Kepler and Mathematical Techniques

Kepler came across John Napier's work on logarithms (published 1614) in 1617, and then Napier's logarithmic tables in an edition by Benjamin Ursinus. He also made use of the tables of Philip Landsberg in his New Astronomy. Lacking any description of their construction, he recreated his own tables by a new geometrical procedure. These tables were crucial to his Rudolphine Tables. Wilhelm Schickard at the University of Tübingen designed a calculating machine to help with Kepler's logarithmic calculations. In the Epitome of Copernican Astronomy, Kepler introduced what is now known as 'Kepler's equation' for the solution of planetary orbits:

E - e sin E = M
E: eccentric anomaly
e: eccentricity of the ellipse
M: mean anomaly

(need diagram for this)

M is easily found if E is known, but to find E given the time, there is no simple or exact solution. In the Rudophine Tables, Kepler solved the equation for a uniform grid of E values and provided an interpolation scheme for the desired values of M.

Recommended Reading

Owen Gingerich, 'Kepler', in the Dictionary of Scientific Biography, vol. 7 & 8, New York 1981, 289-312.

John North, The Fontana History of Astronomy and Cosmology, London 1994, pp. 309-26

Full Bibliography