Big Bang - Simon Singh

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      But a spherical Earth raised a question that still bothers children today — what stops people in the southern hemisphere from falling off? The Greek solution to this puzzle was based on the belief that the universe had a centre and that everything was attracted to this centre. The centre of the Earth supposedly coincided with the hypothetical universal centre, so the Earth itself was static and everything on its surface was pulled towards the centre. Hence, the Greeks would be held on the ground by this force, as would everybody else on the globe, even if they lived down under.

      The feat of measuring the size of the Earth was first accomplished by Eratosthenes, born in about 276 BC in Cyrene, in modern-day Libya. Even when he was a little boy it was clear that Eratosthenes had a brilliant mind, one that he could turn to any discipline, from poetry to geography. He was even nicknamed Pentathlos, meaning an athlete who participates in the five events of the pentathlon, hinting at the breadth of his talents. Eratosthenes spent many years as the chief librarian at Alexandria, arguably the most prestigious academic post in the ancient world. Cosmopolitan Alexandria had taken over from Athens as the intellectual hub of the Mediterranean, and the city’s library was the most respected institution of learning in the world. Forget any notion of strait-laced librarians stamping books and whispering to each other, because this was a vibrant and exciting place, full of inspiring scholars and dazzling students.

      While at the library, Eratosthenes learned of a well with remarkable properties, situated near the town of Syene in southern Egypt, near modern-day Aswan. At noon on 21 June each year, the day of the summer solstice, the Sun shone directly into the well and illuminated it all the way to the bottom. Eratosthenes realised that on that particular day the Sun must be directly overhead, something that never happened in Alexandria, which was several hundred kilometres north of Syene. Today we know that Syene lies close to the Tropic of Cancer, the most northerly latitude from which the Sun can appear overhead.

      Aware that the Earth’s curvature was the reason why the Sun could not be overhead at both Syene and Alexandria simultaneously, Eratosthenes wondered if he could exploit this to measure the circumference of the Earth. He would not necessarily have thought about the problem in the same way we would, as his interpretation of geometry and his notation would have been different, but here is a modern explanation of his approach. Figure 1 shows how parallel rays of light from the Sun hit the Earth at noon on 21 June. At exactly the same moment that sunlight was plunging straight down the well at Syene, Eratosthenes stuck a stick vertically in the ground at Alexandria and measured the angle between the Sun’s rays and the stick. Crucially, this angle is equivalent to the angle between two radial lines drawn from Alexandria and Syene to the centre of the Earth. He measured the angle to be 7.2°.

      Figure 1 Eratosthenes used the shadow cast by a stick at Alexandria to calculate the circumference of the Earth. He conducted the experiment at the summer solstice, when the Earth was at its maximum tilt and when towns lying along the Tropic of Cancer were closest to the Sun. This meant that the Sun was directly overhead at noon at those towns. For reasons of clarity, the distances in this and other diagrams are not drawn to scale. Similarly, angles may be exaggerated.

      Next, imagine somebody at Syene who decides to walk in a straight line towards Alexandria, and who carries on walking until they circumnavigate the globe and return to Syene. This person would go right round the Earth, traversing a complete circle and covering 360°. So, if the angle between Syene and Alexandria is only 7.2°, then the distance between Syene and Alexandria represents 7.2/360, or 1/50 of the Earth’s circumference. The rest of the calculation is straightforward. Eratosthenes measured the distance between the two towns, which turned out to be 5,000 stades. If this represents 1/50 of the total circumference of the Earth, then the total circumference must be 250,000 stades.

      But you might well be wondering, how far is 250,000 stades? One stade was a standard distance over which races were held. The Olympic stade was 185 metres, so the estimate for the circumference of the Earth would be 46,250 km, which is only 15% bigger than the actual value of 40,100 km. In fact, Eratosthenes may have been even more accurate. The Egyptian stade differed from the Olympic stade and was equal to just 157 metres, which gives a circumference of 39,250 km, accurate to 2%.

      Whether he was accurate to 2% or 15% is irrelevant. The important point is that Eratosthenes had worked out how to reckon the size of the Earth scientifically. Any inaccuracy was merely the result of poor angular measurement, an error in the Syene—Alexandria distance, the timing of noon on the solstice, and the fact that Alexandria was not quite due north of Syene. Before Eratosthenes, nobody knew if the circumference was 4,000 km or 4,000,000,000 km, so nailing it down to roughly 40,000 km was a huge achievement. It proved that all that was required to measure the planet was a man with a stick and a brain. In other words, couple an intellect with some experimental apparatus and almost anything seems achievable.

      It was now possible for Eratosthenes to deduce the size of the Moon and the Sun, and their distances from the Earth. Much of the groundwork had already been laid by earlier natural philosophers, but their calculations were incomplete until the size of the Earth had been established, and now Eratosthenes had the missing value. For example, by comparing the size of the Earth’s shadow cast upon the Moon during a lunar eclipse, as shown in Figure 2, it was possible to deduce that the Moon’s diameter was about one-quarter of the Earth’s. Once Eratosthenes had shown that the Earth’s circumference was 40,000 km, then its diameter was roughly (40,000 ÷ π) km, which is roughly 12,700 km. Therefore the Moon’s diameter was (1/4 × 12,700) km, or nearly 3,200 km.

      Figure 2 The relative sizes of the Earth and the Moon can be estimated by observing the Moon’s passage through the Earth’s shadow during a lunar eclipse. The Earth and Moon are very far from the Sun compared with the distance from the Earth to the Moon, so the size of the Earth’s shadow is much the same as the size of the Earth itself.

      The diagram shows the Moon passing through the Earth’s shadow. In this particular eclipse – when the Moon passes roughly through the centre of the Earth s shadow – it takes 50 minutes for the Moon to go from touching the shadow to being fully covered, so 50 minutes is an indication of the Moon’s own diameter. The time required for the front of the Moon to cross the entire Earth’s shadow is 200 minutes, which is an indication of the Earth’s diameter. The Earth’s diameter is therefore roughly four times the Moon’s diameter.

      It was then easy for Eratosthenes to estimate the distance to the Moon. One way would have been to stare up at the full Moon, close one eye and stretch out your arm. If you try this you will notice that you can cover the Moon with the end of your forefinger. Figure 3 shows that your fingernail forms a triangle with your eye. The Moon forms a similar triangle, with a vastly greater size but identical proportions. The ratio between the length of your arm and the height of your fingernail, which is about 100:1, must be the same as the ratio between the distance to the Moon and the Moon’s own diameter. This means that the distance to the Moon must be roughly 100 times greater than its diameter, which gives a distance of 320,000 km.

      Next, thanks to a hypothesis by Anaxagoras of Clazomenae and a clever argument by Aristarchus of Samos, it was possible for Eratosthenes to calculate the size of the Sun and how far away it was. Anaxagoras was a radical thinker in the fifth century BC who deemed the purpose of life to be ‘the investigation of the Sun, the Moon and the heavens’. He believed that the Sun was a white-hot stone and not a divinity, and similarly he believed that the stars were also hot stones, but too far away to warm the Earth. In contrast, the Moon was supposed to be a cold stone that did not emit light, and Anaxagoras argued that moonshine was nothing more than reflected sunlight. Despite the increasingly tolerant intellectual climate in Athens, where Anaxagoras lived, it was still controversial to claim that the Sun and Moon were rocks and not gods, so much so that jealous rivals accused Anaxagoras of heresy and organised a campaign that resulted in his exile to Lampsacus, in Asia Minor. The Athenians had a penchant for adorning their city with idols, which is

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