The Mathematical Approach

Abstract

Johannes Kepler (1571–1630) is known primarily as the discoverer of three fundamental laws of planetary motion.1 He made Copernicus’ heliocentric theory much more plausible than it had been before by showing that the planetary orbits need not be represented by some 50 cumbersome circles. Rather, 6 neat ellipses, one for every planet, sufficed for accounting for all known astronomical data. His other two laws concern the relationship between orbital velocity and distance from the sun (the radius vector sweeps equal areas in equal times), and between period of revolution and mean distance from the sun (the former squared is proportional to the third power of the latter). Central to these astronomical discoveries was Kepler’s revolutionary hypothesis of a force emanating from the sun, which somehow governed the motions of the planets. An extensive account of these discoveries (apart from the third law) as well as the way Kepler had reached them was given in Astronomia Nova (1609; ‘The New Astronomy’); he summarized them in text-book fashion in the Epitome Astronomiae Copernicanae (1618 – 1621 ; ‘Abstract of Copernican Astronomy’). The original announcement of the third law is contained in Kepler’s other major work, the Harmonices Mundi Libri V (1619; ‘Five Books on the Harmony of the World’). Apart from the third law, the content of this book has not contributed to positive science to the extent the other books mentioned have (as well as Kepler’s work in fields like geometrical optics and pure mathematics).