by Paul Murdin
The Shape of the Earth
Our planet, a flattened sphere
A Frenchman who arrives in London will find philosophy, like everything else, very much changed there.…In Paris, you think of the Earth as a melon; in London it is flattened on both sides.
Voltaire, Letters from England, 1731
The ancient discovery that the Earth was round rather than flat was only the beginning. Over the past 2,000 years, a clock pendulum, a librarian’s horseback journey to Alexandria and a wayward satellite have helped us to establish the exact size and shape of the Earth. It turns out that our planet is not a perfect sphere, but resembles a squashed, dimpled golf ball.
Since antiquity, every educated person has known that the Earth is approximately spherical. The question of whether Christopher Columbus would fall off the edge of the world if he sailed westwards from Spain was founded in ignorance. The real doubts centred on whether he would survive the dangers of the journey (unpredictable weather, sailing hazards, sea monsters) and whether he would be able to discover an alternative route to the East Indies. As history tells us, Columbus survived the ocean crossing and in 1492 landed in what he called the West Indies, actually part of the Americas.
Ancient astronomers argued that the Earth was spherical because the shadow that the Earth cast on the Moon during a lunar eclipse was always circular. It was well known, too, how a lookout at the top of a ship’s mast would see land before his fellow sailors on deck, because the lookout was able to see over the curvature of the Earth. Greek philosophers of the Pythagorean school in the sixth century BCE disseminated these standard arguments for a spherical Earth throughout the educated world.
In the third century BCE, Eratosthenes, the librarian of Alexandria, determined the size of the Earth. He had heard that at Syene (present-day Aswan) in Upper Egypt the Sun was directly overhead at noon on the day of the summer solstice – the Sun’s rays reached the bottom of a deep well. He determined the length of the shadow of a vertical post at Alexandria on the same day and found that the angle of the Sun was 1⁄50 of a circle to the south of the zenith. It is said that he determined the distance between Syene and Alexandria by driving a carriage between the two cities and counting the revolutions of the wheels. He multiplied this distance – 5,000 stadia – by 50 to calculate that the circumference of the Earth was 250,000 stadia. The modern equivalent of a stadium is not securely established, but Eratosthenes’ figure is thought to be the equivalent of about 45,000 kilometres, remarkably close to the modern measurement of the Earth’s circumference as 40,000 kilometres.
However, by the seventeenth century CE it had become clear that the Earth was not perfectly spherical. The first evidence came from a clock pendulum. In 1671 the Paris Academy of Sciences sent Jean Richer to Cayenne in Guyana, South America, on the Equator, to observe the close approach of Mars to the Earth in 1672 in order to establish its distance and thus the scale of the Solar System. To accomplish this, Richer needed an accurate clock. He took a clock with a pendulum that had beaten seconds correctly in Paris. However, in Cayenne the same clock ran slow and lost two and a half minutes every day. To make it beat seconds accurately in Cayenne, Richer discovered that he had to shorten the pendulum by about 3 millimetres. The reason for this was a mystery.
In 1687 Isaac Newton offered a solution to Richer’s discovery that a pendulum beat slower at the Equator than in France: the Earth is not exactly spherical, but bulges at the Equator and is squashed at the poles. It rotates once every twenty-four hours, and the resulting centrifugal force raises the region along the Equator. For the same reasons, gravity is reduced at the Equator, which is why Richer’s pendulum beat more slowly in Cayenne.
During the eighteenth century Newton’s explanation was confirmed by a massive body of work, chiefly organized by the Academy of Sciences of Paris, and initiated partly as a test to decide between Newton’s theory of gravity (which suggested that the Earth was flattened at the poles, like a tangerine) and Descartes’ theory of gravity (which could be read to suggest that it was pointy at the poles, like an American football or rugby ball). The measurement was also intended to provide a universal standard of length, the metre, defined in terms of the Earth’s circumference. The magnitude of the task is represented by the long list of astronomers involved: the four astronomers of the Cassini dynasty (Jean-Dominique Cassini, his son Jacques Cassini, his grandson César-François Cassini de Thury and his great-grandson, also called Jean-Dominique Cassini, all four of them being successive directors of the Paris Observatory); the astronomers Jean-Baptiste-Joseph Delambre and Pierre Méchain; the French mathematicians Pierre Maupertuis, Pierre Bouguer and Louis Godin; the explorer Charles-Marie de La Condamine; and the Swedish astronomer Anders Celsius, whose name is remembered in the centigrade temperature scale. These astronomers carefully measured the three-dimensional shape of France. Some of them participated in adventures to the Equator in Ecuador and to the Arctic Circle in Lapland to measure the curvature of the Earth. They discovered that the Earth was indeed a flattened sphere. The modern value for the flattening is 1⁄298.25 – there is a difference of more than 21 kilometres between the Earth’s radius at the equator (6,378 kilometres) and its radius at the pole (6,357 kilometres).
The shape of the Earth affects the motion of orbiting satellites – lumps that spoil the uniform spherical shape pull satellites off course. Some satellites, like the LAGEOS, or Laser Geodynamics Satellites, are simple spheres covered with reflectors so that their position can be measured to millimetres when laser pulses are reflected from them. Others, like JASON-1, TOPEX/Poseidon and ENVISAT, carried radar to measure the wrinkles on the Earth’s surface to an accuracy of centimetres.
The geodynamic satellites have discovered that the Earth’s ocean surface is dimpled like a golf ball, with wind-driven currents piling water up into mounds against the continental shores, and warmer sea areas standing higher, in the same way that mercury rises in a thermometer. Overall the height of Earth’s ocean surface is lower by about 150 metres in the north Indian Ocean (off the south coast of India) than in the western Pacific Ocean (off New Guinea); travelling eastwards from the sea off New Guinea to the sea off California is downhill by 90 metres. In the northern Atlantic Ocean, the sea off Florida is 130 metres lower than the sea off Iceland.
Additionally, the shape of Earth changes over the seasons and the years, as the mass of water covering the Earth shifts in position. Global-scale climate changes (such as the El Niño phenomenon) have melted sub-polar glaciers and changed the currents in the Southern, Pacific and Indian Oceans, causing the bulge in the Earth’s equator to grow larger and mass to move away from the poles.
It is easy to imagine how the ocean surface is made irregular, because the flow of water is something that we experience on a small scale and we can extrapolate to the large scale. The irregular shape of the solid Earth is more difficult to envisage. The surface of the Earth is changed over geological time by the circulation of its inner liquid core pushing against its plastic near-surface layers. Below the surface of the Earth, the circulation of the liquid core causes plate movements that crack the continents and raise mountains. As measured by precision mapping using GPS satellites, the Tibetan Plateau in the Himalayas is rising by about 5 millimetres every year. Volcanoes grow where magma upwells from the interior, sinking when the magma is released in an eruption.
The rotation of the Earth plays its part by flattening the polar regions. And climate change affects the shape of the Earth: an ice cap grows at the South Pole and flows outwards to the edge of Antarctica, while depressed land areas released from the weight of melting glaciers spring upward. The Earth is a dynamic, almost a living, creature.
The Southern Constellations
Hidden stars revealed by the tilting Earth
The sky is more the domain of science than of poetry. It is the stars as not known to science that I would know, the stars which the lonely traveller knows.
Henry David Thoreau, Journal, 185
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How did stars that cannot be seen from Europe and the Mediterranean come to have Greek and Roman names? Although the traditional constellations were named thousands of years ago, their visibility has changed dramatically since antiquity. In some parts of the world new stars have risen in the sky while ancient constellations have disappeared below the horizon. These changes are caused by a 26,000-year cycle of ‘wobbles’ in the Earth’s rotation.
If you look up at the stars from the North Pole of the Earth, only half the sky is visible, the half that is centred around the North Pole of the sky immediately above your head (the point at the extension of the Earth’s axis of rotation into the sky is called the North Celestial Pole). The other half of the sky is perpetually below the horizon, even though the Earth rotates. But if you are at the Equator, you will be able to see every part of the sky in turn at different times of the year. At intermediate European latitudes, where most of the classical constellations were named after figures from Greco-Roman mythology, half the southern sky is perpetually out of sight. Because the constellations in this part of the southern sky could not be seen from Europe or the Mediterranean, they were not named by Europeans until sailors began to explore the southern seas in the fifteenth and sixteenth centuries CE. The oldest printed star charts published in Europe date from 1515. They are woodcuts, produced in Nuremberg, Germany, the product of an innovative collaboration between the German artist Albrecht Dürer, the eminent Viennese cartographer Johannes Stabius and the German astronomer Conrad Heinfogel. The map of the southern constellations shows a remarkable ‘hole’ in the region never visible from the north, where no constellations had been described.
There are two peculiar exceptions to this simplified account. In one part of the sky that lies south of the bright star Formalhaut and is, in fact, readily visible from Europe, there are no constellation figures that have mythological names dating back to classical times. On the opposite side of the celestial globe is an area of the southern sky, which, although it never rises above the horizon even in southern Europe, contains a substantial part of a constellation that was known to Greek and Roman classical scholars even though they were never able to see its stars. This constellation is called Argo, the name of the ship in which, according to classical mythology, Jason sailed with the Argonauts in search of the Golden Fleece. The situation seems very puzzling: stars that were not visible from Europe came to have European classical names, while visible stars were for some reason left unlabelled. The solution to the mystery is precession.
The traditional constellations are centred on Polaris, the North Star. This star, the brightest in the constellation Ursa Minor, lies near to the centre of the 24-hour rotation of the stars, but it has not always been in ‘pole position’. The axis of the rotation of the Earth shifts, cyclically, in space, wobbling like the stem of a spinning top and pointing to different stars from time to time. This wobbling is called ‘precession’. The effect of precession is to twist the axis of the Earth’s diurnal rotation in a circle on the sky. The Earth’s axis slowly follows this circle over a period of 26,000 years. At this speed the changes in the constellations are not readily noticeable from generation to generation, but may be perceived from civilization to civilization.
In the several thousand years that have passed since the constellation figures were first recorded, precession has twisted the Earth’s axis from its original position to the present North Pole. By 1515, the date of Dürer’s map, the hole in the constellations in the south was quite obviously offset from the present position of the south celestial pole. This had the effect of hiding part of the sky mapped by classical astronomers, while revealing another area, which contains stars that could not be seen from Europe and the Mediterranean in classical times, and was therefore not mapped until much later. A further effect of the twist is that constellation figures (such as Orion) that used to stand erect in the sky, with their heads facing the North Pole, now lean askew, at an angle. These changes started to be apparent to astronomers as early as the second century BCE, when the Greek astronomer Hipparchus noticed discrepancies between his own observations of the sky and the constellations that had been recorded by his predecessors Eudoxus and Aratus two centuries earlier.
Precession also affects the part of the sky in which the Sun appears at the spring equinox. For roughly 2,000 years before the start of the Christian era, the Sun appeared near the constellation Aries at the spring equinox, shifting gradually into Pisces towards the beginning of the Christian era. Soon Aquarius will become the constellation of the spring equinox (some say that it already has), and this will be (or has been) the ‘dawning of the Age of Aquarius’. An ‘age’ in this sense lasts about 2,000 years – the period of precession, 26,000 years, divided among the twelve signs of the Zodiac.
Using the known speed of precession and working backwards, it is possible to calculate that all the classical constellation figures were visible and stood erect in the sky around 2800 BCE (plus or minus 300 years) as seen from latitude 36 degrees. This corresponds to the time and place where the constellations were formulated: during the height of the great civilizations of the Tigris–Euphrates valley, which straddles this latitude.
While most of the constellations of the northern sky are named for figures from classical mythology, many southern constellation figures commemorate modern inventions, having been named by seventeenth- and eighteenth-century astronomers during expeditions to southern lands. The eighteenth-century French astronomer Nicolas-Louis de Lacaille carried out an extended astronomical expedition to the Cape of Good Hope, South Africa. He invented constellations celebrating what were at the time modern inventions such as Fornax (the Chemical Furnace) and Horologium (the Pendulum Clock). He broke down one large southern constellation, Argo Navis, into more conveniently sized component parts including the Keel, the Poop Deck and the Sails.
Known in Europe as a separate constellation only since the sixteenth century (Amerigo Vespucci claimed to be the first European to see its stars on his third voyage of 1501), the constellation of Crux, the Cross, which lies near to the South Celestial Pole, is of particular significance in Christian cultures because of its cruciform shape. In modern times the Southern Cross has become a sentimental symbol of Southern-Hemisphere patriotism – it appears on the flags of Australia, Papua New Guinea, New Zealand, Samoa and Brazil. The four stars of the Southern Cross were in fact known to Ptolemy as part of the constellation Centaurus but were ‘lost’ to European eyes as the Earth tilted away from the constellation due to precession. The Southern Cross ceased to be visible from the British Isles at the time that the building of Stonehenge was started (about 3000 BCE) and from northern Mediterranean shores at the time of the collapse of the Roman Empire (about 500 CE).
Because the southern stars were imagined but unseen by Europeans, and associated with exploration and long voyages, they are often used symbolically in literature and art set in the strange lands overhung by the southern skies to convey a sense of not belonging, of adventure and nineteenth-century imperialism. For example, in Thomas Hardy’s poem ‘Drummer Hodge’ (1899), the drummer-boy killed in the Boer War and buried in the Karoo desert in the Cape lies in a grave on an isolated hill, where ‘strange-eyed constellations reign / His stars eternally’.
The Sun
At the centre of the Solar System
If there should chance to be any mathematicians who, ignorant in mathematics yet pretending to skill in that science, should dare, upon the authority of some passage of Scripture wrested to their purpose, to condemn and censure my hypothesis, I value them not, and scorn their inconsiderate judgement.
Nicolas Copernicus, De revolutionibus orbium coelestium, 1543
In the first half of the sixteenth century, the Polish cleric Nicolaus Copernicus outlined a hypothesis to replace the 1,500-year-old Ptolemaic cosmological system, proposing that all the planets, save the Moon, revolved around the Sun. Few scientific discoveries have demanded such a fundamental transformatio
n of human thought. Yet Copernicus’s revolutionary theory was actually the product of centuries of careful astronomical observation that had gradually exposed the failure of the Ptolemaic system to predict the movement of the planets.
Since the second century CE, the geocentric theory, called the Ptolemaic system, had held that the Earth was stationary at the centre of the Universe. The theory survived unchallenged for over 1,500 years as it contradicted neither literal readings of the Bible nor the immediate evidence of the five senses. Yet by the sixteenth century the Ptolemaic theory was beginning to suffer a progressive loss of confidence. It had become clear that the geocentric model required constant additions and changes to make it correspond with astronomers’ actual observations. Astronomers were beginning to feel that these successive add-ons were arbitrary and did not give a decisive overall explanation for the observed behaviour of the heavenly bodies. The most serious problem was in the addition of epicycles to explain why some planets did not appear to orbit the Earth as predicted by the Ptolemaic theory.
Because the Earth has a shorter orbit than the outer planets (Mars, Jupiter, Saturn, Uranus and Neptune), it overtakes them from time to time as it revolves around the Sun. When viewed from the Earth on these occasions, the outer planets seem to halt in their orbits and move backwards in a loop. This is called ‘retrograde motion’. As first proposed by Appolonius of Perga (c. 200 BCE) and Hipparchus (c. 130 BCE), Ptolemy added epicycles to his system to account for this loop.
An epicycle was envisaged as a kind of revolving wheel that carried the planet on its outer rim, while itself revolving in an orbit around the Earth. The combination of the two motions was thought to produce the retrograde loop. In modern engineering, the concept of epicycles survives in the name of so-called ‘planetary gears’, in which a small gear wheel rotates outside a central one, all enclosed within a hollow toothed chamber.
