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set out in the Secret of the Universe was too simplistic.

The judgement of history relegates Kepler's polyhedral hypothesis for the planetary spacings, which fills most of the Secret of the Universe, to an interesting curiosity. But three of the twenty-three chapters are about a different problem - that of explaining the speeds of the planets - and here Kepler's treatment proved extremely significant. Kepler noted that as one moved out through the planets, the periods of their orbits increased at a greater rate than their distances from the Sun. Hence, the speeds of the planets decreased. Kepler's conclusion was that the driving force behind the Universe comes from the Sun (he referred to a 'moving soul' within the Sun) and that the effect of this 'force' weakens as one moves away from the Sun. This also provided added justification for the position of the Sun at the centre of the Universe.

Quite how the orbital periods depended on the distances from the Sun eluded Kepler for the time being - he simply did not have data accurate enough for him to find the correct law46 - but in retrospect we know that he was asking the right questions. Kepler also realized that his physical hypothesis implied that the planets moved at varying speeds as they moved round their orbits, by virtue of the fact that the distance to the Sun varied. Again, Kepler did not have the information at his disposal that could point him to the correct relationship between speed and distance, but the desire to find a physical cause for the planetary motions had led him to a crucial realization: planets do not move at a constant speed. Of course, he did not yet have any proof for his hypothesis, but he hadbroken away from the 2000-year-old dogma of uniform circular motions.

Kepler realized that Ptolemy had achieved just such a change in speed by his introduction of the equant. When a planet is closest to the Earth in Ptolemy's theory and, hence, furthest from the equant, it must move more quickly than at

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