The Science of Discworld Revised Edition

resemble the Earth’s mantle.
    This line of theorising may be losing the plot, though, because it was that very resemblance that needed explanation in the first place, and gave rise to the giant impact theory of the Moon’s formation. Anything that explains why the impactor was like the mantle, such as ‘it formed at the same distance from the Sun as the Earth did,’ can probably explain why the Moon is like the mantle, without an impactor being needed. Maybe both the Moon and the Earth’s mantle were splashed off something
else
by an impact.
    Because Earth has weather – especially back then, oh boy, did it have weather
then
– the resulting impact craters all got eroded away; but because the Moon has no weather, the lunar impact craters didn’t get eroded away, and a lot of them are still there now. The great charm of this theory is that it explains many different features of the Moon in one go – its similarity to the Earth’s mantle, the fact that its surface seems to have undergone a sudden and extreme amount of heating about 4 billion years ago, its craters, its size, its spin – even those sea-like maria, released as the proto-Moon slowly cooled. The early solar system was a violent place.
    In fact, the Dean’s mis-designed sun might have done us some good after all …
    The Moon affects life on Earth in at least two or three ways that we know of, probably dozens more that we haven’t yet appreciated.
    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 (21 m) – 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