Rear Admiraless Josh asks

In The Empire Strikes Back, there’s a bit where the Falcon goes into an asteroid field pursued by a bunch of TIE fighters, and they have to avoid a load of rocks flying around very fast in close proximity. It’s what a lot of people think of asteroid fields as being like, but logically that’s can’t be right, as the rocks would just bash each other into sand over the course of a couple of centuries. So what is the inside of an asteroid field really like? What is the largest thing you can swing around while reasonably expecting not to hit anything?

Ooooh, “rocks just bash each other into sand over the course of a couple of centuries” is so close, and yet so far.

I actually have mentioned collisional evolution before on here but it was rather in passing so you can be forgiven for missing it; in short, the long-term evolution of any belt-type collection of objects is going to be primarily driven by two things:

1)     The average velocity (and hence kinetic energy) of an impacting body in the belt.

2)     The critical energy density required to blow a body in the belt to smithereens without it eventually reforming under its own gravity.

So basically you have to be going fast enough to cause some real damage, and the thing you’re hitting has to be weak enough that that damage will be lasting. As ever, the hardest part about blowing massive objects up in space is that in addition to actually physically destroying the target you have to give most of the resulting fragments enough energy so that they’re accelerated up above the object’s escape velocity. I mostly dealt with the larger type of object in my Ph.D research – dwarf planets and the like – so gravity was Kind Of A Big Deal for them, but… *rummages through paper archive*

This is the result of some computer modelling done in a paper by Durda et al. (1999, Icarus, 135, 431-440.) which attempts to figure out how the strength of asteroids increases with their size. There’s actually a whole bunch of models there but they all follow the same basic behaviour of an initial decrease in the material strength of an asteroid as its size increases (this is because it is easier for cracks to propagate through big bodies than it is through small ones) and then a sudden upswing at around the 1km diameter mark. This is the point at which the object is large enough that its gravitational strength becomes the primary factor working against its destruction, and material strength becomes more or less irrelevant. In other words it doesn’t matter if you’re hitting an object made out of rock or taffeta; if it’s 10km on a side it’s the gravity of the object you’re going to have to overcome, not its material strength.

So how big are the asteroids in the asteroid belt? Obviously their sizes vary, and the overall size distribution looks something like this.

(Taken from this great American novel via a second-hand source because obviously I don’t have sixty-five quid what are you crazy.)

This is the expected power law distribution of any large collection of objects driven by collisional evolution, with the only aberrations being those two small bumps. The interesting thing about the asteroid belt, though, is that this size distribution has remained static over time. That is, if you were to go back in time a couple of million years (this being the timescale over which collisional evolution operates) and take a similar survey of the asteroid belt, the size distribution graph would look much the same, implying that whatever is going on in the asteroid belt has produced a population of bodies which is stable over solar-system timescales.

It was not always thus, of course. The asteroid belt originally had far more mass in it (about one Earth) than it does today (about 0.01 Earth masses), so the population we see in the asteroid belt right now are the stable one percent survivors of whatever happened to eject the other ninety-nine percent. “Whatever happened” is overwhelmingly likely to be the chaotic gravitational interactions, peturbations and resonances of the solar system’s early years. For example, there’s lots of very large, very conspicuous gaps in the asteroid belt at certain orbital radii which are down to resonances with Jupiter amplifying the planet’s gravity and shooting anything unfortunate enough to be found in those gaps out of the solar system. So it’s not just asteroids colliding with each other that can “destroy” them, it’s outside influences as well.

Anyway, that was something of a tangent. The thing to take away from this is that while collisional evolution was a big factor in the initial makeup of the belt, the current population is — more or less — stable and unchanging. With that in mind, what would flying through it in a spacecraft be like? Immensely boring, I suspect; the average distance separating asteroids in the belt is about one million kilometres, although that is a number based on the volume of the belt and the number of asteroids rather than any hard and fast measurements of actual distance separations. Certainly it’s sparsely populated enough that every single interplanetary probe we have sent to explore the outer solar system – Jupiter, Saturn, Uranus, Neptune and Pluto – has made it through without even the faintest glimmering of an incident. A million kilometre gap is quite a large target to aim for, after all, especially when it has more million kilometre gaps on either side. You’d be lucky to see an asteroid at all, let alone the swarms of them seen in Empire Strikes Back.

(Speaking of, I’m fairly confident saying that an asteroid field of the type seen in Empire could never actually happen. The only way you could get so much debris so densely packed is by destroying a planet – which isn’t completely out of the question given the Empire’s Death Star – but if the fragments were produced by that kind of process then they’d all be flying away from a central point at some ridiculous velocity, not just sitting there chilling and occasionally bumping up against their buddies.)

The post Never Tell Me The Odds. appeared first on The Scientific Gamer.