Astronomy and Astrophysics – Astronomy
Scientific paper
Jul 2003
adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=2003ahes...57..355d&link_type=abstract
Archive for History of Exact Sciences (ISSN 0003-9519), Vol. 57, No. 5, p. 355 - 393 (2003)
Astronomy and Astrophysics
Astronomy
1
History Of Astronomy, Kepler Laws
Scientific paper
After the discovery of his three laws, Kepler invented a way of proving the Area Law when applied to the path of a primary planet (the ellipse with one focus at the Sun). The law states that the area swept out by the line joining the planet to the Sun measures the time taken: Kepler was therefore dealing with a restricted version of Newton's general area-proposition. Kepler's demonstration was set out in Epitome V (1621), and consisted of matching an element of area to an element of time, where each was mathematically determined. His treatment of the area depended solely on the geometry of Euclid's Elements, involving only straight-line and circle propositions - so we have to account for his deliberate avoidance of the sophisticated conic-geometry associated with Apollonius. We show also how his proof could have been made watertight according to modern standards, using methods that lay entirely within his power. The greatest innovation, however, occurred in Kepler's fresh formulation of the measure of time. We trace this concept in relation to early astronomy and conclude that Kepler's treatment unexpectedly entailed the assumption that time varied nonuniformly; meanwhile, a geometrical measure provided the independent variable. Even more surprisingly, this approach turns out to be entirely sound when assessed in present-day terms. Kepler himself attributed the cause of the motion of a single planet around the Sun to a set of 'physical' suppositions which represented his religious as well as his Copernican convictions; and we have pared to a minimum - down to four - the number he actually required to achieve this. In the Appendix we use modern mathematics to emphasize the simplicity, both geometrical and kinematical, that objectively characterizes the Sun-focused ellipse as an orbit. Meanwhile we highlight the subjective simplicity of Kepler's own techniques (most of them extremely traditional, some newly created). These two approaches complement each other to account for his success.
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