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      Figure 12 Tycho’s model makes the same error as Ptolemy’s and places the Earth at the centre of the universe, being orbited by the Moon and the Sun. His main breakthrough was to realise that the planets (and the fiery comet) orbit the Sun. This illustration is from Tycho’s De mundi ætherei.

      Before Tycho could continue to the next stage of his programme of astronomical observation and theorising, his research suffered a severe blow. His patron, King Frederick, died after a session of binge drinking in the same year that Tycho published De mundi ætherei, and the new king, Christian IV, was no longer prepared to fund Tycho’s lavish observatory or tolerate his hedonistic lifestyle. Tycho had no option but to abandon Uraniborg and leave Denmark with his family, assistants, Jepp the dwarf and cartloads of astronomical equipment. Fortunately, Tycho’s instruments had been designed to be transportable, because he had shrewdly realised: ‘An astronomer must be cosmopolitan, because ignorant statesmen cannot be expected to value their services.’

      Tycho Brahe migrated to Prague, where Emperor Rudolph II appointed him Imperial Mathematician and allowed him to establish a new observatory in Benatky Castle. The move turned out to have a silver lining, because it was in Prague that Tycho teamed up with a new assistant, Johannes Kepler, who would arrive in the city a few months later. The Lutheran Kepler had been forced to flee his previous home in Graz when the fiercely Catholic Archduke Ferdinand had threatened to execute him, in keeping with his stated declaration that he would rather ‘make a desert of the country than rule over heretics’.

      Fittingly, Kepler set out on his journey to Prague on 1 January 1600. The start of a new century would mark the start of a new collaboration that would lead to a reinvention of the universe. Together, Tycho and Kepler made the perfect double act. Scientific advance requires both observation and theory. Tycho had accumulated the best collection of observations in the history of astronomy, and Kepler would prove to be an excellent interpreter of those observations. Although Kepler suffered from myopia and multiple vision from birth, he would ultimately see farther than Tycho.

      It was a partnership that was formed in the nick of time. Within a few months of Kepler’s arrival, Tycho attended a dinner hosted by the Baron of Rosenberg and drank to his usual excess, refusing nonetheless to break etiquette by leaving the table before the Baron. Kepler recorded: ‘When he drank more, he felt the tension in his bladder increase, but he put politeness before his health. When he got home, he was scarcely able to urinate.’ That night he developed a fever, and from then on he alternated between bouts of unconsciousness and delirium. Ten days later he was dead.

      On his deathbed, Tycho repeatedly uttered the phrase: ‘May I not have lived in vain.’ There was no need to fear, because Kepler would guarantee that Tycho’s meticulous observations bore fruit. In fact, it is quite possible that Tycho had to die in order for his work to flourish, because while he was alive he carefully guarded all his notebooks and never shared his observations, always dreaming of publishing a solo masterwork. Tycho certainly never considered embracing Kepler as an equal partner – he was, after all, a Danish aristocrat, whereas Kepler was a mere peasant. However, seeing the deeper meaning of his own observations was beyond Tycho, and required the skills of a trained mathematician such as Kepler.

      Kepler was born into a lowly family that struggled to survive the upheavals caused by war, religious strife, a wayward criminal father and a mother who had been exiled after accusations of witchcraft. Not surprisingly, he grew up as an insecure hypochondriac with little self-esteem. In his own self-deprecating horoscope, written in the third person, he described himself as a little dog:

      He likes gnawing bones and dry crusts of bread, and is so greedy that whatever his eyes chance on he grabs; yet, like a dog, he drinks little and is content with the simplest food… He continually seeks the goodwill of others, is dependent on others for everything, ministers to their wishes, never gets angry when they berate him and is anxious to get back into their favour… He has a dog-like horror of baths, tinctures and lotions. His recklessness knows no limits, which is surely due to Mars in quadrature with Mercury and in trine with the Moon.

      His passion for astronomy seems to have been his only respite from self-loathing. At the age of twenty-five he wrote Mysterium cosmographicum, the first book to defend Copernicus’s De revolutionibus. Thereafter, convinced of the veracity of the Sun-centred model, he dedicated himself to identifying just what it was that made it inaccurate. The greatest error was in predicting the exact path of Mars, a problem that had plagued Copernicus’s assistant, Rheticus. According to Kepler, Rheticus had been so frustrated with his failure to solve the Mars problem that ‘he appealed as a last resort to his guardian angel as an Oracle. The ungracious spirit thereupon seized Rheticus by the hair and alternately banged his head against the ceiling, then let his body down and crashed it against the floor.’

      With access at last to Tycho’s observations, Kepler was confident that he could solve the problem of Mars and remove the inaccuracies in the Sun-centred model within eight days; in fact, it took him eight years. It is worth stressing the amount of time that Kepler spent perfecting the Sun-centred model– eight years!– because the brief summary that follows could easily underplay his immense achievement. Kepler’s eventual solution was the result of arduous and tortuous calculations that filled nine hundred folio pages.

      Kepler made his great breakthrough by jettisoning one of the ancient tenets, namely that the planets all move in paths that are circles or combinations of circles. Even Copernicus had clung loyally to this circular dogma, and Kepler pointed out that this was just one of Copernicus’s flawed assumptions. In fact, Kepler claimed that his predecessor had wrongly assumed the following three points:

      1. the planets move in perfect circles,

      2. the planets move at constant speeds,

      3. the Sun is at the centre of these orbits.

      Although Copernicus was right in stating that the planets orbit the Sun and not the Earth, his belief in these three false assumptions sabotaged his hopes of ever predicting the movements of Mars and the other planets with a high degree of accuracy. However, Kepler would succeed where Copernicus had failed because he discarded these assumptions, believing that the truth emerges only when all ideology, prejudice and dogma are set aside. He opened his eyes and mind, took Tycho’s observations as his rock and built his model upon Tycho’s data. Gradually an unbiased model of the universe began to emerge. Sure enough, Kepler’s new equations for the orbits matched the observations, and the Solar System took shape at last. Kepler exposed Copernicus’s errors, and showed that:

      1. the planets move in ellipses, not perfect circles,

      2. the planets continuously vary their speed,

      3. the Sun is not quite at the centre of these orbits.

      When he knew he had the solution to the mystery of planetary orbits, Kepler shouted out: ‘O, Almighty God, I am thinking Thy thoughts after Thee.’

      In fact, the second and third points in Kepler’s new model of the Solar System emerge out of the first, which states that planetary orbits

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