Wednesday, June 22, 2011

Artificial Gravity: Space Stations

So if you've paid any attention at all to the International Space Station (ISS)—or, really, Mir and/or Skylab—you will have noticed that the astronauts and cosmonauts up there float around in microgravity. Effectively, they're in free-fall and, although Earth is still exerting a gravitational pull on them, they can't feel it because they and the space station are falling around the Earth all at the same time (also known as orbiting).

However, in books and movies we see (on screen or in our mind's eye) people on space stations walking around and generally acting gravitationally enabled. A notable hard SF example that springs to mind is Clarke and Kubrick's 2001: A Space Odessey. (I say hard SF because soft SF isn't necessarily going to stick to physics as rigorously.) How do they get away with this? The short answer is by spinning them up. The long answer follows.

Spinning Around

You may have been to some sort of theme park which has a ride called the Gravitron or something along those lines. The ride I'm talking about is a flat cylinder where you get it, stand along one of the curved walls and then it spins up and, once it's at full spin, the floor falls away or something, and you discover that you are somehow being held to the wall. It's the fictitious centripetal force, combined with friction that is holding you up. Why is it fictitious? Long story, but the short version is: there are only four real forces (two if you count electroweak as only one, but let's not go into that today) and gravity is the only one we care about for today.

In our Gravitron ride, gravity is still pulling you downwards but the tendency of things to want to keep travelling in a straight line rather than around in a circle means that you are constantly accelerating and where there's acceleration, there's a force. There are a few technical details here about exactly which way the force is pointing and whether we should call it centrifugal or centripetal. The centripetal force is whatever force is keeping you going around in a circle. In the Gravitron, the wall pushing on you stops you from flying out of the ride. In space, the Earth's gravity keeps you in orbit and stops you from drifting off. The centripetal force is the force that's pushing you outward; it's the force pushing you into the wall and the force that gravity needs to balance to keep you in orbit. It's easy to see why these two are often confused or used interchangeably.

When something is travelling around in a circle, the acceleration it feels is given the square of the velocity divided by the radius of the circle:

And if you recall, we were able to characterise gravity on the surface of a planet by the acceleration due to gravity. On Earth, acceleration due to gravity, g = 9.8 m/s2. So if we equate these, we can work out how fast we have to spin something to make it feel like we're standing on Earth.

Knowing the velocity, how fast the edge of our space station is moving around, isn't that helpful for getting an idea of how much we have to spin it up. The period, how quickly it completes a full revolution, is more helpful:

T is the period.

So now, let's suppose we have two bits of space station joined by a kilometre-long cable and we want to set it up so that we have Earth-strength gravity in the two end capsules when they spin about the centre of the joining capsule. How fast would it need to spin? Plugging the numbers in, and remembering that there are 1000 metres in a kilometre we get... a period of 63 seconds. The whole thing would have to complete an entire revolution in just over a minute which, considering the distance each capsule travels in that time is about 6.3 km (the circumference of the circle is 2πr) is incredibly fast. At any given time it's linear velocity would be almost 100 metres per second which is more than 350 km/h. Whoosh!

Admittedly, once we got up to that speed it would be much easier to maintain it, but it would still be difficult to access the capsules. A better setup would be to have a tube or tunnel connecting them. That way, spaceships could dock at the centre where to match (angular) velocities with the eye they would only need to rotate once a minute (since the period is 63 seconds everywhere because it's all connected). Spinning a ship around once in a minute is much easier than a kilometre-long space station.

Of course, if you look at the last equation there, the bigger the radius of the circle, the longer the period but even then we quickly run into engineering problems. Not that our two capsules aren't engineering problem enough.

Reducing the gravity requirements doesn't help enough either. If you only require half Earth gravity, then our capsules still have to complete a revolution in a minute and a half and the speed becomes 250 km/h . Moon gravity? Two and a half minutes and 150 km/h. Maybe that last one is manageable, but are the health benefits great enough to justify the cost of setting it up as compared with a non-spun space station? (I have no idea; no one's lived on the moon for a significant amount of time yet to find out.)

Another practical problem is maintenance. On the outer edge of one of the capsules (or giant ring, as Clarke used in 2001), a maintenance worker would feel as though they were hanging from the capsule with their feet hanging down into open space. Same thing on the sides except that they'd be falling towards the outside or "bottom" side. This sets up some pretty dangerous working conditions. Add to that the fact that the space station is hurtling so fast the stars would be a spinning blur and I know what job I wouldn't want to have.

Reiterating: Why doesn't the ISS spin?

A few reasons, mostly technological:
  1. It would have to spin pretty damn fast, and we just don't have the technology to do that well yet
  2. It's powered by solar power and the panels are set up so that they're always facing the sun. This is harder to do if the whole thing is spinning; another technological limitation
  3. Even if we could get it spinning fast enough, ignoring the above, we only just finished assembling it which means we would only just now be spinning it up anyway (it would be a lot harder to assemble a space station that was constantly rotating.

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