Terry Pratchett - The Science of Discworld

by Terry Pratchett

  Right... all that is what a theory of the origins of the solar sys­tem has to explain. It was all a lot easier when we thought there were six planets, plus the Sun and the Moon, and that was it. As for the solar system being an act of special creation by a supernatural being - why would any self-respecting supernatural being make the thing so complicated?

  Because it makes itself complicated - that’s why. We now think that the solar system was formed as a complete package, starting from quite complicated ingredients. But it us took a while to realize this.

  The first theory of planetary formation that makes any kind of sense by modern standards was thought up by the great German philosopher Immanuel Kant about 250 years ago. Kant envisaged it all starting as a vast cloud of matter - big lumps, small lumps, dust, gas ­which attracted each other gravitationally and clumped together.

  About 40 years later the French mathematician Pierre-Simon de Laplace came up with an alternative theory of enormous intrinsic beauty, whose sole flaw is that it doesn’t actually work. Laplace thought that the Sun formed before the planets did, perhaps by some cosmic aggregation process like Kant’s. However, that ancient Sun was much bigger than today’s, because it hadn’t fully collected together, and the outer fringes of its atmosphere extended well beyond what is now the orbit of Pluto. Like the wizards of Unseen University, Lapkce thought of the Sun as a gigantic fire whose fuel must be slowly burning away. As the Sun aged, it would cool down. Cool gas contracts, so the Sun would shrink.

  Now comes a neat peculiarity of moving bodies, a consequence of another of Newton’s laws, the Law(s) of Motion. Associated with any spinning body is a quantity called ’angular momentum’ - a combination of how much mass it contains, how fast it is spinning, and how far out from the centre the spinning takes place. According to Newton, angular momentum is conserved

  -it can be redistrib­uted, but it neither goes away norappears of its own accord. If a spinning body contracts, but the rate of spin doesn’t change, angu­lar momentum will be lost: therefore the rate of spin must increase to compensate. This is how ice skaters do rapid spins: they start with a slow spin, arms extended, and then bring their arms in close to their body. Moreover, spinning matter experiences a force, cen­trifugal force, which seems to pull it outwards, away from its centre.

  Laplace wondered whether centrifugal force acting on a spin­ning gascloud might throw off a belt of gas round the equator. He calculated that this ought to happen whenever the gravitational force attracting that belt towards the centre was equal to the cen­trifugal force trying to fling it away. This process would happen not once, but several times, as the gas continued to contract

  -so the shrinking Sun would surround itself with aseries of rings of mate­rial, all lying in the same plane as the Sun’s equator. Now suppose that each belt coalesced into a single body ... Planets!

  What Laplace’s theory got right, but Kant’s did not, was that the planets lie roughly in a plane and they all rotate round the Sun in the same direction that the Sun spins. As a bonus, something rather similar might have occurred while those belts were coalescing into planets, in which case the motion of satellites is explained as well.

  It’s not hard to combine the best features of Kant’s and Laplace’s theories, and this combination satisfied scientists for about a cen­tury. However, it slowly became clear that our solar system is far more unruly than either Kant or Laplace had recognized. Asteroids have wild orbits, and some satellites revolve the wrong way. The Sun contains 99% of the solar system’s mass, but the planets pos­sess 99% of its angular momentum: either the Sun is rotating too slowly or the planets are revolving too quickly.

  As the twentieth century opened, these deficiencies of the Laplacian theory became too great for astronomers to bear, and sev­eral people independently came up with the idea that a star developed a solar system when it made a close encounter with another star. As the two stars whizzed past each other, the gravita­tional attraction from one of them was supposed to draw out a long cigar-shaped blob of matter from the other, which then condensed into planets. The advantage of the cigar shape was that it was thin at the ends and thick at the middle, just as the planets are small close to the Sun or out by Pluto, but big in the middle where Jupiter and Saturn live. Mind you, it was never entirely clear why the blob had to be cigar-shaped ...

  One important feature of this theory was the implication that solar systems are rather uncommon, because stars are quite thinly scattered and seldom get close enough together to share a mutual cigar. If you were the sort of person who’d be comforted by the idea that human beings are unique in the universe, then this was a rather appealing suggestion: if planets were rare, then inhabited planets would be rarer still If you were the sort of person who preferred to think that the Earth isn’t especially unusual, and neither are its life-forms, then the cigar theory definitely put a crimp on the imagination.

  By the middle of the twentieth century, the shared-cigar theory had turned out to be even less likely than the Kant-Laplace theory. If you rip a lot of hot gas from the atmosphere of a star, it doesn’t con­dense into planets ­it disperses into the unfathomable depths of interstellar space like a drop of ink in a raging ocean. But by then, astronomers were getting a much clearer idea of how stars origi­nated, and it was becoming clear that planets must be created by the same processes that produce the stars, A solar system is not a Sun that later acquires some tiny companions: it all comes as one pack­age, right from the start. That package is a disc - the nearest thing in our universe (so far as we know) to Discworld. But the disc begins as a cloud and eventually turns into a lot of balls (Stibbons’s Third Rule).

  Before the disc formed, the solar system and the Sun started out as a random portion of a cloud of interstellar gas and dust. Random jigglings triggered a collapse of the dustcloud, with everything heading for roughly - but not exactly - the same central point. All it takes to start such a collapse is a concentration of matter some­where, whose gravity then pulls more matter towards it: random jigglings will produce such a concentration if you wait long enough. Once the process has started, it is surprisingly rapid, taking about ten million years from start to finish. At first the collapsing cloud is roughly spherical. However, it is being carried along by the rotation of the entire galaxy, so its outer edge (relative to the centre of the galaxy) moves more slowly than its inner edge. Conservation of angular momentum tells us that as the cloud collapses it must start spinning, and the more it collapses, the faster it spins. As its rate of spin increases, the cloud flattens out into a rough disc.

  More careful calculations show that near the middle this disc thickens out into a dense blob, and most of the matter ends up in the blob. The blob condenses further, its gravitational energy gets traded for heat energy, and its temperature goes up fast. When the temperature rises enough, nuclear reactions are ignited: the blob has become a star. While this is happening, the material in the disk undergoes random collisions, just as Kant imagined, and coalesces in a not terribly ordered way. Some clumps get shoved into wildly eccentric orbits, or swung out of the plane of the disc; most clumps, however, are better behaved and turn into decent, sensible planets. A miniature version of the self-same processes can equip most of those planets with satellites.

  The chemistry fits, too. Near the Sun, those incipient planets get very hot - too hot for solid water to form. Further out - around the orbit of Jupiter for a dustcloud suitable for making our Sun and solar system - water can freeze into solid ice. This distinction is important for the chemical composition of the planets, and we can see the main outlines if we focus on just three elements: hydrogen, oxygen, and silicon. Hydrogen and oxygen happen to be the two most abundant elements in the universe, apart from helium which doesn’t undergo chemical reactions. Silicon is less abundant but still common. When silicon and oxygen combine together, you get silicates - rocks. But even if the oxygen can mop up all the available silicon, some 96% of the oxygen is still unattached, and it com
bines with hydrogen to make water. There is so much hydrogen - a thou­sand times as much as oxygen - that virtually all of the oxygen that doesn’t go into rocks gets locked away in water. So by far the most common compound in the condensing disc is water.

  Close to the star, that water is liquid, even vapour, but out at Jovian distances, it’s solid ice. You can pick up a lot of solid mass if you’re condensing in a region where ice can form. So the planets there are bigger, and (at least to begin with) they are icy Nearer the star, the planets are smaller, and rocky. But now the big guys can parky their initial weight advantage into an even bigger one. Anything that is ten times the mass of the Earth, or greater, can attract and retain the two most abundant elements of the disc, hydrogen and helium. So the big balls soak up large amount of extra mass in the form of these two gases. They can also retain com­pounds like methane and ammonia, which are volatile gases closer to the star.

  This theory explains rather a lot. It gets all the main features of the solar system pretty much right. It allows for the odd exceptional motion, but not too many. It agrees with observations of condens­ing gas clouds in distant regions of space. It may not be perfect, and some special pleading might be necessary to explain odd things like Pluto, but most of the important features click neatly into place.

  The future of the solar system is at least as interesting as its past. The picture of the solar system that emerged from the ideas of Newton and his contemporaries was very much that of a clockwork universe - a celestial machine that, once set ticking, would continue to follow some simple mathematical rules and continue ticking mer­rily away forever. They even built celestial machines, called orreries, with lots and lots of cogwheels, in which little brass planets with ivory moons went round and round when you turned a handle.

  We now know that the cosmic clockwork can go haywire. It won’t happen quickly, but there may be some big changes to the solar system on the way. The underlying reason is chaos - chaos in the sense of ’chaos theory’, with all those fancy multicoloured ’frac­tal’ things, a rapidly expanding area of mathematics which is invading all of the other sciences. Chaos teaches us that simple rules need not lead to simple behaviour - something that Ponder Stibbons and the other wizards are in the process of discovering. In fact, simple rules can lead to behaviour that in certain respects has distinct elements of randomness. Chaotic systems start out behav­ing predictably, but after you cross some ’prediction horizon’ all predictions fail. Weather is chaotic, with a prediction horizon of about four days. The solar system, we now know, is chaotic, with a prediction horizon of tens of millions of years. For example, we can’t be sure which side of the Sun Pluto will be in a hundred mil­lion years’ time. It will be in the same orbit, but its position in that orbit is completely uncertain.

  We know this because of some mathematical work that was done, in part, with an orrery - but this was a ’digital orrery’, a custom-built computer that could do celestial mechanics very fast. The digital orrery was developed by Jack Wisdom’s research group, which in competition with its rival headed by Jaques Laskar - has been extending our knowledge of the solar system’s future. Even though a chaotic system is unpredictable in the long run, you can make a whole series of independent attempts at predicting it and then see what they agree about. According to the mathematics, you can be pretty sure those things are right.

  One of the most striking results is that the solar system is due to lose a planet. About a billion years from now, Mercury will move outwards from the Sun until it crosses the orbit of Venus. At that point, a close encounter between Venus and Mercury will fling one or the other, possibly both, out of the solar system altogether -unless they hit something on the way, which is highly unlikely, but possible. It might even be the Earth, or the passing Venus might join with us in a cosmic dance whose end result is the Earth being flung out of the solar system. The details are unpredictable, but the gen­eral scenario is very likely.

  This means that we’ve got the wrong picture of the solar system. On a human timescale it’s a very simple place, in which nothing much changes. On its own timescale, hundreds of millions of years, it’s full of drama and excitement, with planets roaring all over the place, whirling around each other, and dragging each other out of orbit in a mad gravitational dance.

  This is vaguely reminiscent of Worlds in Collision, a book pub­lished in 1950 by Immanuel Velikovsky, who believed that a giant comet was once spat out by Jupiter, passed close to the Earth twice, had a love affair with Mars (giving rise to a brood of baby comets), and finally retired to live in peace as Venus. Along the way it gave rise to many strange effects that became stories in the Bible. Velikovsky was right about one thing: the orbits of the planets are not fixed forever. He wasn’t right about much else.

  Do other solar systems encircle distant stars, or are we unique? Until a few years ago there was a lot of argument about this ques­tion, but no hard evidence. Most scientists, if they had to bet, would have backed the existence of other solar systems, because the collapsing dustcloud mechanism could easily get going almost any­where there’s cosmic dust - and there are a hundred billion stars in our own galaxy, let alone the billions upon billions of others in the universe, all of which once were cosmic dust. But that’s only indi­rect evidence. Now the position is much clearer.

  Characteristically, however, the story involves at least one false start, and a critical re-examination of evidence that at first looked rather convincing.

  In 1967 Jocelyn Bell, a graduate student at the University of Cambridge, was working for a doctorate under the direction of Anthony Hewish. Their field was radio astronomy Like light, radio is an electromagnetic wave, and like light, radio waves can be emit­ted by stars. Those radio waves can be detected using parabolic dish receivers - today’s satellite TV dishes are a close relative - rather misleadingly called ’radio telescopes’, even though they work on very different principles from normal optical telescopes. If we look at the sky in the radio part of the electromagnetic spectrum, we can often ’see’ things that are not apparent using ordinary visible light. This should be no surprise: for example military snipers can ’see in the dark’ using infra-red waves - detecting things by the heat they emit. The technology in those days wasn’t terribly slick, and the radio signals were recorded on long rolls of paper using automatic pens that drew wiggly curves in good old-fashioned ink. Bell was given the task of looking for interesting things on the paper charts - carefully scanning about 400 feet of chart per week. What she found was very strange - a signal that pulsated about thirty times per second. Hewish was sceptical, suspecting that the signal was somehow generated by their measuring instruments, but Bell was convinced it was genuine. She searched through three miles of pre­vious charts and found several earlier instances of the same signal, which proved she was right. Something out there was emitting the radio equivalent of a reverberating whistle. The object responsible was named a ’pulsar’ - a pulsating starlike object.

  What could these strange things be? Some people suggested they were radio signals from an alien civilization, but all attempts to extract the alien equivalent of The Jerry Springer Show failed (which was possibly just as well). There seemed to be no structured messages hidden in the signals. In fact, what they are now believed to be is even stranger than an alien TV programme. Pulsars are thought to be neutron stars - stars composed of highly degenerate matter containing only neutrons, usually a mere 12 miles (20 km) in diameter. Recall that neutron stars are incredibly dense, formed when a larger star undergoes gravitational collapse. That initial star, as we have seen, will be spinning, and because of conservation of angular momentum, the resulting neutron star has to spin a lot faster In fact, it typically spins through about thirty complete revolutions every second. For a star, that’s pretty speedy. Only a tiny star like a neutron star can do it: if an ordinary star were to revolve that fast, its surface would have to be travelling faster than light, which wouldn’t greatly please Einstein. (More realis
tically, a normal star would be torn apart at much lower speeds.) But a neutron star is small, and its angular momentum is comparatively large, and pirou­etting thirty times a second is no problem at all.

  For a helpful analogy, contemplate our own Earth. Like a pulsar, it spins on an axis. Like a pulsar, it has a magnetic field. The mag­netic field has an axis too, but it’s different from the axis of rotation - that’s why magnetic north is not the same as true north. There’s no good reason for magnetic north to be the same as true north on a pulsar, either. And if it isn’t, that magnetic axis whips round thirty times every second. A rapidly spinning magnetic field emits radia­tion, known as synchrotron radiation - and it emits it in two narrow beams which point along the magnetic axis. In short, a neutron star projects twin radio beams like the spinning gadgetry on top of a ter­restrial lighthouse. So if you look at a neutron star in radio light, you see a bright flash as the beam points towards you, and then vir­tually nothing until the beam comes round again. Every second, you see thirty flashes. That’s what Bell had noticed.

  If you’re a living creature of remotely orthodox construction, you definitely do not want your star to be a pulsar. Synchrotron radiation is spread over a wide range of wavelengths, from visible light to x-rays, and x-rays can seriously damage the health of any creature of remotely orthodox construction. But no astronomer ever seriously suspected that pulsars might have planets, anyway. If a big star collapses down to an incredibly dense neutron star, surely it will gobble up all the odd bits of matter hanging around nearby. Won’t it?

  Perhaps not. In 1991 Matthew Bailes announced that he had detected a planet circling the pulsar PSR 1829-10, with the same mass as Uranus, and lying at a distance similar to that of Venus from the Sun. The known pulsars are much too far away for us to see planets directly - indeed all stars, even the nearest ones, are too far away for us to see planets directly. However, you can spot a star that has planets by watching it wiggle as it walks. Stars don’t sit motion­less in space - they generally seem to be heading somewhere, presumably as the result of the gravitational attraction of the rest of the universe, which is lumpy enough to pull different stars in dif­ferent directions. Most stars move, near enough, in straight lines. A star with planets, though, is like someone with a dancing partner. As the planets whirl round the star, the star wobbles from side to side. That makes its path across the sky slightly wiggly. Now, if a big fat dancer whirls a tiny feather of a partner around, the fat one hardly moves at all, but if the two partners have equal weight, they both revolve round a common centre. By observing the shape of the wig­gles, you can estimate how massive any encircling planets are, and how close to the star their orbits are.