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Ptolemy used another device, the
equant
, which was original with him, not inherited from earlier astronomy. The equant was an imaginary point in the opposite direction (as viewed from the Earth) from the centre of the eccentric. This invention kept the motion of a planet uniform with respect to the equant, while from the Earth its speed appeared to vary. Using this device, Ptolemy was able to predict the changing speed of a planet (as seen from the Earth) almost as well as Johannes
Kepler
would do in the 17th century. Kepler’s is the way modern astronomy solves the problem, but Ptolemy’s solution came close to being its geometric equivalent.

Ptolemy combined these devices – epicycle/deferent, eccentric, equant – in an elaborate and highly successful model of heavenly movement. To a degree of accuracy that astounds us who believe we know a much better way of thinking about it, his astronomy predicted and accounted for the observed movements of the five planets known in his time and of the Sun and the Moon, without removing the Earth from its position as unmoving centre. Ptolemy centred the seven orbits not on one point but on seven different points near the Earth. Adjusting epicycles, deferents, eccentrics and equants, he succeeded in doing what his forebears had hoped for for so long – devising a system that could explain all the observed movement in the heavens in terms of spheres and circles.

When ancient and medieval astronomers, and also early Copernicans, spoke of ‘spheres’, they weren’t referring to the planets themselves. Since Aristotle first introduced the idea, long before Ptolemy, most astronomers had visualized the movement of each planet as taking place within the confines of its own invisible ‘crystalline sphere’. Not everyone agreed as to the nature and mechanics of these spheres.

In order to understand this concept, you must not imagine a flat drawing of circles within circles, but picture instead a three-dimensional glass object made up of transparent (invisible) spheres-within-spheres-within-spheres, nested like Russian dolls – or like the bubbles within bubbles that skilled bubble-pipe blowers can produce. In the Ptolemaic arrangement, the Earth, at the centre, is surrounded by a sphere within which the Moon moves, and both of these are surrounded by a larger sphere representing the level at which Mercury moves, which in turn is surrounded by a still larger sphere representing the level at which Venus moves. Surrounding these three spheres is a sphere representing the level at which the Sun
moves
, and so on and so forth – larger and larger nested spheres representing the levels at which each of the other planets moves. The outermost sphere represents the level of the stars.

In Ptolemaic astronomy, each sphere leaves enough room for all that planet’s epicycles. However, it leaves room for no
more
than that. Ptolemy took from Aristotle the notion that the cosmos is a plenum. In other words, it is ‘full’ in the sense that there can be no empty spaces between the spheres of the planets. Unlike Russian dolls or bubbles from a bubble pipe, the arrangement leaves no area that is not part of a sphere. The borders of the spheres ‘touch’. For instance, the sphere of Jupiter, defined by Jupiter’s nearest and furthest distances from the Earth, has an ‘inner border’ that is right up against the ‘outer border’ of the sphere of Mars – and so on and so forth with each planet’s sphere and the spheres of its neighbours. Ptolemaic astronomy saw the spheres as pushing one another along. Movement originating in the sphere of the stars was thus transferred to the spheres of the planets, causing their circular movement.

In his most famous work, the
Almagest
, Ptolemy was chiefly concerned with predicting the positions of the heavenly bodies, not their distances. However, working from Ptolemy’s planetary scheme in that book, it’s possible to calculate the ratio between the planets’ greatest and least relative distances from Earth, and Ptolemy was later to insist that this could be transformed into
absolute
distances. Ptolemy did the calculation first for the Moon and found that the least distance to the Moon was 33 times the radius of the Earth (that radius was known from Eratosthenes’s measurement), and the greatest distance 64 times the Earth’s radius. In a work that came after the
Almagest
, called
Planetary Hypotheses
, he applied the same thinking to the planets and to the Sun, taking the scheme that had been largely of mathematical significance in the
Almagest
and treating it as ‘real’ in terms of absolute distances. Ptolemy was unable to make it all work out without any glitches, but a strong argument
in
favour of his method nevertheless was that, with only small discrepancies, the results were largely in agreement with results of the study of eclipses.

As Ptolemy summed up his findings: the distance to the borders of the region ‘of air and fire’ (the ‘sublunar’ region) is 33 times the radius of the Earth’s surface (‘the spherical surface of earth and water’). At that radius, the sphere of the Moon begins. Its further border is 64 times that of the radius of the Earth (this was roughly where Aristarchus placed the Moon), and that is where the sphere of Mercury begins. And so on from there. The outer border of the sphere of Mercury is 166 times the Earth’s radius; Venus, 1,079 times; the Sun, 1,260 (which agreed with Aristarchus’s erroneous measurement to the Sun); Mars, 8,820; Jupiter, 14,189; Saturn, 19,865. That radius is where the sphere of the fixed stars begins. When it came to the absolute distance to the fixed stars, Ptolemy wrote: ‘The boundary that separates the sphere of Saturn from the sphere of the fixed stars lies at a distance of five myriad myriad and 6,946 myriad stades and a third of a myriad stades.’ That comes out to 569,463,333 stades. Translated into modern miles, roughly 50 million miles. Today we measure the distance to the nearest star as over 25 trillion miles.

The term ‘Ptolemaic astronomy’ is a bit of a misnomer. It doesn’t refer to a specific set of solutions coming from Ptolemy himself or any one of his successors. Instead, it means the combination and recombination of Ptolemy’s devices as astronomers used them over the centuries. It is ironic to note that modern physicists and astronomers – who believe so firmly in a moving Earth – can recognize the power of these devices better today than 16th-century Ptolemaic astronomers could. It takes understanding acquired through Copernican astronomy, as well as more highly developed mathematics than were available to ancient and medieval scholars, to appreciate how successful the older system potentially
was
.

Ptolemy’s work wasn’t lost with the decline of ancient
civilizations
. It had reached Baghdad in the eighth century
AD
, and there it was translated into Arabic. The
Almagest
is an Arabic title meaning ‘The Greatest’. From the eighth to the 13th and 14th centuries, the development of ‘Western’ mathematics, astronomy and astrology (astronomy and astrology were one and the same discipline then and continued to be even as late as the 17th century) took place not in Latin Europe but in the Middle East, north Africa and Moorish Spain. Most scholars there who were responsible for this growth were Islamic, but not all, for these societies were cosmopolitan and tended to be tolerant of non-Islamic thinkers. Mathematicians and astronomers moved beyond the mathematical methods of the Greeks and Ptolemy, constructing observatories in Baghdad, Cairo, Damascus and other leading cities. These observatories contained no telescopes, of course, but they did have intricate apparatuses – some inherited from the ancients and others that were newer inventions – to help plot the movements of the planets. Astronomical instruments came both in large bulky sizes, made of masonry, and in smaller portable models.

Islamic astronomers seem never to have questioned the Earth-centred model. However, they did criticize Ptolemy on details, particularly for the use of the equant, which, of his devices, seemed nearest to violating the requirement of uniform circular motion. When Ptolemaic astronomy later became a well-established field of study in European centres of learning, European scholars did not forget their debt to Islamic scholarship. Copernicus mentioned some of his Islamic scientific forebears by name in his book
De revolutionibus
.

There were attempts among Islamic astronomers to estimate the distances to the planets and the stars. One man who tried was Al Fargani, a ninth-century Arab astronomer who attempted to gauge the sizes of the spheres and worked out relationships among these sizes. As Ptolemy had done, he allowed each sphere to be large enough to contain its planet’s epicycles. Starting from a measurement of the Earth’s radius of
3,250
Roman miles, he then used these relationships to calculate the distances to all the known planets and to the sphere of the stars. His measurement of the distance to the stars had them more than 75 million miles from the Earth, half again as far as Ptolemy put them. The modern distance measurement to the nearest star is in the neighbourhood of a million times greater than Al Fargani estimated to the sphere of the stars, but 75 million miles from the Earth was still a huge distance, and the sublunar (lower than the Moon) region in Al Fargani’s universe was tiny indeed by comparison.

Ptolemaic astronomy, preserved and improved by Islamic scholars, filtered slowly into Latin Europe beginning as early as the 11th century, but European scholars were much quicker to assimilate other ancient thinking and much more strongly influenced by it. The translation of Aristotle into Latin in the 12th century had a profound impact. Scholars came to revere him not just as
a
philosopher, but as ‘
the
Philosopher’ – no other identification required – and the final authority on science and cosmology. With the passage of time, Aristotelian cosmology as interpreted by medieval scholars merged with medieval Christian thought and, somewhat later, with Ptolemaic astronomy – which agreed with Aristotle in many, but not all, respects. Scholars, who at that time were also clergy, after a period of disagreement and debate settled on ways to reconcile the Bible with Aristotle. In order to accomplish this, they gave scripture a less literal, more metaphorical reading. They also eventually succeeded, to their satisfaction, in resolving contradictions among Ptolemy, Aristotle and other ancient scholars to produce a coherent body of philosophical, religious and scientific thought.

Aristotelian/Ptolemaic astronomy provided a visual, geometric structure for abstract medieval Judaeo-Christian concepts, with all the rest of creation centring on that stationary Earth that is the home of humankind – a singularly unsavoury place in Aristotle’s philosophy, fallen from God’s grace in
Judaeo
-Christian teaching, and minuscule according to Al Fargani. By the 13th century, educated Europeans were taking it for granted that this world-view represented reality, and Dante, in the 14th century, both reflected and reinforced it in his
Divine Comedy
. He described a descent through the nine circles of hell towards the centre of the Earth – the vilest point in the universe – and an ascent through the celestial spheres in which the planets move, to the throne of God.

By the time Copernicus was born in the 15th century, the simple Aristotelian picture of the cosmos and complex Ptolemaic astronomy (as received from the Arabs) had been mingling for at least two hundred years in the minds of European thinkers. Decked out in poetry and metaphor by Dante, this Aristotelian/Ptolemaic/Judaeo-Christian view of the universe now not only described and predicted heavenly movement with reasonable accuracy and served as a map of the physical universe, but had also come to portray the human condition and the geography of the spiritual universe: among all creatures, only humans, fallen though they were, combined the material and the spiritual. Humanity was torn between the two, stuck on the debased squalid central Earth but always within view of and reaching out for the holy, pure and changeless realms beyond.

At the same time, the notion that the Aristotelian/Ptolemaic picture of the universe might be wrong was not completely absent from European thought. In the 14th century it took the form of a challenge to Aristotle, not to Ptolemy, when Parisian Nicole Oresme wrote a commentary criticizing Aristotle’s conclusion that the Earth didn’t move. Oresme didn’t propose that the Earth moved in orbit. There is no suggestion that he thought of that. Actually, he didn’t even conclude that it rotated, only that Aristotle had not proved it
didn’t
. A century later, Cardinal Nicholas of Cusa, a scholar who died nine years before Copernicus’s birth, also suggested that the Earth was not lying motionless in the centre of the universe. Nicholas of Cusa, however, failed to suggest another centre. The next and far
stronger
challenge to Aristotle, Ptolemy and Dante was to come from Copernicus.

Today the Polish city of Torun on the banks of the Vistula River has large modern buildings, but there also still exists a section of Old Town whose narrow cobbled streets can’t have changed much since 1473, when Mikolaj Kopernik was born here. It was common practice in scholarly circles to Latinize one’s name. Mikolaj Kopernik became Nicolaus Copernicus.

Poland has had a tumultuous history and has often been divided and dominated by foreigners, but the period during which Copernicus lived was a relatively peaceful, prosperous time. Copernicus’s father and grandfather evidently were merchants – well off if not spectacularly wealthy – and his mother came from a prominent Torun family. When Copernicus was 10, his father died and his mother’s brother took charge of Copernicus’s upbringing and education. That uncle rose to become Bishop of Warmia, an influential position from which to advance the careers of his nephews.

When Copernicus was 18 and his brother Andrzej (Latinized to Andreas) 20, the two young men enrolled in the Jagiellonian University in Krakow, one of the most celebrated seats of learning in Europe and renowned for its astronomy. One of Copernicus’s purchases while he was a student there was a set of the Alphonsine Tables. These tables, used for finding the positions of the Sun, Moon and planets based on Ptolemy’s theories and Islamic observations, had been computed in the 13th century at the behest of King Alphonso of Castille. Copernicus’s copy still exists. Judging from the stains, he used it a great deal.