The Magic of Reality Read online

  Now that we have met the ellipse we can go back to our super-powerful cannon. It has already fired a cannonball into an orbit which we assumed to be nearly circular. If we now make it more powerful still, what happens is that the orbit becomes a more ‘stretched’, less circular ellipse. This is called an ‘eccentric’ orbit. Our cannon ball zooms quite a long way from the Earth, then turns around and falls back. Earth is one of the two ‘pins’. The other ‘pin’ doesn’t really exist as a solid object, but you can think of it as an imaginary pin out there in space. The imaginary pin helps to make the mathematics understandable for some people but if it confuses you just forget about it. The important thing to realize is that the Earth is not in the centre of the ‘egg’. The orbit stretches much further away from the Earth on one side (the side of the ‘imaginary pin’) than on the other (the side where the Earth itself is the ‘pin’).

  We go on making our cannon more and more powerful. The cannonball is now travelling a long, long way from the Earth and is only just pulled back around to fall back towards Earth. The ellipse is now very long and stretched indeed. And there will eventually come a point where it ceases to be an ellipse altogether: we fire the cannonball even faster, and now the extra speed just pushes it beyond the point of no return, where the Earth’s gravity can’t summon it back. It has reached ‘escape velocity’ and disappears for ever (or until captured by the gravity of another body, such as the sun).

  Our increasingly powerful cannon has illustrated all the stages towards and beyond the establishment of an orbit. First the ball just flops into the sea. Then, as we fire successive balls with increasing force, the curve of their travel becomes increasingly horizontal until the ball reaches the necessary speed to go into a near-circular orbit (remember that a circle is a special case of an ellipse). Then, as the speed of firing increases more and more, the orbit becomes less circular and more elongated, more obviously elliptical. Finally, the ‘ellipse’ becomes so elongated that it ceases to be an ellipse at all: the ball reaches escape velocity and disappears altogether.

  The Earth’s orbit around the sun is technically an ellipse, but it is very nearly the special case of a circle. The same is true of all the other planets except Pluto (which is not considered a planet nowadays anyway). A comet, on the other hand, has an orbit like a very long, thin egg. The ‘pins’ that you use to draw its ellipse are very far apart.

  One of the two ‘pins’ for a comet is the sun. Once again, the other ‘pin’ is not a real object in space: you just have to imagine it. When a comet is at its furthest distance from the sun (called ‘aphelion’, pronounced app-heeleeon) it travels at its slowest rate. It is in free fall the whole time, but some of the time it is falling away from the sun, rather than towards it. Slowly it turns the corner at aphelion, then it falls in the direction of the sun, falling faster and faster until it zooms round the sun (the other ‘pin’) and reaching its highest speed when it is at its closest point to the sun, called perihelion. (‘Perihelion’ and ‘aphelion’ come from the name of the Greek sun god Helios; peri is the Greek for ‘near’ and apo means ‘far’.) The comet whizzes fast around the sun at perihelion, and carries on away from it at high speed on the other side of perihelion. After slinging itself around the sun, the comet gradually loses speed as it falls away from the sun all the way to aphelion, where it is at its slowest; and the cycle keeps repeating itself over and over again.

  Space engineers use something called the slingshot effect to improve the fuel economy of their rockets. The Cassini space probe, which was designed to visit the distant planet Saturn, travelled there by what seems like a roundabout route, but was actually cunningly planned to exploit the slingshot effect. Using far less rocket fuel than would have been needed to fly directly to Saturn, Cassini borrowed from the gravity and orbital movement of three planets on the way: Venus (twice), then a return swing around Earth, then a final mighty heave from Jupiter. In each case it fell around the planet like a comet, gaining speed by hanging onto its gravitational coat tails as the planet whizzed around the sun. These four slingshot boosts hurled Cassini out towards the Saturn system of rings and 62 moons, from where it has been sending back stunning pictures ever since.

  Most of the planets, as I said, orbit the sun in near-circular ellipses. Pluto is unusual, not just in being too small to be called a planet any more, but also in having a noticeably eccentric orbit. Much of the time it is outside the orbit of Neptune, but at perihelion it swoops inside and is actually closer to the sun than is Neptune, with its near circular orbit. Even the orbit of Pluto, however, is nothing like as eccentric as that of a comet. The most famous one, Halley’s Comet, becomes visible to us only near perihelion, when it is closest to the sun and reflects the sun’s light. Its elliptical orbit takes it far, far away, and it returns to our neighbourhood only every 75 to 76 years. I saw it in 1986 and showed it to my baby daughter Juliet. I whispered in her ear (of course she couldn’t understand what I was saying, but I obstinately whispered it anyway) that I would never see it again, but that she would have another chance when it returned in 2061.

  The ‘tail’ of a comet, by the way, is a train of dust, but it is not streaming out behind the head of the comet as we might think. Instead, it is ‘blown’ by a stream of particles coming from the sun, which we call the solar wind. So the tail of the comet always points away from the sun, no matter which way the comet is travelling. There’s an exciting proposal, once confined to science fiction stories but now being implemented by Japanese space engineers, to use the solar wind to propel spacecraft equipped with gigantic ‘sails’. Like sailing yachts on the sea using real wind, solar wind space-yachts would theoretically provide a very economical way to travel to distant worlds.

  A sideways look at summer

  Now that we understand orbits, we can go back to the question of why we have winter and summer. Some people, you’ll remember, wrongly think it is because we are closer to the sun in summer and further away in winter. That would be a good explanation if Earth had an orbit like Pluto’s. In fact Pluto’s winter and summer (both very much colder than anything we experience here) are caused in exactly that way.

  The Earth’s orbit, however, is almost circular, so the planet’s closeness to the sun cannot be what causes the changing seasons. For what it is worth, the Earth is actually closest to the sun (perihelion) in January and furthest (aphelion) in July, but the elliptical orbit is so close to circular that it makes no noticeable difference.

  Well then, what does cause the change from winter to summer? Something quite different. The Earth spins on an axis, and the axis is tilted. This tilting is the true reason why we have seasons. Let’s see how it works.

  As I said before, we could think of the axis as an axle, a rod running right through the globe and sticking out at the North Pole and the South Pole. Now think of the orbit of the Earth around the sun as a much larger wheel, with its own axle, this time running through the sun, and sticking out at the sun’s ‘north pole’ and the sun’s ‘south pole’. Those two axles could have been exactly parallel to each other, so that the Earth did not have a ‘tilt’ – in which case the noonday sun would always seem to be directly overhead at the equator, and day and night would be of equal length everywhere. There would be no seasons. The equator would be perpetually hot, and it would become colder and colder the further you moved away from the equator and towards either of the poles. You could get cool by moving away from the equator, but not by waiting for winter because there would be no winter to wait for. No summer, no seasons of any kind.

  In fact, however, the two axles are not parallel. The axle (axis) of the Earth’s own spinning is tilted relative to the axle (axis) of our orbit around the sun. The tilt is not particularly great – about 23.5 degrees. If it were 90 degrees (which is about the tilt of the planet Uranus) the North Pole would be pointing straight towards the sun at one time of year (which we can call the northern midsummer) and straight away from the sun at the northern midwinter. If Earth
were like Uranus, in midsummer the sun would be overhead all the time at the North Pole (there’d be no night there), while it would be icy cold and dark at the South Pole, with no suggestion of day. And vice versa six months later.

  Since our planet is actually tilted at only 23.5 degrees instead of 90 degrees, we are about a quarter of the way from the no seasons extreme of no tilt at all towards the Uranus extreme of near total tilt. This is enough to mean that, as on Uranus, the sun never sets at the Earth’s North Pole in midsummer. It is perpetual day; but, unlike on Uranus, the sun is not overhead. It seems to loop around the sky as the Earth rotates, but it never quite dips below the horizon. That is true throughout the Arctic Circle. If you stood right on the Arctic Circle, say on the north-west tip of Iceland, on midsummer day, you’d see the sun skim along the northern horizon at midnight, but never actually set. Then it would loop around to its highest position (not very high) at midday.

  In northern Scotland, which is a little way outside the Arctic Circle, the midsummer sun dips below the horizon far enough to make a sort of night – but not a very dark night, because the sun is never very far below the horizon.

  So, the tilt of the Earth’s axis explains why we have winter (when the bit of the planet where we are is tilted away from the sun) and summer (when it’s tilted towards the sun), and why we have short days in winter and long days in summer. But does that explain why it is so cold in winter and so hot in summer? Why does the sun feel hotter when it is directly overhead than when it is low, near the horizon? It’s the same sun, so shouldn’t it be equally hot no matter what the angle at which we see it? No.

  You can forget the fact that we are slightly nearer the sun when tilted towards it. That’s an infinitesimal difference (only a few thousand miles) compared to the total distance from the sun (about 93 million miles), and still negligible compared to the difference between the sun’s distance at perihelion and the sun’s distance at aphelion (about 3 million miles). No, what matters is partly the angle at which the sun’s rays hit us, and partly the fact that the days are longer in summer and shorter in winter. It’s that angle that makes the sun feel hotter at midday than in the late afternoon, and it’s that angle that makes it more important to put on sunscreen at midday than in the late afternoon. It’s a combination of the angle and the day length that makes the plants grow more in summer than in winter, with all that follows from that.

  So why does this angle make such a difference? Here’s one way to explain it. Imagine that you are sunbathing at midday in the middle of the summer, and the sun is high overhead. A particular square inch of skin in the middle of your back is being hit by photons (tiny particles of light) at a rate that you could count with a light meter. Now, if you sunbathe at midday in winter, when the sun is relatively low in the sky because of the Earth’s tilt, light reaches the Earth at a shallower, more ‘sideways’ angle: therefore a given number of photons are ‘shared out’ over a larger area of skin. This means that the original square inch of skin gets a smaller share of the available photons than it did at midsummer. What is true of your skin is also true of the leaves of plants, and that really matters because plants use sunlight to make their food.

  Night and day, winter and summer: these are the great alternating rhythms that rule our lives, and the lives of all living creatures except perhaps those that live in the dark, cold depths of the sea. Another set of rhythms that are not so important for us but matter greatly to other creatures, such as those that live on seashores, are the rhythms imposed by the orbiting moon, acting mostly through the tides. Lunar cycles are also the subject of ancient and disturbing myths – of werewolves and vampires, for example. But I must reluctantly leave this subject now and move on to the sun itself.

  6

  WHAT IS

  THE SUN?

  THE SUN IS so dazzlingly bright, so comforting in cold climates, so mercilessly scorching in hot ones, it is no wonder many peoples have worshipped it as a god. Sun worship often goes together with moon worship, and the sun and the moon are frequently regarded as being of opposite sex. The Tiv tribe of Nigeria and other parts of west Africa believe the sun is the son of their high god Awondo, and the moon is Awondo’s daughter. The Barotse tribe of south-east Africa think the sun is the moon’s husband rather than her brother. Myths often treat the sun as male and the moon as female, but it can be the other way around. In the Japanese Shinto religion the sun is the goddess Amaterasu, and the moon is her brother Ogetsuno.

  Those great civilizations that flourished in South and Central America before the Spaniards arrived in the sixteenth century worshipped the sun. The Inca of the Andes believed that the sun and the moon were their ancestors. The Aztecs of Mexico shared many of their gods with older civilizations in the area, such as the Maya. Several of these gods had a connection with the sun, or in some cases were the sun. The Aztec ‘Myth of the Five Suns’ held that there had been four worlds before the present one, each with its own sun. The earlier four worlds were destroyed, one after the other, by catastrophes, often engineered by the gods. The first sun was the god called Black Tezcatlipoca; he fought with his brother, Quetzalcoatl, who knocked him out of the sky with his club. After a period of darkness, with no sun, Quetzalcoatl became the second sun. In his anger, Tezcatlipoca turned all the people into monkeys, whereupon Quetzalcoatl blew all the monkeys away, and then resigned as the second sun.

  The god Tlaloc then became the third sun. Annoyed when Tezcatlipoca stole his wife Xochiquetzal, he sulked and refused to allow any rain to fall, so there was a terrible drought. The people begged and begged for rain, and Tlaloc became so fed up with their begging that he sent down a rain of fire instead. This burned up the world, and the gods had to start all over again.

  The fourth sun was Tlaloc’s new wife, Chalchiuhtlicue. She started out well, but then Tezcatlipoca so upset her that she cried tears of blood for 52 years without stopping. This completely flooded the world, and yet again the gods had to start from scratch. Isn’t it strange, by the way, how exactly myths specify little details? How did the Aztecs decide that she cried for 52 years, not 51 or 53?

  The fifth sun, which the Aztecs believed is the present one that we still see in the sky, was the god Tonatiuh, sometimes known as Huitzilopochtli. His mother, Coatlicue, gave birth to him after being accidentally impregnated by a bundle of feathers. This might sound odd, but such things would have seemed quite normal to people brought up with traditional myths (another Aztec goddess was impregnated by a gourd, which is the dried skin of a fruit like a pumpkin). Coatlicue’s 400 sons were so enraged to find their mother pregnant yet again that they tried to behead her. However, in the nick of time she gave birth to Huitzilopochtli. He was born fully armed and lost no time in killing all of his 400 half-brothers, except a few who escaped ‘to the south’. Huitzilopochtli then assumed his duties as the fifth sun.

  The Aztecs believed that they had to sacrifice human victims to appease the sun god, otherwise he would not rise in the east each morning. Apparently it didn’t occur to them to try the experiment of not making sacrifices, to see whether the sun might, just possibly, rise anyway. The sacrifices themselves were famously gruesome. By the end of the Aztecs’ heyday, when the Spaniards arrived (bringing their own brand of gruesomeness), the sun cult had escalated to a gory climax. It is estimated that between 20,000 and 80,000 humans were sacrificed for the rededication of the Great Temple of Tenochititlan in 1487. Various gifts could be offered to appease the sun god, but what he really liked was human blood, and still-beating human hearts. One of the main purposes of warfare was to collect lots of prisoners of war so that they could be sacrificed, usually by having their hearts cut out. The ceremony normally took place on high ground (to be closer to the sun), for example on top of one of the magnificent pyramids for which the Aztecs, Maya and Inca are famous. Four priests would hold the victim down over the altar, while a fifth priest wielded the knife. He worked as fast as possible to cut the heart out so that it was still beating when
held up to the sun. Meanwhile the heartless and bloody corpse would roll down the slopes of the hill or pyramid to the bottom, where it would be collected up by the old men and then dismembered, often to be eaten in ritual meals.

  We also associate pyramids with another ancient civilization, that of Egypt. The ancient Egyptians, too, were sun-worshippers. One of the greatest of their gods was the sun god Ra.

  An Egyptian legend regarded the curve of the sky as the body of the goddess Nut, arched over the Earth. Every night the goddess swallowed the sun, and then the following morning she gave birth to him again.

  Various peoples, including the ancient Greeks and the Norsemen, had legends about the sun being a chariot driven across the sky. The Greek sun god was called Helios, and he has given his name to various scientific terms associated with the sun, as we saw in Chapter 5.

  In other myths, the sun is not a god but one of the first creations of a god. In the creation myth of the Hebrew tribe of the Middle Eastern desert, the tribal god YHWH created light on the first of his six days of creation – but then, surprisingly, he didn’t create the sun until the fourth day! ‘And God made two great lights: the greater light to rule the day, and the lesser light to rule the night: he made the stars also.’ Where the light came from on the first day, before the sun and stars existed, we are not told.

  It is time to turn to reality, and the true nature of the sun, as borne out by scientific evidence.

  What is the sun, really?

  The sun is a star. It’s no different from lots of other stars, except that we happen to be near it so it looks much bigger and brighter than the others. For the same reason, the sun, unlike any other star, feels hot, damages our eyes if we look straight at it, and burns our skin red if we stay out in it too long. It is not just a little bit nearer than any other star; it is vastly nearer. It is hard to grasp how far away the stars are, how big space is. Actually, it’s more than hard, it’s almost impossible. There’s a lovely book called Earthsearch by John Cassidy, which makes an attempt to grasp it, using a scale model.