Hostname: page-component-7b7567c8c-kwt9d Total loading time: 0 Render date: 2026-11-12T09:58:27.815Z Has data issue: false hasContentIssue false
  • English
  • Français

How Kepler discovered the elliptical orbit

Published online by Cambridge University Press:  22 September 2016

Eric J. Aiton
Eric J. Aiton*
Affiliation:
Didsbury College of Education, Wilmslow Road, Manchester M20 8RR
Get access

Extract

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.

Information

Type
Research Article
Information
The Mathematical Gazette , Volume 59 , Issue 410 , December 1975, pp. 250 - 260
Copyright
Copyright © Mathematical Association 1975

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

Article purchase

Temporarily unavailable

References

1. Koyré, A., Newtonian studies, p. 128. Chapman and Hall (1965).Google Scholar
2. Aiton, E. J., Kepler’s second law of planetary motion, Isis 60, 75–90 (1969).Google Scholar
3. Wilson, C., Kepler’s derivation of the elliptical path, Isis 59, 5–25 (1968).Google Scholar
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).Google Scholar
5. Hofmann, J. E., Ueber einige fachliche Beiträge Keplers zur Mathematik, in Internationales Kepler-Symposium (1973).Google Scholar
6. Aiton, E. J., Infinitesimals and the area law, in Internationales Kepler-Symposium (1973).Google Scholar
7. Gingerich, O., Kepler’s treatment of redundant observations, in Internationales Kepler-Symposium (1973).Google Scholar
8. Wilson, C., How did Kepler discover his first two laws? Scient. Am. 226, 93–106 (1972).Google Scholar
9. Fladt, K., Das Keplersche Ei, Elem. Math. 17, 73–78 (1962).Google Scholar
10. Aiton, E. J., The vortex theory of planetary motions, pp. 16–17. Macdonald and Elsevier (1972).Google Scholar
11. Whiteside, D. T., Keplerian planetary eggs, laid and unlaid, 1600–1605, J. Hist. Astron. 5, 1–15 (1974). See especially p. 14.Google Scholar