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How Kepler discovered the elliptical orbit

  • Eric J. Aiton (a1)


In his Newtonian studies Alexandre Koyré remarked that, from the area law of planetary motion, Kepler erroneously deduced that the planets move in their orbits with speeds inversely proportional to the distances from the sun. It was this assertion, which I suspected to be false, that led me to make a detailed study of the discovery of the area law. Quite independently and unknown to me, Curtis Wilson had been making a similar study of the discovery of the elliptical orbit. Since the arguments leading to the two Keplerian laws are inter-dependent, our researches may be described as variations on the same theme. What I wish to do this evening is to explain in simple terms our reconstruction of Kepler’s path to the elliptical orbit and the area law.



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1. Koyré, A., Newtonian studies, p. 128. Chapman and Hall (1965).
2. Aiton, E. J., Kepler’s second law of planetary motion, Isis 60, 7590 (1969).
3. Wilson, C., Kepler’s derivation of the elliptical path, Isis 59, 525 (1968).
4. Schiffers, N., von Theologie, Das Verhältnis und Kepler, Naturwissenschaft bei, and Hübner, J., Naturwissenschaft als Lobpreis des Schöpfers, in Krafft, F., Meyer, K., Sticker, B. (eds.), Internationales Kepler-Symposium Weil der Stadt 1971, Gerstenberg (Hildesheim, 1973).
5. Hofmann, J. E., Ueber einige fachliche Beiträge Keplers zur Mathematik, in Internationales Kepler-Symposium (1973).
6. Aiton, E. J., Infinitesimals and the area law, in Internationales Kepler-Symposium (1973).
7. Gingerich, O., Kepler’s treatment of redundant observations, in Internationales Kepler-Symposium (1973).
8. Wilson, C., How did Kepler discover his first two laws? Scient. Am. 226, 93106 (1972).
9. Fladt, K., Das Keplersche Ei, Elem. Math. 17, 7378 (1962).
10. Aiton, E. J., The vortex theory of planetary motions, pp. 1617. Macdonald and Elsevier (1972).
11. Whiteside, D. T., Keplerian planetary eggs, laid and unlaid, 1600–1605, J. Hist. Astron. 5, 115 (1974). See especially p. 14.

How Kepler discovered the elliptical orbit

  • Eric J. Aiton (a1)


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