defined another point close to the Earth, whose influence contributed to the variable speed of the planet. It is hard to imagine this increasingly complicated explanation for planetary orbits, but essentially it consisted of nothing more than circles on top of more circles within yet more circles.
Figure 9 The Ptolemaic model of the universe explained the loopy orbits of planets such as Mars using combinations of circles. Diagram (a) shows the main circle, called the deferent, and a pivoted rod with a planet on the end. If the deferent does not rotate, but the rod does rotate, then the planet follows the smaller, bold circle mapped out by the end of the rod, which is called an epicycle.
Diagram (b) shows what happens if the pivoted rod remains fixed and the deferent is allowed to rotate. The planet follows a circle with a large radius.
Diagram (c) shows what happens when both the rod rotates around its pivot, and the pivot rotates with the deferent. This time the epicycle is superimposed on the deferent, and the planet’s orbit is the combination of two circular paths, which results in the loopy retrograde orbit associated with a planet such as Mars. The radii of the deferent and epicycle can be adjusted and both speeds of rotation can be tuned to mimic the path of any planet.
The best analogy for Ptolemy’s model of the universe is to be found in a fairground. The Moon follows a simple path, a bit like a horse on a rather tame merry-go-round for young children. But the path of Mars is more like a wild waltzer ride, which locks the rider in a cradle that pivots at the end of a long rotating arm. The rider follows a circular path while spinning in the cradle, but at the same time he is following another, much larger, circular path at the end of the long arm that holds the cradle. Sometimes the two motions combine, giving rise to an even greater forward speed, while sometimes the cradle is moving backwards relative to the arm and the speed is slowed or even reversed. In Ptolemaic terminology, the cradle spins around an epicycle and the long arm traces out the deferent.
The Ptolemaic Earth-centred model of the universe was constructed to comply with the beliefs that everything revolves around the Earth and that all celestial objects follow circular paths. This resulted in a horribly complex model, replete with epicycles heaped upon deferents, upon equants, upon eccentrics. In The Sleepwalkers, Arthur Koestler’s history of early astronomy, the Ptolemaic model is described as ‘the product of tired philosophy and decadent science’. But despite being fundamentally wrong, the Ptolemaic system satisfied one of the basic requirements of a scientific model, which is that it predicted the position and movement of every planet to a higher degree of accuracy than any previous model. Even Aristarchus’ Sun-centred model of the universe, which happens to be basically correct, could not predict the motion of the planets with such precision. So, all in all, it is not surprising that Ptolemy’s model endured while Aristarchus’ disappeared. Table 2 summarises the key strengths and weaknesses of the two models, as understood by the ancient Greeks, and it serves only to reinforce the apparent superiority of the Earth-centred model.
Ptolemy’s Earth-centred model was enshrined in his Hè megalè syntaxis (‘The Great Collection’), written in about AD 150, which became the most authoritative text on astronomy for centuries to come. In fact, every astronomer in Europe for the next millennium was influenced by the Syntaxis, and none of them seriously questioned its Earth-centred picture of the universe. Syntaxis reached an even wider audience in AD 827, when it was translated into Arabic and retitled the Almagest (‘The Greatest’). So, during the lull in scholasticism during the European Middle Ages, Ptolemy’s ideas were kept alive and studied by the great Islamic scholars in the Middle East. During the golden age of the Islamic empire, Arab astronomers invented many new astronomical instruments, made significant celestial observations and built several major observatories, such as the al-Shammasiyyah observatory in Baghdad, but they never doubted Ptolemy’s Earth-centred universe with its planetary orbits defined by circles within circles within circles.
As Europe finally began to emerge from its intellectual slumber, the ancient knowledge of the Greeks was exported back to the West via the Moorish city of Toledo in Spain, where there was a magnificent Islamic library. When the city was captured from the Moors by the Spanish King Alfonso VI in 1085, scholars all over Europe were given an unprecedented opportunity to gain access to one of the world’s most important repositories of knowledge. Most of the library’s contents were written in Arabic, so the first priority was to establish an industrial-scale bureau of translation. Most translators worked with the aid of an intermediary to translate from Arabic into the Spanish vernacular, which they then translated into Latin, but one of the most prolific and brilliant translators was Gerard of Cremona, who learned Arabic so that he could achieve a more direct and accurate interpretation. He had been drawn to Toledo by rumours that Ptolemy’s masterpiece was to be found at the library and, of the seventy-six seminal books that he translated from Arabic into Latin, the Almagest was his most significant achievement.
Thanks to the efforts of Gerard and other translators, European scholars were able to reacquaint themselves with the writings of the past, and astronomical research in Europe was reinvigorated. Paradoxically, progress became stifled, because there was such reverence for the writings of the ancient Greeks that nobody dared to question their work. It was assumed that the classical scholars had mastered everything that could ever be understood, so books such as the Almagest were taken as gospel. This was despite the fact that the ancients had made some of the biggest blunders imaginable. For example, the writings of Aristotle were considered sacred, even though he had stated that men have more teeth than women, a generalisation based on the observation that stallions have more teeth than mares. Although he was married twice, Aristotle apparently never bothered to look into the mouth of either of his wives. He might have been a superlative logician, but he failed to grasp the concepts of observation and experimentation. The irony is that scholars had waited for centuries to recover the wisdom of the ancients – and then they had to spend centuries unlearning all the ancients’ mistakes. Indeed, after Gerard’s translation of the Almagest in 1175, Ptolemy’s Earth-centred model of the universe continued to survive intact for another four hundred years.
In the meantime, however, a few minor criticisms did emerge from such figures as Alfonso X, King of Castile and León (1221—84). Having made Toledo his capital, he instructed his astronomers to draw up what became known as the Alphonsine Tables of planetary motion, based partly on their own observations and partly on translated Arabic tables. Although he was a strong patron of astronomy, Alfonso remained resolutely unimpressed with Ptolemy’s intricate system of deferents, epicycles, equants and eccentrics: ‘If the Lord Almighty had consulted me before embarking upon Creation, I should have recommended something simpler.’
Table 2
This table lists various criteria against which the Earth-centred and Sun-centred models could be judged, based on what was known in the first millennium AD. The ticks and crosses give crude indications of how well each theory fared in relation to the seven criteria, and a question mark
| Criterion | Earth-centred model | Success |
|---|---|---|
| 1. Common sense | It seems obvious that everything revolves around the Earth |
 |
| 2. Awareness of motion | We do not detect any motion, therefore the Earth cannot be moving |
|
| 3. Falling to the ground | The centrality of the Earth explains why objects appear to fall downwards, i.e. objects are being attracted to the centre of the universe |