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One thing I always wondered was if a giant spinning space station that was providing artificial gravity would slow down without any energy input. I would assume that energy is being lost to heat as the station's inhabitants are pulled towards the ground. If so, is there some mathematical formula for calculating how much energy you need to put in to maintain the spin?

Most spinning spacecraft concepts I have seen don't look like they have big reaction wheels on their inside. Is this just artistic license, or are they not needed?

Thanks!

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Classically at least, the conservation of angular momentum has never been known to fail. As long as everything on the station stays on the station, the total angular momentum of the whole thing will remain constant. People can jump up and down, move around, make lots of heat, all go to one side, or the middle, it doesn't matter. The angular momentum of a closed system will remain constant.

The key there is closed system. If they vent gas or waste or shoot thrusters, then that can either add or remove angular momentum from the station (the make-up is in the angular momentum of the stuff moving away).

Sunlight or solar wind or other torques from the gravity of nearby objects can have very small effects that might build up over time, but people know about these things and the can be zeroed out by balancing torques.

So if you build a large rotating space station, or build it non-rotating and spin it up, it will pretty much rotate for millions of years unless you do something wrong. The only reason you'd need reaction wheels would be if you wanted to add attitude control, or adjust the speed of the spin slightly.

One reason that O'Neill cylinder come in counter-rotating pairs is to cancel out precession due to torque from other bodies. They need to remain pointed towards the Sun. One cylinder would keep rotating at about the same speed, but its axis could precess over time.

Another advantage is that the total angular momentum of the pair is zero. So you can build them at rest, and start spinning them in opposite directions using electric or other motors, without using any propellant.

So in some sense you could think of one cylinder as the reaction wheel for it's twin cylinder.

You could also use that with geometries other than cylinder pairs, run it as a net-zero angular momentum system with counter-rotating components. In that case you can have your reaction wheel if you want it.

Pair of O'Neill cylinders from here:

Pair of counter-rotating O'Neill cylinders

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A rotating space station in a low Earth orbit (about 400 km) will gradually slow down. The drag caused by the non perfect vacuum not only lowers the orbit, it will also slow down rotation.

But the circumferential speed of the space station is much lower than the orbital speed, so the rotation slow down will be very, very small.

This is only true for a low orbit, not for a high Earth orbit or a space station leaving our solar system.

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  • $\begingroup$ This is not true in general, but only if there are no competing torques. If you put blades on it like a fan or a propellor you may be able to use drag to make it spin faster or slower by adjusting the angle. $\endgroup$ – uhoh May 16 at 8:23
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I would say that yes, a spining space station will slow down, if it has disipative sinks of energy.

All real world mechanisms have some dissipation, when a part of ordered macroscopic movement energy transforms to stochastic thermal momement of atoms. For example when astronauts push from the walls deformations are not absolutely elastic. Some tiny part of energy transits to the walls as heat.

So, even absolutely isolated space station - in absolute weightlessness (not microgravity), absolute vacuum and with zero external electromagnetic radiation - will lose its rotation energy slowly, at least if it has moving parts.

If it has no moving parts - hm, I think in absolute isolation it could maintain rotation endlessly. But maybe there are some tiny efects that I overlooked.)

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    $\begingroup$ It doesn't matter if it has moving parts, if it's isolated the angular momentum will be conserved. A freely spinning object can not spin down due only to internal lossy processes. It seems like it's possible, but it isn't.That angular momentum has go leave the system somehow. Moving parts doesn't have anything to do with it unless those parts detach and fly away. I'm not sure if some strange charge distribution could radiate ELF photons with angular momentum, or if it could produce gravitational waves, but these would be really really really weak. $\endgroup$ – uhoh May 16 at 11:56
  • $\begingroup$ @uhoh for real world physical systems conservation of angular momentum is a "good approximation", that is. But really dissipation occurs and angular momentum is not strictly conserved. For example it's known that Moon-Earth mean distance grows about 4 centimeters per year, and Earth rotation slows too. Both because tidal interactions. Can we say that angular momentum of Moon-Earth conserved? Energy conservation and second law of thermodynamics always work, but momentum and angular momentum are conserved only in ideal systems, with no mechanical energy loss. So I insist I'm right :) $\endgroup$ – Heopps May 17 at 4:59
  • $\begingroup$ Angular momentum in the Earth-Moon system is still conserved. The "moving parts" in this case are the tidal deformations of the bodies. Angular momentum is exchanged between the two separate bodies via this interaction, but the internal friction or tidal heating does not somehow dissipate angular momentum. You can fill a space station with water or magma or other dissipative materials, but that can't cause it to lose angular momentum. $\endgroup$ – uhoh May 17 at 5:04
  • $\begingroup$ @uhoh not agree. Let's look at mathematical definition of angular momentum. It's vector product between momentum and radius. When mechanical movement energy transfers to thermal energy - movements of particles are chaotic. If you make a vector product of particles' individual momenta and radiuses and sum them - it will not be the same as macroscopic angular momentum. Also examples of angular momentum loss - single pulsar spinning down, or black holes mergers. In both mechanical energy transfers to another form. I can ask question at Physics.SE :) $\endgroup$ – Heopps May 17 at 6:00
  • $\begingroup$ A single closed system like a space station is not the same as the Earth-Moon two body system nor is it like a continuum of fluid or gas. In the case of a closed space station, "moving parts" inside can't result in a dissipation of angular momentum. You could exchange it in a conservative way with one or more internal wheels so that the outside shell would stop turning, but you can't dissipate or get rid of the angular momentum in a closed space station. $\endgroup$ – uhoh May 17 at 6:20

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