Tycho Brahe's Copernican Campaign

TBOO = Dreyer J. L. E. (ed.), Tychonis Brahe Dani opera omnia (Copenhagen, 1913–29). In the citations line numbers are given after the colon.

A sentiment repeatedly expressed by Tycho , for example, in De mundi aetherei recentioribus phaenomenis, TBOO , iv, 156: 186–8 (translated in Boas Marie and Hall Rupert A. , “Tycho Brahe's System of the World”, Occasional notes of the Royal Astronomical Society, iii, no. 21 (1959), 258); in the Progymnasmata, TBOO , iii, 175: 16; in a letter to Peucer Caspar , 13 September 1588, TBOO, vii, 129: 35–37; and in a letter to Hagecius Thaddeus , 1 November 1589, TBOO, vii, 199: 27–29.

We have found Tycho's mature planetary observations to have been consistently accurate to within about 1′, in agreement with Dreyer's and Thoren's assessments. See Thoren Victor E. , “New light on Tycho's instruments”, Journal for the history of astronomy, iv (1973), 25–45, pp. 41–42.

TBOO, vii, 80: 8–16.

TBOO, vi, 70: 29f.

TBOO, vii, 129: 8f.

TBOO, vi, 179: 1f.

TBOO, vii, 199: 17f.

Donahue William H. (transl.), Johannes Kepler: New Astronomy (Cambridge, 1992), 203.

Gingerich Owen , “Dreyer and Tycho's world system”, Sky & telescope, xliv (1982), 138–40, reprinted in Gingerich Owen , The great Copernicus chase (Cambridge, 1992), 251–6.

TBOO, vii, 129: 8–18.

Tycho is speaking here of the diurnal parallactic motion and not the predicted daily motion in the ephemerides, as the following tabulation of the positions of Mars makes clear, for in each case the daily motion is exactly the same, namely 24′: 1582 Magini Leovitius Observed December [Prutenics] [Alfonsines] [Tuckerman] 26 19°38′ 15°08′ 17°42′ 27 19°14′ 14°44′ 17° 1′ 28 18°50′ 14°20′ 16°54′.

TBOO, vii, 129: 18–26.

The omitted phrase reads: “now and then at different times both on the meridian and also around setting, and even for another special reason around 24 February 1597, when in the course of one day or another I saw her both in the evening and in the morning (which is otherwise quite rare).” Tycho was quite surprised to see a bright object near the eastern horizon just before dawn on the morning of 24 February, and subsequently realized that it was Venus, which was also in the evening sky. This was possible because Venus was near its maximum latitude of 7° north. He did not make any measurements of its position, so despite the insinuation in the letter, this did not afford an occasion to test Venus's parallax. It is interesting that this was a date on which he observed all the night through, working on the diurnal parallax of Mars.

TBOO, vii, 129: 26–35.

See Thoren , “Tycho's instruments” (ref. 2), 30–4.

Ibid., 35; Raeder Hans Strömgren Elis , and Strömgren Bengt (transl. and eds), Tycho Brahe's description of his instruments and scientific work (Copenhagen, 1946), 95–96 and 72–75. Tycho says he built three of the trigonal sextants, one presumably being reworked from the bifurcated sextant.

TBOO, x, 160.

TBOO, x, 204.

According to Thoren , “Tycho's instruments” (ref. 2), 30–33, the quadrans maior was such a disappointment that it went out of use shortly and was never illustrated. We suggest that the instrument was reworked to become the quadrans volubilis at Stjerneborg (Fig. 6 in the Mechanica), just as Tycho had reworked the unsatisfactory quadrans maximus chalybeus (Fig. 21) into the quadrans magnus chabyleus at Stjerneborg (Fig. 7). See ref. 36.

Raeder (transl. and eds), op. cit. (ref. 16), 96–97. Tycho wrote: “Frankly however, no matter how this radius is constructed it cannot … give stellar distances in accordance with reality, not even smaller distances up to 15 degrees, not to mention the larger ones where the error is still larger”.

What Tycho here refers to as the Quadrans minor is not the one of this name in his instrument book (Fig. 1), but rather, one of the two brass quadrants (Fig. 2 or 3), which each include an azimuth scale. See Thoren , “Tycho's instruments” (ref. 2), 43.

TBOO, x, 200–1.

TBOO, x, 197.

TBOO, x, 244 (17 January 1583).

Donahue (transl)., op. cit. (ref. 8), 204–7. Donahue used an approximate formula in his footnote on p. 204, so his disagreement with Kepler is unfounded, as pointed out by Toomer Gerald , Journal for the history of astronomy, xxvi (1995), 79. The correct formula is cos Δλ = [cos Δ* — sin β₁ sin β₂/cos β₁ cos β₂ where Δ* is the measured distance between the star and planet, and β₁ and β₂ are their respective latitudes.

TBOO, vii, 80: 2–16.

Tycho's letter to Brucaeus, one of only three surviving from an apparently extensive correspondence, is undated, but Brucaeus responded on 12 June 1584 ( TBOO , vii, 85–86), making the date of Tycho's letter probably sometime in the spring. As of late 1585, a preliminary title signature of Tycho's book on the comet of 1577 made no mention of his intention to include his new cosmological system ( Thoren Victor E. , The Lord of Uraniborg: A biography of Tycho Brahe (Cambridge, 1990), 256; TBOO , iv, 491 and 497). Thoren suggests that observations received from Landgrave Wilhelm IV in the summer of 1586, as well as a manuscript by Christoph Rothmann asserting that comets showed planetary spheres were not solid, were the final spur to develop and publish his system ( Thoren , op. cit., 256–8). Goldstein and Barker argue for the influence particularly of Rothmann's treatise on the comet of 1585 in which it is asserted that planets are suspended in air rather that attached to solid spheres; see Goldstein Bernard R. and Barker Peter , “The role of Rothmann in the dissolution of the celestial spheres”, The British journal for the history of science, xxviii (1995), 385–403. This paper and especially its appendix has been highly seminal in furthering our own interest in Tycho's work on the diurnal parallax of Mars. In the throes of his priority dispute with Nicholas Reymers Ursus, Tycho dated his system prior to Ursus's visit to Hven in the autumn of 1584, as for example in his letter to Rothmann of 21 February 1589 ( TBOO , vi, 179). Later that year, he wrote to Hagecius in a letter of 1 November 1589 stretching the claim to 1583 (“very nearly six years ago”), although Dreyer points out that in the draft he had written “five years ago” (TBOO, vii, 199:32 and note on p. 410). And in his 1598 Mechanica, Tycho writes of inventing the system “14 years ago” ( TBOO , v, 115: 10). It seems plausible that the only form of the theory circulating on Hven at the time of Ursus's visit may well have been the diagram showing the spheres of Mars and the Sun not intersecting, which Tycho later claimed was defective and which Ursus stole.

TBOO, x, 385; Thoren , op. cit. (ref. 27), 425.

TBOO, x, 386.

TBOO, x, 390–1. A later note by Dreyer indicates that part of the passage on p. 391 is in Tycho's hand (Corrigenda, p. 430).

TBOO, xi, 84.

TBOO, x, 286; these calculations are in a separate codex, in Vienna, and according to our analysis the statement is anachronistic unless it was added a few years later. Barker and Goldstein , op. cit. (ref. 27), 403, have cited and translated this passage.

Tycho probably interpolated in the parallax table he had already drawn up in 1578, TBOO, x, 58.

TBOO, x, 235.

TBOO, x, 324.

TBOO , x, 330. The instrument noted in the log is the “portatilem”, which generally refers to the instrument called “Another brass quadrant [Quadrans alius orichalcicus]” in the Mechanica, where Tycho explicitly writes, “I generally refer to this as the portable azimuth quadrant” ( Thoren , “Tycho's instruments” (ref. 2), 39; TBOO , v, 20–23; Raeder (transl. and eds), op. cit. (ref. 16), 20–23 — note that the Raeder page numbers agree with those in TBOO, v). There are, however, some anomalous features of these observations that suggest that they may have been made with the q. maius (= q. volubilis?) rigged for angular measurement. First, these observations were taken to 1/4′ accuracy. The “other brass quadrant” was divided to single minutes using transversal points and Tycho writes that by virtue of its small size it cannot be depended on for accuracy of less than 1′ ( Raeder , 21–23). The transversal points on the quadrans volubilis, on the other hand, were “so fine that one-quarter of a minute can be distinguished if the sighting is carefully made” ( Raeder , 33). Second, even apart from the fact that it is shown in alt-azimuth mode in the Mechanica, the “other brass quadrant” does not seem amenable to being rigged for this type of observation, whereas the q. volubilis by virtue of its clear family resemblance to the trigonal sextant seems to have this capability. In the figure depicting the q. volubilis ( TBOO , v, 32), there is a feature labelled D that is not discussed in the accompanying text. It seems to correspond exactly to the feature marked E in the figure depicting the trigonal sextant (TBOO, v, 72), which is the point of attachment for the sextant's ball-and-socket mount. (The letters D and E are shown in our Figs 7 and 6(a) respectively.) Hence it seems likely that the q. maius was originally built as a scaled-up trigonal sextant, with the capability of being mounted either vertically for altitude measurements (as the sextant depicted on TBOO , v, 24) or on the ball-and-socket mount. In 1586, it would have been remounted — perhaps as an experiment preceding the remounting of the q. max. in 1588 — in permanent alt-azimuth mode and renamed the q. volubilis.

TBOO, x, 338.

Raeder (transl. and eds), op. cit. (ref. 16), 71.

In describing Stjerneborg in the Mechanica, Tycho wrote that “My purpose was partly to have placed some of the most important instruments securely and firmly in order that they should not be exposed to the disturbing influence of the wind, and should be easier to use…”, ibid., 135.

In the Mechanica Tycho states that “we have remade most of the instruments described in this book more than once”, ibid., 19.

See ref. 36.

See, for example, the complaint about levelling the q. Max. added to the 1582 log book, TBOO, x, 135, second paragraph.

Mechanica, Fig. 7, p. 36, ibid. , 39; compare with Fig. 21, ibid., 92. Note that the base of the original quadrant was also recycled, to become the base of the great azimuth semicircle, Fig. 8, ibid., 40.

TBOO, x, 352.

The modern value for the refraction at 1° is 25′; in the Progymnasmata Tycho gives 26′ for the solar refraction and 21 ½′ for stellar refraction, so it is not clear if a compensating calculation for a 3′ solar parallax has been included in the 1585 reduction.

TBOO, vi, 70: 29–42.

For the weather conditions, see the meteorological record in TBOO, ix.

TBOO , xi, 182. The 26 February 1587 observation is in the evening, not morning (Mane) as labelled.

TBOO, xi, 187.

The stellar refraction table is given in TBOO , ii, 287, and the solar refraction table in ibid., 64.

TBOO, x, 294.

TBOO , xi, 6. Kepler , in his Astronomiae pars optica, 123, rather similarly derives a solar refraction table from Tycho's data, using observations from 16 January 1587, TBOO, xi, 193. We thank William Donahue for sending us a preliminary version of his new translation, Johannes Kepler: Optics (Santa Fe, 1998).

Maeyama Y. , in “The historical development of solar theories in the late sixteenth and seventeenth centuries”, Vistas in astronomy, xvi (1974), 35–60, has shown how Tycho's spurious solar parallax and resulting solar refraction corrections led to a faulty determination of the eccentricity of the solar orbit. A short but especially clear account is given by Moesgaard K. P. , “Refraction in Tycho Brahe's small universe”, in Debarbat S. (eds), Mapping the sky (International Astronomical Union Symposium 133; Dordrecht, 1987), 87–92.

TBOO, xi, 223: “Nota. Deficiunt a solari refractione quasi 4 minuta ubique”.

The TBOO contains the same error for the refraction at 19°, 1′0” instead of 30”, found in Kepler's Astronomiae pars optica (Frankfurt, 1604), 121; this may in some fashion account for Dreyer's error.

Entitled De novis aetherei mundi generationibus hoc aevo conspectis liber secundus, the signature existed in a sole known copy in the National Library in Berlin, fortunately transcribed and published by Dreyer , TBOO, iv, 491 and 496–7. It is undated, but Tycho refers to it by title in a letter to the Landgrave Wilhelm of Hesse on 1 March 1586 (TBOO, vi, 35: 9).

The earliest date for the availability of the De mundi aetherei recentioribus phaenomenis, 1 May 1588, is a presentation inTycho's hand to Andreas Dudith, in the collection of Owen Gingerich.

TBOO, iv, 156: 14–18.

TBOO, vi, 179; 178:40–179:4.

TBOO, vii, 199: 17–33; see ref. 27 concerning the “very nearly six year” claim.

See Gingerich Owen and Westman Robert S. , The Wittich connection: Priority and conflict in late sixteenth-century cosmology, Transactions of the American Philosophical Society, lxxviii, no. 7 (1988). See also Rosen Edward , Three imperial mathematicians: Kepler trapped between Tycho Brahe and Ursus (New York, 1986), and Jardine N. , The birth of the history and philosophy of science: Kepler's A defence of Tycho against Ursus (Cambridge, 1984).

Called Q. min. in the observing logs; see Thoren , “Tycho's instruments” (ref. 2), 43.

TBOO, xi, 380.

Progymnasmata, TBOO, ii, 64.

Progymnasmata, TBOO, ii, 287.

Deduced from observations of Arcturus made in January and February 1589, TBOO, xi, 377–9.

Deduced from observations of Jupiter made 29 and 30 January 1589, TBOO, xi, 377, and TBOO, xii, 39–40 — some have been erroneously placed by Dreyer under 1590.

Based on observations of Spica made in October and November of 1586 as part of Tycho's intensive study of Mercury; he then specifically tabulated the refraction for Spica: TBOO, xi, 84.

The observations of “Vultur” were the last of the set, 30 December 1589, and tabulated in the final column of Tycho's table, TBOO, xi, 379–80.

Allen C. W. , Astrophysical quantities (3rd edn, London, 1973), 125.

Rothmann arrived on 1 August 1590 and left on 1 September; TBOO, ix, 89 and 91.

Fol. 49 of Observationum stellarum fixarum (Ms Astron. 5, No. 7: Landesbibliothek und Murhardsche Bibliothek der Stadt Kassel), completed after 1588, and probably in the summer of 1589. We thank Peter Barker for providing a copy of the table and this information.

Only a small fraction of the letters surely written by Tycho seem to survive; for example, there are only two known from Tycho in 1594, in 1595, and in 1596.

Progymnasmata, TBOO, ii, 383.

TBOO, iii, 175:41–176:2.

Kepler's Appendix to the Progymnasmata, TBOO, iii, 320: 8.

Nielsen Lauritz , Tycho Brahes Bogtrykkeri (Copenhagen, 1946), 31–40. We thank Kirsti Anderson for her assistence with this reference.

See Christianson's John R. forthcoming On Tycho's island: The birth of big science, 1570–1601.

Donahue (transl.), op. cit. (ref. 8), 200.

Johannes Kepler Gesammelte Werke, i (Munich, 1938), 119: 41–120: 23.

TBOO , vii, 127–41; Dreyer gives as citations for the letter, Nicolsburgensis and Parisiensis. The latter, in the Bullialdus collection in the Bibliothèque Nationale, is only a fragment and does not include this portion. The Dietrichstein Library in Castle Nikolsburg (near Vienna?) was dispersed by auction in 1933, but the auction catalogue does not indicate the sale of manuscript letters. The late Doris Hellman acquired a sixteenth-century copy of a Tycho letter to Peucer, possibly this one, but it has not been identified among the 30-some boxes of her papers at Columbia University Library. The letter was first quoted (with a number of variants) by Maestlin Michael as mentioned in our text, again by Gassendi Petrus in his biography Tychonis Brahei, equitis Dani, vita (Paris, 1654), 62, and first published in full, with idiosyncratic punctuation, in Resenius Johannis Petrus , Inscriptiones Haffnienses … nec non duabus epistolis una Tychonis Brahe ad Peucerum missa … (Copenhagen, 1668), 392–409.

See Kepler Gesammelte Werke, i, 439–40.