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This then was another new star, another change in the changeless heavens. An earlier observer, Peter Bieniwitz, had noticed that comets’ tails always pointed away from the sun, so they appeared to be under solar influence. According to Aristotle this should mean that they were in the sphere of the sun. However, only one object was carried by each planetary sphere. Was there an extra sphere for the comet? Brahe’s data showed incontrovertibly that the comet was moving in an oval path, which meant that it was moving through the planetary spheres. This was impossible.

Brahe’s compromise with Copernicanism. In his model all the planets revolve round the sun, the group of the sun and planets in turn revolving round the earth-moon system. For those who could not accept a full-blooded heliocentric universe, this approach was very popular.

Brahe published his conclusions. ‘There are not really any spheres in the Heavens… it seems futile to undertake this labour of trying to find a real sphere, to which the Comet may be attached… [Comets] cannot by any means be proved to be drawn round by any sphere.rsquo;

Brahe was not prepared to accept a full-blooded Copernican explanation. He devised a compromise system. All the planets orbited the sun, but the sun itself orbited the earth, with the moon. Brahe found no answer for the really difficult problem of oval orbits. If such a thing were possible, how could a non-circular orbit remain regular and not become unstable?

Meanwhile the major question thrown up by his findings was, if the planets were not kept up by crystalline spheres, why did they not fall? And if they were not attached to spheres, in what medium were they moving?

In 1591, the son of an unsuccessful cloth merchant in Pisa went, at the age of twenty-seven, to take up the post of Professor of Mathematics at the university of Padua. His name was Galileo Galilei, and he was to pass an uneventful eighteen years in Padua working on the answer to Brahe’s question. Galileo believed that in the matter of falling objects and flying projectiles there were laws of behaviour that could be applied equally well on earth and in the sky.

Galileo brought about an intellectual revolution by proposing that physicists should dispense with Aristotelian ‘essences’. His view was that the only way to find out what was happening was to observe and experiment; that in experiment one should look for the nearest cause for a phenomenon, and for events or behaviour that were regular in occurrence, which could be repeatedly observed; that the universe could be reliably observed by the senses; and that everything should be reduced, if possible, to mathematics.

The difficulty with finding out how things fell, and reducing the event to mathematics, was that the things fell too fast to be easily studied and behaved in ways that demanded accuracy of measurement to within split seconds. In 1602 Galileo began using the invention of a medical friend, Santorio Santori. The device was a pulse counter, consisting of a stick marked with a scale and with a weighted thread hung from one end. Moving the weight up and down altered the frequency of the swing, and the time taken by the swing could then be read off the scale relating to the position of the weight.

Galileo used this timing instrument to make the great conceptual leap from hypothesising on the behaviour of balls flying through the air to actual experiment, because he had thought the experiment out first in abstract and then applied the result in practice. He reasoned that any object moving in a straight line, whether because of impetus or not, would tend to continue in the same direction until affected by its tendency, or an attractive force of some kind, when it would fall to earth. He had noticed that falling objects accelerated. As a cannon-ball began the downward part of its trajectory, it would speed up: its motion would be a mixture of forward and downward movement, shifting