Inertial Navigation

I just finished reading Abaddon's Gate by James S. A. Corey, part three of a grand space opera trilogy. At one point one of the characters (Melba/Clarrissa, maybe?) comments that it's nice to have gravity back, either gravity or its equivalent in the form of acceleration or centrifugal force. Einstein tells us that if we have no external clues, it is impossible to distinguish between equal forces produced by acceleration or gravity. For long term living in outer space, science fiction writers often propose spinning large wheel shaped space stations to simulate gravity. People have a zillion years of evolution behind them that has adapted us to living in a one gravity force field. Zero gravity might be fun for a bit, but it is not our normal environment. So, artificial gravity.

    The human inner ear is a remarkable sensitive piece of apparatus, witness the amazing feats of skill demonstrated by numerous athletes like acrobats, gymnasts and high divers. Shoot, just walking on two legs is a bit of a trick. So if you are moving about in a rotating space station you might very well be able to detect this rotation. If it was spinning quickly it might even have some unpleasant, perhaps even intolerable, side-effects, like vertigo. Using a longer radius and spinning slower could produce that same effective downward (outward) force and it might reduce the side effects. You should not be able to detect this rotation if you were sitting still. In the worse case you might sleep in the spinning section at full gravity, but spend your waking hours in a non-spinning section in zero gravity.

    One thing that comes up in science fiction stories set in rotating space habitats is that the floor curves upward in the distance. If you have a large structure, and a clear view of a large room or a long hallway, that would be true. But what if you only had a small room, say a ten by ten cell located a half a mile from axis of rotation? If you had a tape measure and a good level (or plumb bob) you might be able to measure the difference in angle between the apparent force of gravity at opposite walls, assuming you pick the right two walls, and they are crosswise to your direction of motion. The difference would only amount to half an inch. Given conventional building standards that is well within what you might expect to find in your average house here on Earth.

    Now imagine we have constructed a large rotating space station and have filled the rim of this structure with a warren of small interconnected rooms. The doorways are offset so you cannot see all the way across more than one room, so you would not be able to see "the floor curving upwards". Imagine walking all the way around the rim of this station and arriving back where you started. Never mind having to continually jog left and right to go through the offset doorways. Imagine not knowing you were in this rotating space station, doing all this walking and ending up where you started. Might be a little disconcerting, eh?

    Take this same ring shaped labyrinth of rooms and place it on the Earth, except instead of curving up and back over, curve around to the side. If you walked through this thing would you be able to tell that you were slowly being turned around?