you are going to have different gravity at different distances. This means you have choices.

1. You have separate rings that spin at different velocities, though this can cause issues with moving between layers.

2. You make the ship like a tin can without the ends, you would only have the mechanical's in there and maybe some kind of drive system, the open end could even act as a scoop collecting matter as it travels through, for supplies or fuel.

3. Much like #2 except it is much larger. If you start with a 2.5 mile diameter and aim to have 1 g at 2.3-2.4 you can get almost a half mile thickness of gravity that is relatively comfortable for people, and it will all be one solid piece. Now you stretch that out for 10-15 miles and you have a LOT of space.

However if you are planning on millions of people living and completely dependent on this ship, then I might think more about a much larger radius, a 10 mile diameter, could have an almost 2 mile thick 'rim' for habitation in reasonable gravity.

• Make sure the lateral cross section is roughly square though; otherwise people walking around would make it start to tumble uncontrollably. Also, having levels with significantly different gravity wouldn't necessarily be a bad thing. I, for one, would be totally okay with putting, say, an Ender's Game style battle area in the center. Feb 21 '15 at 20:36
• There is a definite upper limit on the radius of the ring. The outward momentum of the ring's materials, plus that of any objects resting on the ring, creates a tension on the ring, and if it is too large the ring will fail. The tension increases as either the radius or the rotational velocity increases. Check the math, but a ring that is more than a couple hundred meters in diameter is going to require magically-enhanced structural materials. May 1 '16 at 17:03
• @EvilSnack - your comment makes no sense. Increasing the radius decreases the required rotational velocity proportionally. The tension will stay the same. Sep 4 '17 at 17:33

This is more of a physics question, but based on:

http://www.regentsprep.org/regents/physics/phys06/bartgrav/default.htm

You'll want a velocity equal to the square root of 9.81*r, where r is the radius of your station in meters.

• You will also want the station to be large enough that the effective gravity doesn't change much across your body, which could cause vertigo. Feb 21 '15 at 0:49
• @Oldcat: Of course, if people had to live in an environment with a significant gravity gradient along the length of one's body, they'd adapt fairly quickly (and then start feeling weird if they moved somewhere without that sort of gravity gradient). Sep 6 at 18:29

For a given rotation rate, the pseudogravity you feel is directly proportional to your distance from the axis. Thus, if you have one gee at 1000m (turning once in 63.4 sec), then at 900m you have 0.9 gee.

The formula for centripetal acceleration is $\frac{4 \pi^2 R}{T^2}$, where $R$ is radius and $T$ is period.

For one gee at one rpm, R is 894m; one turn per hour, 3.22 megametres (Mars would not quite fit within this ring); one turn per day (the kind of ringworlds described by Iain Banks), 6.15 light-seconds.