Kepler's First Thoughts on Oval Orbits: Text,Translation,and Commentary

Research for this article was supported by a grant from the American Philosophical Society. The assistance of Dr Volker Bialas of the Kepler Kommission of the Bayerische Akademie der Wissenschaften in preparing the transcription is gratefully acknowledged.

The contents and chronology of the Mars notebook are treated at some length (with a few minor errors) in Gingerich Owen , “Kepler's treatment of redundant observations”, in Internationales Kepler-Symposium Weil der Stadt 1971, ed. by Krafft F. Meyer K. and Sticker B. (Hildesheim, 1973), 309–14. The present account is based largely upon Gingerich's work.

Gingerich ( ibid. , 309–10) dates the ending of the notebook as the end of 1601, largely because he had not succeeded in finding any reference to the oval hypothesis, which Kepler later said he had developed in early 1602 (Letter to Longomontanus, 1605, no. 323 in Gesammelte Werke, xiv, 134–43).

K435 = P307. The first number is Kepler's, while the second is the folium number in vol. xiv of the manuscripts, added by a later hand. This page is a recto; had it been a verso, the second number would have been followed by a superscript ‘v’. Because some of the pages are later insertions, and some of the folium numbers (e.g., P303–P305) are out of order, both numbers (where there are two) are used to refer to a page. It is customary to refer to the manuscripts as the “Pulkovo Kepler manuscripts”, although they are no longer at Pulkovo, because they were for many years kept at the observatory there. To avoid confusion, the Pulkovo folium number is preceded by a ‘P’.

K451 = P315. A selection from these pages was transcribed by Frisch C. , Ioannis Kepleri astronomi Opera omnia (8 vols, Frankfurt and Erlangen, 1858–71), viii, 229–34.

Nevertheless, what he writes here is, “From explorations I have carried out on other pages concerning the physical hypothesis, there arises a new method of seeking out the eccentricity from acronychal observations”. This suggests that the hypothesis was mentioned earlier in the notebook, or that some pages are missing. There is indeed a previous mention, but it appears on an inserted quire of seven folia (P241–P247), not numbered by Kepler but referred to by him as “Supplement to p. 323 “(on K529 = P356). Possibly these are the “other pages” Keper means.

Other than an unrelated mention on K63 = P98, possibly referring to the resultant path of Copernicus's double epicycle. Cf. Gingerich , “Kepler's treatment of redundant observations”, 310, note 8.

Ibid., 309.

For example, on K435 = P307, transcribed by Frisch in Kepler , Opera, viii, 229.

Kepler , Opera, ed. by Frisch , viii, 30.

For an insightful treatment of Kepler's “poetics”, see Hallyn Fernand , The poetic structure of the world: Copernicus and Kepler , transl. by Leslie Donald M. (New York, 1990). The Somnium is considered on pp. 253–80.

Fond 285, Opis' 1.

It should be noted that the Kepler Kommission plans to include a transcription of the entire Mars notebook in vol. xx/2 of Johannes Kepler Gesammelte Werke. It will, however, be at least several years before this will be published.

Kepler Johannes , New astronomy, transl. by Donahue William H. (Cambridge, 1992).

Bialas reads si.

This (532) is the number Kepler wrote. For an account of the numbering of these pages, see the introductory remarks, above.

Bialas reads totum.

The insertion of a sentence break here would make some sense of a syntactically confused sentence.

Bialas reads cadens.

Bialas reads quem.

Here the ms. has the abbreviation tm, which Bialas reads as tamen. On syntactic grounds, to complete the common construction non tantum …, sed et, I prefer tantum.

Bialas reads lineas.

This word is at the end of a line, and the line above has a hyphen, hanging below the line as Kepler's hyphens do. It looks very much like the riser on a lower case ‘d’, which may be why Bialas reads quod here. In any case, quo fits the context, while quod does not.

Originally, this word was Est, but the ‘s’ is crossed out.

Bialas reads id.

Bialas reads sed.

This is on p. 51 of the first edition (Tübingen, 1596), Gesammelte werke, i, 50–51.

This is clear from Kepler's description of computations based upon this hypothesis, appearing on P246 (an inserted page). The distances are to be obtained “ex antiqua tabula”, which must be based upon the circle.

It is not certain what word Kepler began to write here, though it begins sup.

Cf. Astronomia nova, chap. 40, p. 196. See also Bruce Stephenson's admirably clear account in Kepler's physical astronomy (New York, 1987), 81.

Mysterium cosmographicum, chap. 22, p. 79 (Gesammelte Werke, i, 77).

“Nam facultas eius est, continuè moveri, at qui per numerationem temporis movet, non movet continuè.”.

“Planetam metiri accessus et recessus suos confecto in mundo spacio.”.

Astronomia nova, chap. 46, pp. 221–2. For more on this oval and its supposed asymmetry, see the notes to p. 467 of the Donahue translation (ref. 13), as well as Whiteside D. T. , “Keplerian planetary eggs, laid and unlaid, 1600–1605”, Journal for the history of astronomy, v (1974), 1–21.

Astronomia nova, chap. 46, p. 220.

This equivalence is proved by Ptolemy , Almagest III 3 (transl. by Toomer G. J. (New York, 1984), 148–50), and by Copernicus , De revolutionibus (Nürnberg, 1543), III 15, fol. 85^r–86^v.

Astronomia nova, chap. 2, pp. 8–10.

Such an explanation was actually proposed much later by Boulliau Ismael , Astronomia philolaica (Paris, 1645). Each planet moves on the surface of an imperceptible cone, whose dimensions are somehow impressed upon the planet as a kind of “agendi facultas a forma emanens” (I 12, p. 21, and 1 13, pp. 26–28). The planet moves with regular circular motion about the axis of the cone (I 14, p. 37). Boulliau considered it a flaw in Kepler's theory that it required forces or extrinsic movers to move the planets (I 12, pp. 21–22).

Astronomia nova, chap. 45, p. 215.

Aristotle , On the heavens, transl. by Guthrie W. K. C. (Cambridge, Mass., 1960), 288a28–b23. He says, among other things, “Retardation of the movement of anything takes place owing to loss of power, and loss of power is contrary to nature. (Instances of loss of power in animals are all contrary to nature, e.g. old age and decay, and the reason for them is probably that the whole structure of an animal is composed of elements whose proper places are different; none of its parts is occupying its own place.)” (288bl4–19).

Kepler , Mysterium cosmographicum, chap. 22, p. 79: “Deinde esto in quolibet Planeta peculiaris anima, cuius remigio Stella ascendat in suo ambitu…”.

Astronomia nova, chap. 57.

Aristotle , Physics IV 11, 220a25 (my translation).

This is analogous to his view, expressed in a letter to Michael Maestlin of 3 October 1595 (no. 23 in Gesammelte Werke, xiii, 35) that the fixed stars define space by their positions at the extremities of the world.