Space habitats would not necessarily stay in position in stable orbits. It may be desirable to move them, either to different orbits, to other parts of the solar system or, in the interstellar ark case, to other solar systems (Whether at that point one calls them spaceships/starships is a matter of taste although it probably would be influenced by the frequency of such moves and the relative intimacy/permanence of association of the driving engines with the habitat - when does a trailer park home become a caravan and the latter become a camper van?).
If the force of gravity is being simulated in a habitat by rotation, any movement of the habitat as a whole would involve accelerations that would interact with the rotational effects. If the acceleration was perpendicular to the axis of rotation, then the effect would cycle from additive through lateral to subtractive and back again (relative to the rotational pseudogravity for an individual at a point inside the habitat) for every rotation (see Figure 1).
If for no other reason, the preceding would suggest that if one were to move a colony or ship other than very gently it would be best to apply the driving force to give a resultant acceleration along, rather than perpendicular to, the axis of rotation. Obviously this would not always be possible since the very act of pointing the rotation axis in the direction one wished to go would probably involve some manoeuvring accelerations with components perpendicular to the axis of rotation. Even if one could cancel out the total gyroscopic effects of turning a rotating object (see Big Gyros) it would still be necessary to carry out the operation with great delicacy to avoid both tearing the vessel apart and inducing weird effects on the inhabitants.
However, even if forces are applied to induce acceleration along the axis of rotation, the resulting effects can not be ignored. To take the limit case, obviously any acceleration greater than 1g would be unsustainable unless we can learn to both breathe and live in a fluid that would make us neutrally buoyant. Constant acceleration at 1g would mean that no other source of artificial gravity would be required for the period of such acceleration (i.e. any rotation could and should be stopped) and the 'floor' of the craft would be the inner surface of the living quarters that was closest to the engine. However, that same floor would have been a wall when the habitat was rotating to give artificial gravity. The same problem, but to a lesser extent, applies to any acceleration less than 1g, in that any rotation to give artificial gravity should be reduced and the combined effects of the rotation and the acceleration produced by the driving engine would act at an angle to the normal vertical produced by rotation alone. Effectively, for the occupants, the floor would slope when the engine was operating and the greater the acceleration produced by the engine, the greater would be the slope.
There have been a few suggestions for coping with this problem. In some ways the simplest would be to take off directly from an Earth-like planet, accelerate at 1g until you are half way, flip round and decelerate at 1g until you land directly on another Earth-like planet. No need for rotational artificial gravity or any of that nonsense. Simple, but not very practical. The chances of more than one Earth, the energy requirements for constant acceleration at 1g, the time dilation effects for the very high velocities that would rapidly be achieved and the erosive effects of the interstellar medium at such high velocities would all suggest that it is unlikely. At the other limit, all accelerations could be so small as to be negligible and for practical purposes no different from staying at rest. Between these two acceleratory extremes there are some technical approaches that might be useful.
The earliest recollection that I have of an approach for a problem like, although not necessarily the same as, this is of a science fiction drama on British television in which travelers in a spacecraft kept maintained some rails that curved up the wall, although they'd forgotten why they did so. Plants were growing in containers on the rails and eventually, as the drama progressed, the reason for the rails became obvious as the acceleration conditions changed, through braking or something, and the plant containers changed position (if anyone can shed some light on the drama in question please e-mail). Anyway, the dramatic digression aside, one approach is obviously to mount the artifacts of the habitat in such a way as to allow them to assume an appropriate position when the direction of 'down' changes. People have been doing this on boats and ships for a long time, with hammocks, gimbaled cookers etc.. Obviously the gimbals or rails would have to be arranged to allow pivoting or movement fore an aft. This approach may suffice if the acceleration of the habitat is not too great and the resultant floor 'slope' is still manageable for the inhabitants. Keeping the acceleration low might also mean that it would be possible to avoid the necessity for slowing the colony rotation. Assuming a habitat rotating to give 1g, accelerations of , for example, 1/50th g would be acceptable with this approach.
Another aspect of this situation would be that which would exist if there were any large bodies of water as, for example, in a large colony. Arthur Clarke considered this situation in 'Rendezvous with Rama' and, naturally, supplied a solution, which was to have the aft bank of his equatorial 'sea' somewhat higher than was necessary at rest. This would have allowed the water to take up its natural position under acceleration without slopping over the boundaries of its container. An alternative possible approach would be to make sure that acceleration and deceleration only take place in the habitat's winter, when the bodies of water could be frozen to avoid slopping about.
For greater accelerations such as might pertain with smaller, fast, ships, an approach that has been suggested, for example, by Kelly Starks (see 'Heavy Explorer-class starships' in Links) is that instead of gimbaling the contents of the habitat, one could change the position of the whole habitat, or sections of it. Starks' suggested design consists of two segmented tori with each segment capable of being pivoted fore and aft so that the floor is positioned for the current position of 'down'. The two tori would be contra-rotating so that rotation rate could be reduced by braking of one torus against the other, avoiding any net torque on the rest of the ship. Reduction or even elimination of torus rotation would be necessary in this design because of the higher accelerations of the ship as a whole that were envisaged. If the rotation rate were not reduced the net resultant accelerations on the inhabitants (from the addition of the rotational artificial g and the ship acceleration) would have been too high for comfort.
An alternative to this would be to have habitat sections rotating suspended on cables. These would naturally assume a position under any acceleration conditions so that the floor was always correct for the current 'down', but there might be other complications. The swinging back under acceleration could affect both the radius and the rate of rotation, and some braking of the rotation rate or complete prevention of rotation would be necessary, as discussed above. Such braking may be more troublesome with a non-rigid habitat support and the thought of having two contra-rotating sets of cable suspended habitats flexing under braking creates some interesting possibilities for accidents. Also, Starks has pointed out that in such circumstances the erosion shielding for the suspended habitats at relativistic interstellar velocities may be problematic.
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