The Ascent of Gravity

by Marcus Chown

  Just as quickly as it arrives, it has gone, disappearing from view around the next bend in the river, heading for the city of Gloucester where it will be truncated by the city’s docks. Most but not all of its human cargo have gone with it. Two surfers, who collided as they threaded their boards back and forth across the wave front, are now bobbing up and down in the gently undulating water of the bore’s wake, along with the bemused swans.

  The TV crew packs up its equipment into shoulder bags and boxes, while the rest of us head back to our cars. Everyone is laughing, light-headed, exhilarated. No one is in the slightest doubt that what they have just witnessed is one of the wonders of the natural world.

  Interesting bores

  The Severn Bore is one of about sixty bores around the world.3 The biggest and most terrifying by far is on the Ch’ient’ang’kian River in China. In spring, a monster wave as high as a three-storey house surges upriver faster than most people can run.4 So great is its roar that it can be heard from 22 kilometres away. Boats must be lifted clear of the river lest they are smashed to matchwood. And every year, despite abundant warning signs erected by the authorities along the riverbank, some people stand too close and are swept away and drowned.

  The necessary conditions for a bore are a river estuary of a very particular shape and a large tidal range. The Severn estuary, where the water rises as much as 15.4 metres between low and high tide, has the second highest tidal range in the world. The fast-rising water is funnelled into a channel which rapidly becomes narrower and shallower. Eventually, the speed of the water flowing upriver exceeds that of the water flowing downriver, and a step in water height, technically known as a ‘hydraulic jump’, is born and travels rapidly upstream. (A similar phenomenon, though static, can be seen in a kitchen sink when water from a tap strikes a basin and spreads out, creating an abrupt change in water height where its speed matches that of the incoming water.) Just as a tsunami is imperceptible out at sea but amplified when it enters shallow coastal waters, the Severn Bore is an imperceptible ripple out in the estuary but grows and picks up speed as it is funnelled by the ever-shrinking channel.

  The biggest bores occur in spring and autumn. This is because the Severn Bore and its cousins around the world are merely extreme manifestations of the ocean tides, which are at their largest in spring and autumn. Since the tides are the result of the influence of the Moon it follows that so too is the Severn Bore. Remarkably, a super-localised hummock of speeding water, capable of startling swans and delighting surfers and kayakers, owes its existence to an astronomical body 384,000 kilometres away across space.

  The Moon appears so small in the sky it can be covered by a thumb held at arm’s length. That it should be orchestrating such a down-to-earth event on a cold March day on the River Severn seems utterly preposterous. No wonder nobody guessed the cause of the Severn Bore. No wonder nobody guessed the cause of the ocean tides. Not for a long, long time.

  Baffled by the tides

  Nobody knows when the tides were first noticed. But our ancestors left the cradle of Africa and spread across the world on several occasions, beginning 1.8 million years ago with Homo erectus and finishing 60,000 years ago with modern humans. Very probably, they made their way around the globe by following the shoreline of the oceans, thus avoiding the obstacles of mountains, deserts and forests, and ensuring an ever-present source of food in the adjacent sea.5 As they padded barefoot along the wet sand, one thing would have been obvious to our not-quite-human ancestors and our fully human ancestors: twice a day, the sea breathes in and out, surging up a sandy beach before slinking back whence it came. From a clifftop or any other place where the coastline is vertical, it would have been clear that this in-and-out motion is actually a consequence of something more fundamental: twice a day, mysteriously, the ocean rises and falls.

  Time passed. Immense tracts of time. People invented farming, started to live in cities and began to speculate about the phenomena shaping the world they found themselves in. By a quirk of geography, the ancient civilisations of the West bordered a sea – the Mediterranean – which experiences barely noticeable tides. People remained ignorant of the phenomenon, and this ignorance had severe consequences for Julius Caesar whose invasion of Britain in 55 BC and 54 BC required him to take a Roman fleet outside the Mediterranean:

  It happened that night to be a full Moon, which usually occasions very high tides in that ocean; and that circumstance was unknown to our men. Thus, at the same time, the tide began to fill the ships of war which Caesar had provided to convey over his army, and which he had drawn up on the strand; and the storm began to dash the ships of burden which were riding at anchor against each other.6

  ‘Beware the Ides of March’, Julius Caesar is warned by a soothsayer before his murder in the play by William Shakespeare. Perhaps if he had been warned ‘Beware the tides of March’, his invasion fleet would have suffered less heavy damage in the Atlantic. Such a warning should actually have been possible. Although knowledge of the tides was not widespread in Roman times, their key characteristics had been known since about 330 BC when the Greek astronomer and explorer Pytheas sailed from the virtually landlocked Mediterranean all the way to Britain. On emerging for the first time into the vast open expanse of the Atlantic Ocean, Pytheas made a fundamental discovery.7 The tides are biggest at new Moon – when the Moon is completely unlit by the Sun – and at the full Moon – when the Moon is completely lit by the Sun. Bizarrely, the tides appear to be controlled by the Moon.

  Actually, the observation that the highest tides occur when the Moon and Sun are arranged in space so that the Moon is either completely lit or completely unlit by the Sun strongly hints that the Sun also plays a role in the phenomenon, something also realised by Pytheas. The involvement of the Sun is also supported by the fact that the tides are bigger in spring and in autumn, two very particular times in the Earth’s annual journey around the Sun.

  Knowing the key characteristics of the tides is obviously a very important first step on the road to understanding the cause of the phenomenon. Nevertheless, for almost two millennia after Pytheas, no one came even close to explaining the baffling spectacle.

  At the beginning of the eighth century, the Venerable Bede, an English monk and chronicler, noticed that high tide arrives at different times at different ports around the coast of Britain. The implication was that local geography, as well as the influence of the Moon and Sun, plays a role in determining the characteristics of the tides — an observation reinforced by the absence of significant tides in the landlocked Mediterranean and the presence of giant tides in the funnel-shaped estuary of the River Severn.

  As for the cause of the tides, Bede, like everyone else, was, well, totally at sea. He speculated that the Moon blew the ocean inland. And when the Moon had moved a bit so that the ocean was subjected to weaker breath, it returned whence it had come. ‘It is as if [the ocean] were dragged forwards against its will by certain exhalations of the Moon,’ wrote Bede, ‘and when her power ceases, it is poured back again into his proper measure.’

  The first attempt at a scientific explanation came from an Arab physician and astronomer in the thirteenth century. According to Zakariya al-Qazwini, the tides are caused by the Sun and Moon heating the water of the ocean, which causes it to expand outwards from the point of heating. Though eminently plausible, the idea fails to explain why the Moon and not the Sun plays the dominant role. The tides pulled by the Moon are about twice as big as those pulled by the Sun.

  In 1609, Johannes Kepler, very likely influenced by William Gilbert’s recent discovery of the Earth’s magnetic field, proposed that the tides were caused by the magnetic attraction of the Moon and Sun on the oceans. Galileo was a big admirer of Kepler’s, but he was shocked by this ‘childish’ suggestion. To him, the whole idea that astronomical bodies could reach out across empty space and affect the Earth smacked of the ‘occult’. Galileo instead suggested that the tides are caused by the combined effect of the Earth
rotating on its axis and orbiting the Sun, motions which he claimed cause the oceans to slosh back and forth.

  The truth is that nobody had the slightest chance of discovering the origin of the tides because nobody had the right mathematical tools to do so. Nobody, that is, until Isaac Newton.

  Newton alone created a system of the world, which united the Earth and the heavens in one theoretical framework. Newton alone discovered a universal law of gravity. And that law, he realised, had consequences in domains far removed from the realm of the planets orbiting the Sun. Those consequences he explored methodically in his emerging masterwork, the Principia. And chief among them was the tides.

  Tides: the lunar connection

  In estimating the gravitational force exerted by the Earth on the Moon, Newton had assumed that it is the same as if the entire mass of the Earth is concentrated at a single point at its centre. He had even proved this is so with his new-fangled mathematics of integral calculus. But considering the Earth as a point-like mass is merely a good approximation. The Earth in reality, of course, is an extended body. And because it is an extended body, naturally there are parts of the planet that are closer to the Moon than others. The closer parts experience a stronger pull from the Moon than the other parts. Such differences in gravity, Newton realised, have important consequences. And those consequences are most significant for the oceans because water, unlike solid rock, is free to move.

  Consider the point on the ocean immediately below the Moon. The gravitational pull on the water at the surface, which is closer to the Moon, is stronger than the pull on the water at the seabed, which is further from the Moon. This difference in gravity, Newton realised, causes the surface water to be pulled away from the seabed so that the ocean bulges up towards the Moon.

  But this is not all. Consider the ocean at a point on the opposite side of the Earth to the Moon. Here, the gravitational pull of the Moon on the water at the seabed, which is closer to the Moon, is stronger than on the water at the surface, which is further from the Moon. The difference in gravity causes the water at the seabed to be pulled away from the surface so, once again, the ocean bulges upwards.

  According to Newton’s reasoning, then, the Moon creates not one but two bulges in the ocean – one at the point in the ocean closest to the Moon and one at the point in the ocean furthest away from the Moon.8

  The Earth, though, is not static but spins on its axis. This means that the ocean moves through the two bulges every 24 hours. And from the point of view of someone standing on a beach on the edge of the ocean, the water rises and falls twice every 24 hours. Newton had therefore explained what nobody in history had been able to explain: why there are two tides a day. They are nothing more than a consequence of a universal law of gravity which weakens with distance. But, of course, no one knew of such a law before Newton.

  Actually, there is a subtlety here, of which Newton was aware. It is not quite true that the tides at any location repeat every 24 hours. They repeat roughly every 25 hours, something actually noticed by Pytheas in 330 BC.

  Picture the Moon again. It does not simply hang static in the sky above a single location on the ocean while the Earth turns beneath it. Instead, it circles the Earth in the same direction as the Earth’s rotation, taking 27.3 days to make a complete circuit. This means that a point on the ocean directly beneath the Moon will not be directly beneath the Moon again after 24 hours. In the time the Earth has taken to turn once on its axis, the Moon will have moved on its orbit. For the point on the ocean to be directly below the Moon again the Earth must rotate a further 1/27.3 of a complete turn, which takes 1/27.3 of 24 hours, or about 53 minutes. Consequently, two tides are experienced not every 24 hours but every 24 hours and 53 minutes. This is just one of many reasons why predicting the precise times of low and high tide at any location on a coast requires detailed tide tables.

  That the Moon rises 53 minutes later each day and the tides are delayed by 53 minutes each day is yet more evidence that the tides are principally caused by the Moon.

  But why are the tides so small in the Mediterranean? The answer is part geography and part ocean depth. As the Earth rotates, the two tidal bulges move westward through the oceans. But this means they head towards the Mediterranean from the direction of the Indian Ocean. Unfortunately, there is a brick wall standing in the way: the landmass of the Middle East. Consequently, no ocean bulge makes it into the eastern Mediterranean.

  But what about times when the Moon is directly above the Mediterranean? In this case, the Moon will create a bulge in the sea. However, it will be small. The reason is that the difference in the Moon’s gravity experienced by water at the surface of the ocean and at the seabed depends on the depth of the water. If the ocean is shallow, the difference is small, and so too is the tidal bulge; if the ocean is deep, the difference is big, and with it the tidal bulge. The Mediterranean is relatively shallow. In fact, its average depth is 1.5 kilometres compared with the 3.3 kilometres of the Atlantic. Consequently, tides in the Mediterranean are less than half as impressive as in the Atlantic even when the Moon is hanging directly above the Mediterranean.

  It is not often admitted but the twin tidal bulges in the oceans, which are often shown as huge in textbooks and popular science books, are actually ridiculously small. In mid-ocean, the Moon’s gravity lifts the water by at most a metre – little more than a ten-millionth of the Earth’s radius. But, of course, an ocean has a very large area, and a metre-high bulge spread over a very large area accounts for a lot of water. When that water sloshes into the shallows around the land, it is amplified in height exactly like in a tsunami. Though the tides at mid-ocean are unnoticeable, along the shorelines of the ocean they can be more than ten times as big.

  Tides: the solar connection

  As Pytheas discovered, the tides are not caused by the gravitational pull of the Moon alone but by a combination of the pull of the Moon and the Sun. The reason these two bodies are responsible is simple. They are the celestial objects with the dominant gravitational pull on the Earth. The Moon is enormously less massive than the Sun but an awful lot closer – and its closeness wins out. This is why the tides pulled by the Moon are twice as big as those pulled by the Sun – from which it can be deduced that the Moon is twice as dense as the Sun.9

  The biggest tides occur, as expected, when the effects of the Earth and the Sun reinforce each other. This happens in spring and autumn. It is not easy to visualise. But the key thing is that the Earth spins like a top tipped at 23.5 degrees to the vertical. This means that the Moon’s orbit is also tipped.10 The geometry of the situation means that the only time the Moon and Sun can be perfectly aligned and so pull on the Earth’s oceans with maximum force is when the Earth in its orbit is halfway between summer and winter – that is, in spring and autumn.

  The perfect alignment also requires the Moon and Sun to be either on the same side of the Earth, so that the Moon is in shadow – a new Moon – or on opposite sides of the Earth, so that the Moon is completely illuminated – a full Moon. This is why the biggest tides – and the biggest Severn bores – occur in spring and autumn around the time there is a full or new Moon in the sky.11

  The Moon and Sun do not exert a tidal effect only on the oceans; they exert a tidal effect on the whole planet. But, because the rock of the Earth is more rigid than water, the effect on the land is far smaller and much harder to spot. Remarkably, though, tides in the land were first noticed – though not understood – in antiquity.

  Tides in the rock: wells and springs

  The tides have many baffling features. They occur, after all, twice every 25 hours not every 24 hours. They vary according to the seasons and according to the phases of the Moon. And they vary according to local geography. But one feature of the tides -first noticed by the Greek philosopher Poseidonios – seems more baffling than all the rest.

  Poseidonios, who lived between 135 and 51 BC, made observations of the tides in the Atlantic off the coast of Spain. He also obs
erved water in wells. And what he noticed was something very peculiar. As the water in the ocean rises, the water in wells falls, and vice versa. Poseidonios’ original observations are lost. But the Greek geographer Strabon, who lived from 63 BC until about AD 25, reports them in his Geograpbika:

  There is a spring at the [temple of] Heracleium at Gades [Cadiz], with a descent of only a few steps to the water (which is good to drink), and the spring behaves inversely to the flux and reflux of the sea, since it falls at the time of the flood-tides and fills up at the time of the ebb-tides.

  What in the world could cause the water in such a localised region as a spring or well to do the exact opposite of what the water in the ocean is doing? There was unlikely to be an answer while the cause of the tides remained a mystery. In fact, incredibly, the puzzle was solved only in 1940 by an American geophysicist called Chaim Leib Pekeris.12

  A tide can be defined as the distortion in the shape of one body caused by the gravitational pull of another body not simply a distortion in the shape of its water. And, in fact, the pull of the Moon causes a tidal bulge in the rock immediately beneath it in exactly the same way that it causes a tidal bulge in the ocean immediately beneath it. The bulge in the rock is a lot smaller on account of rock being a lot more rigid than water. Twice every 25 hours, then, the solid Earth at any location bulges upwards and shrinks back down again, stretching and squeezing the rock.

  Now, say the rock into which a well is dug is porous so that it contains water. This is not unlikely since the very fact that a well contains water means there must be water in its vicinity. The surrounding rock is therefore like a waterlogged sponge. And, like a waterlogged sponge, it sucks water out of a well when the rock is stretched and squirts it back into the well when the rock is squeezed.