The Day the Universe Changed - James Burke [70]
In 1600 he was invited to become Tycho Brahe’s assistant in Benatky Castle outside Prague, where the great man had become Royal Astronomer to the imperial court. Kepler passed a stormy eighteen months with Brahe, during which he learned the value of Brahe’s obsession with precise observation. When Brahe died in 1602, Kepler took over the mountain of paperwork which the old man had left behind. Over the next few years he buried himself in Brahe’s figures. With twenty years of nightly observation at his fingertips, Kepler was able to study planetary movement in unparalleled detail. He was possessed by the desire to find universal laws which would show that the universe operated ‘like clockwork’. It was the mysterious and persistent anomaly in Brahe’s data on planetary behaviour which led him to those laws.
There was something wrong with the motion of Mars. Its path around the sun was unequal, without the symmetry to be expected from a circular, Aristotelian orbit. The planet’s path was eight minutes of arc longer on one side of the sun than the other. The discovery of this discrepancy was to revolutionise astronomy.
After completing nine hundred pages of calculation during four years’ study of the data, Kepler realised that the orbit was not circular but elliptical. But the extraordinary thing was that the orbit was regular. The only way in which an elliptical orbit could repeat itself as regularly as a circular one would be because of some constantly varying influence on the planet’s behaviour. Kepler noted that the further out from the sun the planets were, the slower they moved. Was there some waning force involved? To Kepler, who believed in Gilbert’s theory of a magnetic sun, this was the obvious answer.
He looked at the orbit of Mars to see how it varied. The results showed that in its elliptical orbit the planet speeded up close to the sun and slowed down far from it at a regular rate. Using this regularity Kepler showed that if a line were drawn from the sun to Mars, as the planet moved in orbit the line would sweep out equal areas of the space contained in the orbit, in equal times. The change in speed was therefore exactly relative to the distance of the planet from the sun.
Kepler’s method of measuring the area swept out by the planet was the old Archimedian way. He divided the area between the sun and the planet into a series of triangles and measured them. The larger the number of triangles, the smaller the loss of accuracy due to the unmeasured area between the bases of the triangles and the curve of the orbit beyond them.
Kepler’s illustration of how the ‘attractive virtue’ of the sun might account for the elliptical nature of planetary orbits. Left, the tortuous geometry needed for calculation before the invention of calculus. The compass needles (top right) indicate his concept of the ‘virtue’ as a kind of magnetism.
Sixteenth-century wine merchants measure the volume of their barrels with dipsticks. It was this method which Kepler worked to improve. Above left: A diagrammatic view of how Kepler arrived at the concept of infinitesimals through measuring wine (see text, left). The technique permitted so much greater accuracy in interpreting Brahe’s observational data on planetary orbits that Kepler was able to confirm the elliptical behaviour of Mars.
Kepler improved on the technique soon after he moved to Linz, in 1612. There he noticed that the local wine-merchants measured the amount of wine held in different shaped