Why does spinning a space station create artificial gravity?

Dear Straight Dope: I was lying awake the other night and started reading some old science fiction by Heinlein, where he talks about rotating space stations. The theory is that the station spins and the centrifugal force creates pseudo-gravity. Now I can see this working when you are in physical contact with a surface but what happens if you are floating and they impress a spin on the ship you are in--does everything else experience “gravity” except you? What happens if you jump--do you go back down or do you head up to the ceiling? Questions like these do not help on a restless night. Steven, London, England

Chronos replies:

Spinning your space station will work (but of course! Would Heinlein lie to you?), but it’s not quite perfect. To understand why, we need to go into the physics of the matter.

The first thing to consider when you’re doing a problem like this is what frame of reference you’re in. You can approach this from an inertial (non-rotating) frame, or from a non-inertial frame that’s rotating with the space station. In the non-rotating frame you’re not experiencing acceleration and Newton’s laws of motion apply. In the rotating frame you are and they don’t. The significance of this will become apparent in a moment.

For your first question, let’s consider the inertial frame. You start off floating, then someone hits the switch and the space station starts rotating. In the inertial frame, things don’t accelerate unless there’s a force on them, and all forces need to be exerted by something. Since the only force on you is from the moving air (which we’ll ignore), you just keep on floating there, in the same position relative to the outside inertial frame. Meanwhile, the solid structure of the space station is moving, so one of the walls will eventually come along and smack into you. Suddenly, you’ve got a force, and very quickly end up going the same speed as the station.

Staying in the inertial frame for a while, you’ve now recovered from hitting the wall (or rather, the wall hitting you), and have your feet on the floor–that is, the space station’s outer rim. You’re moving in a circle, so your direction of motion is constantly changing. Since acceleration is a change in velocity, and velocity includes speed and direction, that means that you’ve got a constant acceleration towards the center of the space station.

We’d better pause, because a lot of people get lost at this point. Let me repeat what I said above: When you’re moving in a circle, you’re under constant acceleration. This is counterintuitive. The space station (merry-go-round, whatever) is turning at a steady rate, and your speed doesn’t appear to vary, so why do we say you’re accelerating?

Because force is constantly being applied to you. Think about it. The laws of inertia tell us that an object in motion tends to remain moving in a straight line. To keep you moving in a circle, the rotating object must continuously apply force to you. As long as force is being applied, you’re accelerating.

The direction of this force is inward, toward the center of the space station, so it’s called the centripetal force (literally, towards the center). The force is being exerted on you by the floor (outer rim) of the space station, which is pushing on the soles of your feet. A force on your shoes from the floor is exactly what you feel here on Earth, so the result feels like gravity.

You may find this talk of centripetal force confusing. Most people are accustomed to thinking of rotating objects as imparting centrifugal force, i.e., one that flings you out rather than pulls you in. They’re not wrong to do so; they’re just using a different frame of reference–the rotating frame, to which we’ll now turn our attention.

In the rotating frame, since you’re just standing there, you’re at rest. It’s not an inertial frame of reference, though, and Newton’s laws are designed only for inertial frames, so we need to fudge things a bit by introducing a couple of “fictitious” forces. Whereas real forces are always exerted by something, fictitious forces are not: They’re just there, as a consequence of the frame you’re in. Don’t say they’re not “real,” though: They’re useful, and that’s all that really matters for physics. Einstein tells us that gravity is actually just a fictitious force, too, but that doesn’t stop physicists from treating it as real.

The two fictitious forces we need to use here are the centrifugal force and the Coriolis force. The centrifugal is the easier to explain, and the more widely understood. Since you’re standing “still” (in the rotating frame), and you can feel the force of the floor on your feet, it’s necessary to posit another force, acting like gravity, pulling you down and countering the force from the floor. Since this force is pointing out from the center, it’s called centrifugal, or “fleeing the center.”

The Coriolis force is a bit more complicated. It only acts on moving objects, and causes their path to curve. The explanation for this is a bit involved, so I’ll omit it here. Suffice it to say that if you jump straight up on the space station, you’ll travel on what (in the co-rotating frame) appears to be an arc, and land “forward” (i.e., in the direction the station is rotating) of where you started. This is a key difference between artificial gravity and the real kind. So, if you wake up some morning and you’re not sure where you are, jump up. If you land where you started, you’re on earth. If you land forward of it, you’re on a space station. Let it never be said we don’t give you news you can use.

Chronos

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Why does spinning a space station create artificial gravity?

A STAFF REPORT FROM THE STRAIGHT DOPE SCIENCE ADVISORY BOARD