The Magic of Reality

OUR LIVES ARE dominated by two great rhythms, one much slower than the other. The fast one is the daily alternation between dark and light, which repeats every 24 hours, and the slow one is the yearly alternation between winter and summer, which has a repeat time of a little over 365 days. Not surprisingly, both rhythms have spawned myths. The day–night cycle especially is rich in myth because of the dramatic way the sun seems to move from east to west. Several peoples even saw the sun as a golden chariot, driven by a god across the sky.

The aboriginal peoples of Australia were isolated on their island continent for at least 40,000 years, and they have some of the oldest myths in the world. These are mostly set in a mysterious age called the Dreamtime, when the world began and was peopled by animals and a race of giant ancestors. Different tribes of aborigines have different myths of the Dreamtime. This first one comes from a tribe who live in the Flinders Ranges of southern Australia.

During the Dreamtime, two lizards were friends. One was a goanna (the Australian name for a large monitor lizard) and the other a gecko (a delightful little lizard with suction pads on its feet, with which it climbs up vertical surfaces). The friends discovered that some other friends of theirs had been massacred by the ‘sun-woman’ and her pack of yellow dingo dogs.

Furious with the sun-woman, the big goanna hurled his boomerang at her and knocked her out of the sky. The sun vanished over the western horizon and the world was plunged into darkness. The two lizards panicked and tried desperately to knock the sun back into the sky, to restore the light. The goanna took another boomerang and hurled it westwards, to where the sun had disappeared. As you may know, boomerangs are remarkable weapons that come back to the thrower, so the lizards hoped that the boomerang would hook the sun back up into the sky. It didn’t. They then tried throwing boomerangs in all directions, in a vague hope of retrieving the sun. Finally, goanna lizard had only one boomerang left, and in desperation he threw it to the east, the opposite direction from where the sun had disappeared. This time, when it returned, it brought the sun with it. Ever since then, the sun has repeated the same pattern of disappearing in the west and reappearing in the east.

Many myths and legends from all around the world have the same odd feature: a particular incident happens once, and then, for reasons never explained, the same thing goes on happening again and again for ever.

Here’s another aboriginal myth, this time from southeastern Australia. Someone threw the egg of an emu (a sort of Australian ostrich) up into the sky. The sun hatched out of the egg and set fire to a pile of kindling wood which happened (for some reason) to be up there. The sky god noticed that the light was useful to men, and he told his servants to go out every night from then on, to put enough firewood in the sky to light up the next day.

The longer cycle of the seasons is also the subject of myths all around the world. Native North American myths, like many others, often have animal characters. In this one, from the Tahltan people of western Canada, there was a quarrel between Porcupine and Beaver over how long the seasons ought to be. Porcupine wanted winter to last five months, so he held up his five fingers. But Beaver wanted winter to last for more months than that – the number of grooves in his tail. Porcupine was angry and insisted on an even shorter winter. He dramatically bit off his thumb and held up the remaining four fingers. And ever since then winter has lasted four months.

I find this a rather disappointing myth, because it already assumes that there will be a winter and summer, and explains only how many months each will last. The Greek myth of Persephone is better in this respect at least.

Persephone was the daughter of the chief god Zeus. Her mother was Demeter, fertility goddess of the Earth and the harvest. Persephone was greatly loved by Demeter, whom she helped in looking after the crops. But Hades, god of the underworld, home of the dead, loved Persephone too. One day, when she was playing in a flowery meadow, a great chasm opened up and Hades appeared from below in his chariot; seizing Persephone, he carried her down and made her the queen of his dark, underground kingdom. Demeter was so grief-stricken at the loss of her beloved daughter that she stopped the plants growing, and people began to starve. Eventually Zeus sent Hermes, the gods’ messenger, down to the underworld to fetch Persephone back up to the land of the living and the light. Unfortunately, it turned out that Persephone had eaten six pomegranate seeds while in the underworld, and this meant (by the kind of logic we have become used to where myths are concerned) that she had to go back to the underworld for six months (one for each pomegranate seed) in every year. So Persephone lives above ground for part of the year, beginning in the spring and continuing through summer. During this time, plants flourish and all is merry. But during the winter, when she has to return to Hades because she ate those pesky pomegranate seeds, the ground is cold and barren and nothing grows.

What really changes day to night, winter to summer?

Whenever things change rhythmically with great precision, scientists suspect that either something is swinging like a pendulum or something is rotating: going round and round. In the case of our daily and seasonal rhythms, it’s the second. The seasonal rhythm is explained by the yearly orbiting of the Earth around the sun, at a distance of about 93 million miles. And the daily rhythm is explained by the Earth’s spinning round and round like a top.

The illusion that the sun moves across the sky is just that – an illusion. It’s the illusion of relative movement. You will have met the same kind of illusion often enough. You are in a train, standing at a station next to another train. Suddenly you seem to start ‘moving’. But then you realize that you aren’t actually moving at all. It is the second train that is moving, in the opposite direction. I remember being intrigued by the illusion the first time I travelled in a train. (I must have been very young, because I also remember another thing I got wrong on that first train journey. While we were waiting on the platform, my parents kept saying things like ‘Our train will be coming soon’ and ‘Here comes our train’, and then ‘This is our train now’. I was thrilled to get on it because this was our train. I walked up and down the corridor, marvelling at everything, and very proud because I thought we owned every bit of it.)

The illusion of relative movement works the other way, too. You think the other train has moved, only to discover that it is your own train that is moving. It can be hard to tell the difference between apparent movement and real movement. It’s easy if your train starts with a jolt, of course, but not if your train moves very smoothly. When your train overtakes a slightly slower train, you can sometimes fool yourself into thinking your train is still and the other train is moving slowly backwards.

It’s the same with the sun and the Earth. The sun is not really moving across our sky from east to west. What is really happening is that the Earth, like almost everything in the universe (including the sun itself, by the way, but we can ignore that), is spinning round and round. Technically we say the Earth is spinning on its ‘axis’: you can think of the axis as a bit like an axle running right through the globe from North Pole to South Pole. The sun stays almost still relative to the Earth (not relative to other things in the universe, but I am just going to write about how it seems to us here, on Earth). We spin too smoothly to feel the movement, and the air we breathe spins with us. If it didn’t, we would feel it as a mighty rushing wind, because we spin at a thousand miles an hour. At least, that is the spin speed at the equator; obviously we spin more slowly as we approach the North or South Pole because the ground we’re standing on has less far to go to complete a circuit round the axis. Since we can’t feel the spinning of the planet, and the air spins with us, it’s like the case of the two trains. The only way we can tell we are moving is to look at objects that are not spinning with us: objects like the stars and the sun. What we see is the relative movement, and – just as with the trains – it looks as though we are standing still and the stars and the sun are moving across our sky.

A famous thinker called Wittgenstein once asked a friend and pupil called Elizabeth Anscombe,

‘Why do people say it was natural to think that the sun went round the Earth rather than that the Earth turned on its axis?’

Miss Anscombe answered,

‘I suppose because it looked as if the sun went round the Earth.’

‘Well,’ Wittgenstein replied, ‘what would it have looked like if it had looked as if the Earth turned on its axis?’

You try and answer that!

If the Earth is spinning at a thousand miles an hour, why, when we jump straight up in the air, don’t we come down in a different place? Well, when you are on a train travelling at 100 mph, you can jump up in the air and you still land in the same place on the train. You can think of yourself as being hurled forwards by the train as you jump, but it doesn’t feel like that because everything else is moving forwards at the same rate. You can throw a ball straight up on a train and it comes straight down again. You can play a perfectly good game of ping-pong on a train, so long as it is travelling smoothly and not accelerating or decelerating or going fast around a corner. (But only in an enclosed carriage. If you tried to play ping-pong on an open truck the ball would blow away. This is because the air comes with you in an enclosed carriage, but not when you are standing on an open truck.) When you are travelling at a steady rate in an enclosed railway carriage, no matter how fast, you might as well be standing stock still as far as ping-pong, or anything else that happens on the train, is concerned. However, if the train is speeding up (or slowing down), and you jump up in the air, you will come down in a different place! And a game of ping-pong on an accelerating or decelerating or turning train would be a strange game, even though the air inside the carriage is dead still relative to the carriage. We’ll come back to this later, in connection with what it is like when you throw things about in an orbiting space station.

Working round the clock – and the calendar

Night gives way to day, and day gives way to night, as the part of the world we happen to be standing on spins to face the sun, or spins into the shade. But almost as dramatic, at least for those of us who live far from the equator, is the seasonal change from short nights and long, hot days in summer to long nights and short, cold days in winter.

The difference between night and day is dramatic – so dramatic that most species of animal can thrive either in the day or in the night but not both. They usually sleep during their ‘off’ period. Humans and most birds sleep by night and work at the business of living during the day. Hedgehogs and jaguars and many other mammals work by night and sleep by day.

In the same way, animals have different ways of coping with the change between winter and summer. Lots of mammals grow a thick, shaggy coat for the winter, then shed it in spring. Many birds, and mammals too, migrate, sometimes huge distances, to spend the winter closer to the equator, then migrate back to the high latitudes (the far north or far south) for the summer, where the long days and short nights provide bumper feeding. A seabird called the Arctic tern carries this to an extreme. Arctic terns spend the northern summer in the Arctic. Then, in the northern autumn, they migrate south – but they don’t stop in the tropics, they go all the way to the Antarctic. Books sometimes describe the Antarctic as the ‘wintering grounds’ of the Arctic tern, but of course that’s nonsense: by the time they get to the Antarctic it is the southern summer. The Arctic tern migrates so far that it gets two summers: it has no ‘wintering grounds’ because it has no winter. I’m reminded of the joking remark of a friend of mine who lived in England during the summer, and went to tropical Africa to ‘tough out the winter’!

Another way some animals avoid the winter is to sleep through it. It’s called ‘hibernation’, from hibernus, the Latin word for ‘wintry’. Bears and ground squirrels are among the many mammals, and quite a lot of other kinds of animals, that hibernate. Some animals sleep continuously through the whole winter; some sleep for most of the time, occasionally stirring into sluggish activity and then sleeping again. Usually their body temperature drops dramatically during hibernation and everything inside them slows down almost to a stop: their internal engines just barely tick over. There’s even a frog in Alaska which goes so far as to freeze solid in a block of ice, thawing out and coming to life again in the spring.

Even those animals, like us, that don’t hibernate or migrate to avoid the winter have to adapt to the changing seasons. Leaves sprout in spring and fall in autumn (which is why it’s called the ‘fall’ in America), so trees that are a lush green in summer become gaunt and bare in winter. Lambs are born in spring, so they get the benefit of warm temperatures and new grass as they are growing. We may not grow long, woolly coats in winter, but we often wear them.

So we can’t ignore the changing seasons, but do we understand them? Many people don’t. There are even some people who don’t understand that the Earth takes a year to orbit the sun – indeed, that’s what a year is! According to a poll, 19 per cent of British people think it takes a month, and similar percentages have been found in other European countries.

Even among those who understand what a year means, there are many who think the Earth is closer to the sun in summer, more distant in winter. Tell that to an Australian, barbecuing Christmas dinner in a bikini on a baking hot beach! The moment you remember that in the southern hemisphere December is midsummer and June is midwinter, you realize that the seasons can’t be caused by changes in how close the Earth is to the sun. There has to be another explanation.

We can’t get very far with that explanation until we have looked at what makes heavenly bodies orbit other heavenly bodies in the first place. So that’s what we’ll do next.

Into orbit

Why do the planets stay in orbit around the sun? Why does anything stay in orbit around anything else? This was first understood in the seventeenth century by Sir Isaac Newton, one of the greatest scientists who ever lived. Newton showed that all orbits were controlled by gravity – the same force of gravity that pulls falling apples towards the ground, but on a larger scale. (Alas, the story that Newton got the idea when an apple bounced off his head is probably not really true.)

Newton imagined a cannon on top of a very high mountain, with its barrel pointing horizontally out to sea (the mountain is on the coast). Each ball it fires seems to start off moving horizontally, but at the same time it is falling towards the sea. The combination of motion out over the sea and falling towards the sea results in a graceful downward curve, culminating in a splash. It is important to understand that the ball is falling all the time, even on the earlier, flatter part of the curve. It’s not that it travels flat horizontally for a while, then suddenly changes its mind like a cartoon character who realizes he ought to be falling and therefore starts doing so!

The cannonball starts falling the moment it leaves the gun, but you don’t see the falling as downward motion because the ball is moving (nearly) horizontally as well, and quite fast.

Now let’s make our cannon bigger and stronger, so that the cannonball travels many miles before it finally splashes into the sea. There is still a downward curve, but it’s a very gradual, very ‘flat’ curve. The direction of travel is pretty nearly horizontal for quite a lot of the way, but nevertheless it is still falling the whole time.

Let’s carry on imagining a bigger and bigger cannon, more and more powerful: so powerful that the ball travels a really long way before it goes into the sea. Now the curvature of the Earth starts to make itself felt. The ball is still ‘falling’ the whole time, but because the planet’s surface is curved, ‘horizontal’ now starts to mean something a bit odd. The cannonball still follows a graceful curve, as before. But as it slowly curves towards the sea, the sea curves away from it because the planet is round. So it takes even longer for the cannonball finally to splash down into the sea. It is still falling all the time, but it is falling around the planet.

You can see the way the argument is going. We now imagine a cannon so powerful that the ball keeps going all the way around the Earth till it arrives back where it started. It is still ‘falling’, but the curve of its fall is matched by the curvature of the Earth so that it goes right round the planet without getting any closer to the sea. It is now in orbit and it will keep on orbiting the Earth for an indefinite time, assuming that there is no air resistance to slow it down (which in reality there would be). It will still be ‘falling’, but the graceful curve of its prolonged fall will go all around the Earth, and around again and again. It will behave just like a miniature moon. In fact, that is what satellites are – artificial ‘moons’. They are all ‘falling’ but they never actually come down. The ones that are used for relaying long-distance telephone calls or television signals are in a special orbit called a geostationary orbit. This means that the rate at which they go around the Earth has been cunningly arranged so that it is exactly the same as the rate at which the Earth spins on its own axis: that is, they orbit the Earth once every 24 hours. This means, if you think about it, that they are always hovering above exactly the same spot on the Earth’s surface. That is why you can aim your satellite dish precisely at the particular satellite that is beaming down the television signal.

When an object, such as a space station, is in orbit, it is ‘falling’ the whole time, and all the objects in the space station, whether we think of them as light or heavy, are falling at the same rate. This is a good place to stop a moment and explain the difference between mass and weight, as I promised to do back in the previous chapter.

All objects in an orbiting space station are weightless. But they are not massless. Their mass, as we saw in that chapter, depends on the number of protons and neutrons they contain. Weight is the pull of gravity on your mass. On Earth we can use weight to measure mass because the pull is (more or less) the same everywhere. But because more massive planets have stronger gravity, your weight changes depending which planet you are on, whereas your mass stays the same wherever you are – even if you are completely weightless in a space station in orbit. You’d be weightless on the space station because you and the weighing machine would both be ‘falling’ at the same rate (in what is called ‘free fall’); so your feet would exert no pressure on the weighing machine, which would therefore register you as weightless.

But although you’d be weightless, you’d be far from massless. If you jumped vigorously away from the ‘floor’ of the space station, you’d shoot towards the ‘ceiling’ (it wouldn’t be obvious which was floor and which ceiling!) and, no matter how far away the ceiling was, you’d bang your head and it would hurt, just as if you had fallen on your head. And everything else in the space station would still have its own mass likewise. If you had a cannonball in the cabin with you, it would float about weightlessly, which might make you think it was light like a beach ball of the same size. But if you tried to throw it across the cabin, you’d soon know that it wasn’t light like a beach ball. It would be hard work to throw it, and you might find yourself shooting backwards in the opposite direction if you tried. The cannonball would feel heavy, even though it would show no special tendency to go ‘downwards’ towards the floor of the space station. If you succeeded in throwing the cannonball across the room, it would behave like any heavy object when it hit something in its path, and it would not be good if it hit one of your fellow astronauts on the head, either directly or after bouncing off the wall. If it hit another cannonball, the two would bounce off each other with a proper ‘heavy’ feel, unlike, say, a pair of ping-pong balls, which would also bounce off each other but lightly. I hope that gives you a feel for the difference between weight and mass. In the space station, a cannon ball has much more mass than a balloon, although both have the same weight – zero.

Eggs, ellipses and escaping gravity

Let’s go back to our cannon on the mountain-top, and make it more powerful still. What will happen? Well, now we need to acquaint ourselves with the discovery of the great German scientist Johannes Kepler, who lived just before Newton. Kepler showed that the graceful curve by which things orbit other things in space is not really a circle but something known to mathematicians since ancient Greek times as an ‘ellipse’. An ellipse is sort of egg-shaped (only ‘sort of’: eggs are not perfect ellipses). A circle is a special case of an ellipse; think of a very blunt egg, an egg so short and squat that it looks like a ping-pong ball.

There’s an easy way to draw an ellipse, while at the same time convincing yourself that a circle is a special case of an ellipse. Take a piece of string and make it into a loop by tying the ends together, in as neat and small a knot as you can. Now stick a pin in a pad of paper, loop the string around the pin, stick a pencil through the other end of the loop, pull it tight and draw all around the pin with the string loop at full stretch. You’ll draw a circle, of course.

Next, take a second pin and stick it in the pad, right next to the first pin so that they are touching. You’ll still draw a circle because the two pins are so close together that they count as a single pin. But now here’s the interesting part. Move the pins apart a few inches. Now when you draw with the string at full stretch, the shape you produce will not be a circle, it will be an ‘egg-shaped’ ellipse. The further apart you place the two pins, the narrower the ellipse will be. The closer you place the two pins to each other, the wider – the more circular – the ellipse will be until, when the two pins become one pin, the ellipse will be a circle – the special case.

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.