Hostname: page-component-78c5997874-4rdpn Total loading time: 0 Render date: 2024-11-05T13:44:26.636Z Has data issue: false hasContentIssue false
  • English
  • Français

Early Numerical Analysis in Kepler's New Astronomy

Published online by Cambridge University Press:  26 January 2010

Steinar Thorvaldsen
Steinar Thorvaldsen*
Affiliation:
University of Tromsø, Norway
Get access Rights & Permissions [Opens in a new window]

Argument

Johannes Kepler published his Astronomia nova in 1609, based upon a huge amount of computations. The aim of this paper is to show that Kepler's new astronomy was grounded on methods from numerical analysis. In his research he applied and improved methods that required iterative calculations, and he developed precompiled mathematical tables to solve the problems, including a transcendental equation. Kepler was aware of the shortcomings of his novel methods, and called for a new Apollonius to offer a formal mathematical deduction. He was also in great need of computational power, and his friend and colleague, Wilhelm Schickard, constructed the first prototype of a true mechanical calculator, although it never came into regular use. The article concludes that Kepler's new astronomy was clearly backed up by numerical methods and embedded concepts and challenges of great importance for the future development of numerical analysis.

Type
Research Article
Information
Science in Context , Volume 23 , Issue 1 , March 2010 , pp. 39 - 63
Copyright
Copyright © Cambridge University Press 2010

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.)

References

Aaboe, Asgar. 1954. “Al-Kashi's Iteration Method for the determination of sin1.” Scripta mathematica 20:24–29.Google Scholar
Aiton, Eric John.1973. “Infinitesimals and the Area Law.” In Internationales Kepler-Symposium Weil der Stadt 1971, edited by Kraft, Fritz et al., 285–305. Hildesheim: H. A. Gerstenberg Verlag.Google Scholar
Applebaum, Wilbur. 1996. “Keplerian astronomy after Kepler: Researches and Problems.” History of Science 34 (106):451–504.CrossRefGoogle Scholar
Beer, Arthur and Beer, Peter. 1975. “Four Hundred Years: Proceedings of Conferences held in Honour of Johannes Kepler.” Vistas in Astronomy 18:3–1034.Google Scholar
Belyi, Ju A. 1975. “Johannes Kepler and the Development of Mathematics.” Vistas in Astronomy 18: 643–660.CrossRefGoogle Scholar
Bialas, Volker. 1969. Die Rudolphinischen Tafeln von Johannes Kepler. Matematische und astronomische Grundlagen. München: Bayerischen Akademie der Wissenschaften.Google Scholar
Bialas, Volker. 1970. Eine doppelte Iterationsrechnung von Johannes Kepler und ihre Programmierung. München: Bayerische Akademie der Wissenschaften.Google Scholar
Cantor, Moritz. 1894–1901. Vorlesungen über Geschichte der Mathematik. Leipzig: Teubner.Google Scholar
Caspar, Max and von Dyck, Walther. 1930. Johannes Kepler in seinen Briefen. Munich and Berlin.Google Scholar
Caspar, Max. [1938] 1993. Johannes Kepler. Translated from German to English by Hellman, C. Doris. Mineola, NY: Dover.Google Scholar
Chabert, Jean-Luc, et al. 1999. A History of Algorithms. Springer-Verlag.CrossRefGoogle Scholar
Colwell, Peter. 1993. Solving Kepler's Equation over Three Centuries. Richmond, VA: William-Bell.Google Scholar
Costabel, Pierre. 1975. “Kepler – Mathematician and Physicist.” Vistas in Astronomy 18:631–660.CrossRefGoogle Scholar
Davis, Ann Elizabeth Leighton. 1992. “Kepler's Resolution of Individual Planetary Motion.” Centaurus 35:97–191.CrossRefGoogle Scholar
Davis, Ann Elizabeth Leighton. 2003. “The Mathematics of the Area Law: Kepler's Successful Proof in Epitome Astronomiae Copernicanae (1621).” Archive for History of Exact Sciences 57 (5):355–393.CrossRefGoogle Scholar
Field, Judith Veronica. 1988. “What is Scientific about a Scientific Instrument?” Nuncius 2 (3):3–26.CrossRefGoogle Scholar
Freytag-Löringhoff, Bruno Baron Von. 1978. “Die Rechenmaschine.” In Wilhelm Schickard, edited by Seck, Friedrich, 288–309. Tübingen: J. C. B. Mohr (Paul Siebrck).Google Scholar
Gingerich, Owen. [1964] 1993. “Computer versus Kepler.” American Scientist 52 (2):218–225. Reprinted in The Eye of Heaven: Ptolemy, Copernicus, Kepler, edited by Owen Gingerich, 357–366. New York: American Institute of Physics.Google Scholar
Gingerich, Owen. [1968] 1993. “The Mercury Theory from Antiquity to Kepler.” In Actes du XIIe Congrès International d'Histoire des Sciences, Vol. 3A, 57–64, Paris, 1968. Reprinted in The Eye of Heaven: Ptolemy, Copernicus, Kepler, edited by Owen Gingerich, 379–387. New York: American Institute of Physics.Google Scholar
Gingerich, Owen. [1973] 1993.“The Computer versus Kepler Revisited.” In Internationales Kepler-Symposium Weil der Stadt 1971, edited by Kraft, Fritz et al. , Hildesheim: H. A. Gerstenberg Verlag, 1973, 307–314. Reprinted in The Eye of Heaven: Ptolemy, Copernicus, Kepler, edited by Owen Gingerich, 367–378. New York: American Institute of Physics.Google Scholar
Goldstine, Herman H. 1977. A History of Numerical Analysis from the 16th Through the 19th Century. New York: Springer-Verlag.CrossRefGoogle Scholar
Hammer, Franz. 1958. “Nicht Pascal sondern der Tübinger Professor Wilhelm Schickard erfand die Rechenmaschine!” Büromarkt 20:1023–1025.Google Scholar
Helden, Albert van. 1976. “The Importance of the Transit of Mercury of 1631.” Journal for the History of Astronomy 7:1–10.CrossRefGoogle Scholar
Hon, Giora. 1987. “On Kepler's Awareness of the Problem of Experimental Error.” Annals of Science 44:545–591.CrossRefGoogle Scholar
Jardine, Nicholas. 1984. The Birth of History and Philosophy of Science: Kepler's A Defence of Tycho against Ursus with Essays on Its Provenance and Significance. Cambridge: Cambridge University Press.Google Scholar
Kennedy, Edward S. and Transue, William R.. 1956. “A Medieval Iterative Algorism.”American Mathematical Monthly 63:80–83.CrossRefGoogle Scholar
Kepler, Johannes. [1609, 1618–21, 1624, 1627] 1937–1990. Gesammelte Werke, Vols. III, VII, IX and X, edited by Caspar, Max et al. Munich: C. H. Beck.Google Scholar
Kepler, Johannes. [1609] 1992. New Astronomy. Translated by Donahue, William. Cambridge: Cambridge University Press.Google Scholar
Kepler, Johannes. [1618–1621] 1953 1995. Epitome of Copernican Astronomy, (book 4 and 5), translated by Wallis, Charles Glenn. New York: Prometheus Books.Google Scholar
Kistermann, Friedrich Wilhelm. 1995. “Die Rechentechnik um 1600 und Wilhelm Schickards Rechenmaschine.” In Zum 400. Geburtstag von Wilhelm Schickard, edited by Seck, Friedrich, 241–272. Sigmarinen: Jan Thorbecke Verlag.Google Scholar
Kistermann, Friedrich Wilhelm. 2001. “How to Use the Schickard Calculator.” Annals of the History of Computing 23 (1):80–85.CrossRefGoogle Scholar
Kollerstrom, Nicholas. 2004. William Crabtree's Venus Transit Observation. Proceedings IAU Colloquium No. 196, edited by Donald W. Kurtz.CrossRefGoogle Scholar
Kozhamthadam, Job. 1994. The Discovery of Kepler's Laws: The Interaction of Science, Philosophy, and Religion. Notre Dame: University of Notre Dame Press.Google Scholar
Lansbergen, Philippi. 1632. Tabulae motum coelestium.Google Scholar
Maeyama, Yasukatsu. 1990. “Kepler's Hypothesis Vicaria.” Archive for History of Exact Sciences 41:53–92.CrossRefGoogle Scholar
Martens, Rhonda. 2000. Kepler's Philosophy and the New Astronomy. Princeton: Princeton University Press.Google Scholar
Methuen, Charlotte. 1998. Kepler's Tübingen: Stimulus to a Theological Mathematics. Brookfield: Ashgate.Google Scholar
Russell, John L. 1964. “Kepler's Laws of Planetary Motion: 1609–1666.” British Journal for the History of Science 2:1–24.CrossRefGoogle Scholar
Small, Robert. [1804] 1963. An Account of the Astronomical Discoveries of Kepler. Madison: University of Wisconsin Press.Google Scholar
Smeur, A. J. E. M. 1978. “The Rule of False Applied to the Quadratic Equation, in three Sixteenth Century Arithmetics.” Archives internationales d'histoire des sciences: revue 28:66–101.Google Scholar
Stephenson, Bruce. 1987. Kepler's Physical Astronomy. New York: Springer.CrossRefGoogle Scholar
Swerdlow, Noel M. 2000. “Kepler's Iterative Solution of Kepler's Equation.” Journal for the History of Astronomy 31:339–341.CrossRefGoogle Scholar
Voelkel, James R. 2001. The Composition of Kepler's Astronomia nova. Princeton: Princeton University Press.Google Scholar
Whiteside, Derek T., ed. 1974. The Mathematical Papers of Isaac Newton, Vol. 6. Cambridge: Cambridge University Press.Google Scholar
Williams, Michael R. 1983. “From Napier to Lucas: The Usage of Napier's Bones in Calculating Instruments.” Annals of the History of Computing 5 (3):279–296.CrossRefGoogle Scholar