The Copernican theory fitted the planet orbits of small eccentricity (Venus, Earth. Jupiter and Saturn), but, as with the Ptolemaic-theory, Mars remained a problem. Discrepancies of more than a degree, unacceptable by any observational standards, still persisted. To Johannes Kepler (1571- 1630). enthralled with the beauty and symmetry of the heavens, the Copernican fit was not sufficient. He considered there must be a simple, geometric relation describing the motions of the celestial bodies.

His first thoughts on the geometric configuration of the heavens were published in 1596 in the ‘Mysterium Cosmographicum’. This account of the relations between the numerical quantities occur¬ring in the Solar System represents the beginning of his search for a harmonic relationship between the sizes of orbits of the various planets and their periods of revolution about the Sun, a search which was to last about 25 years. But first he had to find out why Mars would not obey the Copernican heliocentric theory. He began this project under the supervision of Tycho Brahe, (1546-1601). around the year 1600. Tycho had made an incomparable series of observations including regular observations of Mars over a long period. After Tycho’s death in 1601, Kepler fortunately succeeded in getting control of the greater part of them. Many years of arduous computation and guess-work began.

Initially, Kepler proceeded along Copernican lines. Eventually he abandoned this approach in favour of an entirely new one. He decided to try and determine the actual shape of the orbit so a whole new series of calculations began. He first tried combination after combination of eccentric. epicycle and equant until he reached a scheme which could represent the observations to an accuracy of eight minutes of arc. This was not close enough, so he forsook circles in favour of various ovals. Finally he achieved the long-sought and far-reaching synthesis with an ellipse and found that, if the Sun were at one focus, it satisfied the problem beautifully. He had solved the problem of the shape of the orbit, and proceeded to find out how the planet moved in this known orbit. Again many attempts were necessary before he made his second elegant discovery, that the straight line joining the planet to the Sun sweeps out equal areas in equal times. Both these results, now known as Kepler’s laws were published in the ‘Astronomia Nova’ in 1609. His full investigation of Mars, ‘Commentaries on the Motions of Mars’ was also published in that year. In the following years he satisfied himself that these rules applied to the whole Solar System and investigated other astronomical problems.

By 1619 he had proposed a further empirical rule – the square of the period of revolution of any planet is proportional to the cube of its mean distance from the Sun. This was published in his ‘Harmony of the World’ and is now known as Kepler’s third law. Kepler’s three” rules suddenly made the problem of describing planetary motions look simple. They were, however, empirical rules with no dynamical basis. The link between these rules and the laws of physics was found by Newton.

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