Kepler followed the ancients in always starting to measure at the point furthest from the Sun. (The time is measured by the fraction of the total time taken for the planet to complete one whole circuit, that being called its period T T T. Law II (the Area Law ) - the time taken by a planet to reach a particular position is represented by the area swept out by the radius vector drawn from the fixed Sun.įrom these we can find either what the position of the planet is at a given time, or, the time when the planet is in a given position.Law I (the Ellipse Law ) - the curve or path of a planet is an ellipse whose radius vector is measured from the Sun which is fixed at one focus.These are found in Astronomia Nova Ⓣ ( New Astronomy ) 1609, underpinned by important work in Epitome Ⓣ ( Epitome of Copernican Astronomy ) Book V (1621). There were such three laws, but here we shall deal only with the first two - those that govern the motion of an individual planet. The greatest achievement of Kepler (1571- 1630) was his discovery of the laws of planetary motion. These are listed on the web site mentioned at the end they also contain references to traditional accounts which are becoming superseded. While analysis of his success has led to some unexpected conclusions, the present overview has been endorsed in detail by articles published in learned historical journals. But Kepler was a highly-talented geometer, and until now has there been no investigation of his work (derived from the original Latin ) which has highlighted the mathematical aspect of his brilliance. This account of Kepler's mathematical astronomy may well challenge some cherished and long-held beliefs, since most of what has been written about Kepler has either been based on secondary or tertiary sources, or has concentrated on his astronomical background and techniques.
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