UK Space Design Competition
So last weekend, I did something pretty exciting: I actually got a chance to use some physics. I went to Imperial College London, with a group of students from my school, where we were grouped together with another school team to from a Company of about 25 students. We were promptly told that the year was 2044, and our company received a Request for Proposal- to build a space settlement at L4, a Lagrangian Point, which would mine and process ore into high quality components and have a workforce of up to fifty people.
There was a lot to take in, and we did quite a few things badly to be honest. I'm going to discuss some basic physics that was at play first: L4 is one of 5 Lagrangian points, and one of only two stable ones. A Lagrangian point is an orbit that does not move relative to the Earth (we were at the Earth-Sun L4 point. Another one exists for the Earth-Moon system, which is a constant distance from the moon.) In an idealised solar system model, the farther from the Sun you are the slower you orbit, so being slightly closer to the Sun produces a different angular velocity (rate of change of angle, an important concept that we'll get to in a second!) This would not be a Lagrange point. The trick is that the Earth also has mass, and so there are two effects at play:
1) The small orbiting body (the space settlement) is attracted away from the Sun, toawrds the Earth by a small amount.
2) The centre of rotation is the centre of mass not of the Sun, but of both the Sun and the Earth (this actually causes the Sun to wobble a little, and this oscillation can be used to detect orbiting planets around distant stars).
The result is five orbits which have the same angular velocity as the Earth, and so don't move with respect to it, a very handy property when trying to communicate. L4 has another useful property: stability. Instability can be thought of as a ball on top of a hill- it's balanced and not moving, but a slight nudge will cause it to roll away and probably never return. Stable points are like valley, however: a restoring force acts to return the ball back to the bottom. This causes debris to gather in the relatively stable orbits of L4 and L5, which are both one AU from the Earth, where one AU is the mean distance of the Earth to the Sun (and is equal to 150 million km, or 1.5X10^11m).
One mistake we may have made was researching the nature of Lagrangian Points too much. The only two important facts to us were:
1) Constant distance of 1AU (just over 8 light minutes). For our purposes this ruled out any real time communication because of a nearly 17 minutes signal delay.
2) Stable. Although we were made to build our settlement at L4, this was a useful trait not only for the reason that the orbit did not need maintainance, but also because this gave us a number of 'local' asteroids to mine.
So, knowing our location, the next real physics question was a topic familiar to anyone with even a passing idea of what physics is: gravity.
Those with a science fiction background will know that in order to create artificial gravity, you want to set your space settlement spinning. As a group, we collectively agreed that the centrifugal force experienced by a rotating space settlement would cause an outwards force of 'gravity' to be felt by our workforce. From a practical point of view, we wanted low gravity inside the factory in order to maneouvre heavy machinery and ores, whilst we wanted as close to 1g as posible in the living quarters. The solution to this dilemma becomes more obvious once you know the physics of the situation: the acceleration caused by circular motion is given by v^2/r. This however, is not a good format to use! Why? Because this falsely makes it seem that you get the most gravity at the centre, where r is less.
This ought to seem immediately wrong, and of course it is. You can't have gravity tending towards infinity at the centre of something spinning! V^2/r is not wrong, but it is misleading, because in fact the velocity is equal to v=wr, where w is something called angular velocity. Angular velocity is simply a measure of how fast you pass through some fixed angle (angular velocity is measured in radians/second or just s^-1). This is a more useful form of the equation, because w is constant everwhere on the space settlement, and from this we can see that a=w^2r, in other words we have a linear dependance on distance from centre, and the strongest gravity as farthest out. This suggests a central factory at low gravity, with living quarters at a more comfortably high gravity further out.
Now, design wise. this led to the necessity of high tech lifts that could cope with a pretty sharp change in gravity as they moved. It also gave us a way to calculate the basic dimensions of our settlement. The automation department wanted 0.2g of gravity at the edge of the factory, which they wanted 30m away from the centre of rotation. The human management department wanted 0.7g in the living habitations. Well, the linear dependance means you don't actually have to bother working out w in th first place! You can simply say:
0.2g=w^2 * 30
0.7g=w^2 * ?
Clearly the answer is 115m, which is 75m away from the factory, since we needed to know the length of the elavator shafts. The discussion of artificial gravity probably lead to a pretty large error: spending too much time sorting out complicated problems and not important ones. Conceptually, this was relatively hard to sort out and so we wasted a lot of time explaining and designing elevators et cetera, when really we should have been designing our manufacturing process.
That actually covers the majority of the physics that we had to rely on, so I'm going to stop here for now. I might write a more concept-based post about our design later, but for now the main points of last weekend were:
Lagrangian points
Stability
Angular velocity
Centripetal acceleration
Artificial gravity
Which, frankly, made the entire day much more challenging and enjoyable. The fact that we did end up analysing these facts prevented the day from simply being a sci-fi design competition and gave the whole competition a thoroughly enjoyable aspect which may not have been possible otherwise. And despite our company spending too much time working out the exact layout of bunks for our 50 workers and almost no time at all on the factory (and effectively zero time on asteroid mining- a complete lack of focus to blame for this), we still won our regionals and so I get to do the whole thing again for finals in March! Anyone reading this, I reccomend seeking this competition out as it's great fun and highly rewarding.
