Terry Pratchett - The Science of Discworld I

The most obvious effect of the Moon on the Earth is the tides -a fact that the wizards are stumbling towards. Like most of science, the story of the tides is not entirely straightforward, and only loosely connected to what common sense, left to its own devices, would lead us to expect. The common sense bit is that the Moon's gravity pulls at the Earth, and it pulls more strongly on the bit that is closest to the Moon. When that bit is land, nothing much hap­pens, but when it's water, and more than half our planet's surface is ocean, it can pile up. This explanation is a lie-to-children, and it doesn't agree with what actually happens. It leads us to expect that at any given place on Earth, high tide occurs when the Moon is overhead, or at least at its highest point in the sky. That would lead to one high tide every day, or, allowing for a little complexity in the Earth-Moon system, one high tide every 24 hours 50 minutes.

Actually, high tides occur twice a day, 12 hours and 25 minutes apart. Exactly half the figure.

Not only that: the pull of the Moon's gravity at the surface of the Earth is only one ten millionth of the Earth's surface gravity; the pull of the Sun is about half that. Even when combined together, these two forces are not strong enough to lift masses of water through heights of up to 70 feet (21m)- the biggest tidal move­ment on Earth, occurring in the Bay of Fundy between Nova Scotia and New Brunswick.

An acceptable explanation of the tides eluded humanity until Isaac Newton worked out the law of gravity and did the necessary calculations. His ideas have since been refined and improved, but he had the basics.

For simplicity, ignore everything except the Earth and the Moon, and assume that the Earth is completely made of water. The watery Earth spins on its axis, so it is subjected to centrifugal force and bulges slightly at the equator. Two other forces act on it: the Earth's gravity and the Moon's. The shape that the water takes up in response to these forces depends on the fact that water is a fluid. In normal circumstances, the surface of a standing body of water is horizontal, because if it wasn't, then the fluid on the higher bits would slosh sideways into the lower bits. The same kind of thing happens when there are extra forces acting: the surface of the water settles at right angles to the net direction of the combined forces.

When you work out the details for the three forces we've just mentioned, you find that the water forms an ellipsoid, a shape that is close to a sphere but very slightly elongated. The direction of elongation points towards the Moon. However, the centre of the ellipsoid coincides with the centre of the Earth, so the water 'piles up' on the side furthest from the Moon as well as on the side near­est it. This change of shape is only partly caused by the Moon's gravity 'lifting' the water closest to it. Most of the motion, in fact, is sideways rather than upwards. The sideways forces push more water into some regions of the oceans, and take it away from others. The total effect is tiny, the surface of the sea rises and falls through a distance of 18 inches (half a metre).

The coast, where land meets sea, is what creates the big tidal movements. Most of the water is moving sideways (not up) and its motion is affected by the shape of the coastline. In some places the water flows into a narrowing funnel, and then it piles up much more than it does elsewhere. This is what happens in the Bay of Fundy. This effect is made even bigger because coastal waters are shallow, so the energy of the moving water gets concentrated into a thinner layer, creating bigger and faster movements.

Finally, let's put the sun back. This has the same kind of effect as the Moon, but smaller. When Sun and Moon are aligned, either both on the same side of the Earth, in which case we see a new moon, or both on opposite sides (full moon), their gravitational pulls reinforce each other, leading to so-called 'spring tides' in which high tide is higher than normal and low tide is lower. These have nothing to do with the season Spring. When the Sun and Moon are at right angles as seen from Earth, at half moon, the Sun's pull cancels out part of the Moon's, leading to 'neap tides' with less movement than normal (these presumably have nothing to do with the season Neap ...).

By putting all these effects together, and keeping good records of past tides, it is possible to predict the times of high and low tide, and the amount of vertical movement, anywhere on Earth.

There are similar tidal effects (large) on the Earth's atmosphere, and (small) on the planet's land masses. Tidal effects occur on other bodies in the solar system, and beyond. It is thought that Jupiter's moon lo, whose surface is mostly sulphur and which has numerous active volcanoes, is heated by being 'squeezed' repeatedly by tidal effects from Jupiter.

Another effect of the Moon on the Earth, discovered in the mid-'90s by Jaques Laskar, is to stabilize the Earth's axis. The Earth spins like a top, and at any given moment there is a line running through the centre of the Earth around which everything else rotates. This is its axis. The Earth's axis is tilted relative to the plane in which the Earth orbits the Sun, and this tilt is what causes the seasons. Sometimes the north pole is closer to the sun than the south pole is, and six months later it's the other way round. When the northern end of the axis is tilted towards the Sun, more sunlight falls on the northern half of the planet than on the southern half, so the north gets summer and the south gets winter. Six months later, when the axis points the other way relative to the sun, the reverse applies.

Over longer periods of time, the axis changes direction. Just as a top wobbles when it spins, so does the Earth, and over 26,000 years its axis completes one full circle of wobble. At every stage, however, the axis is tilted at the same angle (23°) away from the perpendicu­lar to the orbital plane. This motion is called precession, and it has a small effect on the timing of the seasons, they slowly shift by a total of one year in 26,000. Harmless, basically. However, the axes of most other planets do something far more drastic: they change their angle to the orbital plane. Mars, for example, probably changes this angle by 90° over a period of 10-20 million years. This has a dramatic effect on climate.

Suppose that a planet's axis is at right angles to the orbital plane. Then there are no seasonal variations at all, but everywhere except the poles there is a day/night cycle, with equal amounts of day and night. Now tilt the axis a little: seasonal variations appear, and the days are longer in summer and shorter in winter. Suppose that the axis tilts 90°, so that at some instant the north pole, say, points directly at the sun. Half a year later, the south pole points at the Sun. At either pole, there is a 'day' of half a year followed by a 'night' of half a year. The seasons coincide with the day/night cycle. Regions of the planet bake in high heat for half a year, then freeze for the other half. Although life can survive in such circum­stances, it may be harder for it to get going in the first place, and it may be more vulnerable to extremes of climate, vulcanism, or meterorite impacts.

The Earth's axis can change its angle of tilt over very long peri­ods of time, much longer than the 26,000 year cycle of precession, but even over hundreds of millions of years the angle doesn't change much. Why? Because, as Laskar discovered when he did the calculations, the Moon helps keep the Earth's axis steady. So it is at least conceivable that life on Earth owes quite a lot to the calming influence of its sister world, however much it may madden us indi­vidually.

A third influence of the Moon was discovered in 1998: a clear association between tides and the rate of growth of trees. Ernst Ziircher and Maria-Giulia Cantiani measured the diameters of young spruce trees grown in containers in the dark. Over periods of several days the diameters changed in step with the tides. The sci­entists interpret this as an effect of the Moon's gravity on the transport of water within the tree. It can't be variations in moon­light, which would perhaps affect photosynthesis, because the trees were grown in darkness. But the effect may be similar to one that occurs with creatures that live on the seashore. Because they evolved to live there, they have to respond to the tides, and evolu­tion sometimes achieves this by creating an internal dynamic that runs in step with the tides. If you remove the creatures to the labo­ratory, this internal dynamic makes them continue to 'follow' the tides.