Galileo and the Discovery of the Phases of Venus

Westfall Richard S. , “Science and patronage: Galileo and the telescope”, Isis , lxxvi (1985), 11–30.I have quoted the article from Peter Dear (ed.), The scientific enterprise in early modern Europe: Readings from “Isis” (Chicago and London, 1997), 113–32, pp. 127–9.

Westfall , “Science and patronage” (ref. 1), 127ff. “Dishonesty” is used by Westfall, on p. 131. See also Krämer-Badoni Rudolf , Galileo Galilei (Munich, 1985). The author qualifies the whole episode as a “Pikanterie” ( ibid. , 79), a “Schwindel” ( ibid. , 82), and “ein unerfreuliches Trickspiel” ( ibid. ). The Italian historian, Raffaello Caverni, was the first to propose the dishonesty thesis at the turn of the nineteenth century. Caverni's interpretation of the episode has been rejected by Westfall (“Science and patronage” (ref. 1), 130). In 1919, Antonio Favaro, the editor of the National Edition of Galileo's works, refuted Caverni's main argument, in his article “Galileo Galilei, Benetto Castelli e la scoperta delle fasi di Venere”, Archivio di storia della scienza , i (1919–20), 283–96. Favaro's refutation was based on a gross error made by Caverni, who had attributed to the hand of Vincenzo Viviani a copy of a letter that had been written by Castelli himself. Cf. the details in ibid. , 290–1. There is no proof that Galileo actually received Castelli's letter on 11 December 1610. This hypothesis simply suits the dishonesty thesis. The Italian original of Castelli's letter is published in the National Edition of Galileo's works (Galileo Galilei, Le opere di Galileo Galilei, Edizione Nazionale, ed. by Antonio Favaro (20 vols, Florence, 1890–1909); hereafter OGG). I have quoted the National Edition using the following abbreviation: OGG, followed by the Roman numeral of the volume and page numbers in Arabic numerals.

Westfall , “Science and patronage” (ref. 1), 126ff. See Castelli's letter in OGG, x, 480ff.

Gingerich Owen , “Phases of Venus in 1610”, Journal for the history of astronomy , xv (1984), 209–10, and Peters William T. , “The appearances of Venus and Mars in 1610”, Journal for the history of astronomy , xv (1984), 211–14. The work by Gingerich was based on a modern pattern projected backwards in time by offsetting a difference in dates of 37 days. Peters's work was more quantitative and arrived at a diagram showing the percentage of Venus's illumination during the second half of 1610.

Peters , “The appearances” (ref. 4), 213.

OGG , x, 500, my translation.

OGG , x, 503. Cf. Galileo's answer to Castelli in OGG, x, 502–5.

OGG , x, 503.

OGG , x, 500.

On 25 February 1611, Galileo wrote a letter in which he was more precise than in his account to Clavius and said the Venus remained semicircular for about one month at the time of maximum elongation. The person to whom the letter was written is not known. Cf. OGG , xi, 53.

In his letters to Clavius and Castelli, Galileo also predicted the future evolution of the phases. “Now [i.e. on 30 December], it [Venus] begins to assume a notable corniculate shape. Thus, it will continue to decrease during the period in which it is visible in the evening sky and, in due course, we shall see it in the morning sky, with its thin corns on the other side from the Sun…” ( OGG , v, 500).

See Peters's attempt to observe Venus with a replica of Galileo's telescope. Cf. Peters , “The appearances” (ref. 4), 211–14.

Westfall , “Science and patronage” (ref. 1), 130.

OGG , xi, 48, my translation. The letter is dated 12 February 1611. What was Galileo's source for the attribution to Aristotle of this order of planets? It might have been either Cristoph Clavius or some other scholastic material. Actually, Aristotle does not mention the question of the order of the planets. According to Edward Grant, Clavius attributed to Aristotle the descending order Mercury, Venus, Sun, and referred to this order as the “Egyptian system”. This order is not in Aristotle's works in the places cited by Clavius in his Sphere, but in the pseudo-Aristotle's De mundo, which Clavius also cites. Cf. Edward Grant's discussion in his Planets, stars, and orbs: The medieval cosmos, 1200–1687 (Cambridge, 1994), 312ff. See also Van Helden Albert , Measuring the universe: Cosmic dimensions from Aristarchus to Halley (Chicago, 1985), 20–23. Van Helden discusses in detail Ptolemy's ideas on the order of the planets. In Galileo's Juvenilia there is a scholastic tract on the Order of celestial orbs, in which Galileo attributes to the Egyptians the descending order Mercury, Venus, Sun and quotes the pseudo-Aristotle's De mundo. See OGG, i, 50. For an English translation and an attempt to show that this tract depends on material from the Collegium Romanum, cf. Wallace William A. , Galileo's early notebooks: The Physical Questions (Notre Dame and London, 1977).

Roger Ariew argues that “the existence and qualitative appearance of the phases of Venus do not seem to constitute a crucial anomaly for Ptolemaic astronomy”. The author does not furnish any explanation for this assertion. He speaks of “some modifications” needed to accommodate Venus's phases in Ptolemaic astronomy without further expanding on this question. Cf. Ariew Roger , ‘The phases of Venus before 1610”, Studies in history and philosophy of science , xviii (1987), 81–92, p. 86. I cannot think of any modification that could save Ptolemaic astronomy in the face of the complete cycle of Venus's phases. Nor am I aware of any attempt to accommodate Venus's complete phase cycle in the Ptolemaic system during the seventeenth century. On the contrary, there is evidence that, in the seventeenth century, accommodating Venus's phases in an astronomical system implied the abandonment of Ptolemy's system. For example, Andrea Argoli, a successor of Galileo at the chair of mathematics at Padua University, believed that both the Ptolemaic and the Copernican systems were untenable and proposed a semi-Tychonic system, in which Mercury and Venus rotated around the Sun, while the other planets rotated around the immobile Earth. In his Pandosion sphaericum, Argoli acknowledged that such a planetary system had already been put forward by Martianus Capella, but pointed out that until the seventeenth century no-one had calculated ephemerides according to this system. He was keen to stress that he had achieved this by publishing tables for almost the entire seventeenth century. Cf. Andrea Argoli, Pandosion sphaericum (Padua, 1644), 10. On Argoli, see Schofield Christine J. , Tychonic and semi-Tychonic world systems (New York, 1981), 175–6, and Soppelsa Laura Maria , Genesi del metodo Galileiano e tramonto dell’ Aristotelismo nella scuola di Padova (Padua, 1974), 71–79.

Westfall , “Science and patronage” (ref. 1), 126 and 129. The cipher was vague and simply said that Venus showed phases similar to those of the Moon. As we have seen, from 1 October 1610 to 11 December 1610 Galileo had attributed to Venus a change of phase from circular to semicircular. He must have reckoned that this was enough to attribute phases to Venus.

Stillman Drake thinks that Galileo decided to write to Kepler on 11 December because he “risked anticipation by another astronomer”, possibly by astronomers at the Collegium Romanum. See Drake Stillman , “Galileo, Kepler, and phases of Venus”, Journal for the history of astronomy , xv (1984), 198–208. Quotation from: Drake Stillman , Essays on Galileo and the history and philosophy of science (3 vols, Toronto, Buffalo and London, 1999), i, 400.

Gingerich Owen , “Astronomical scrapbook: Galileo and the phases of Venus”, Sky and telescope , lxviii (1984), 520–2, reprinted in his The great Copernican chase and other episodes in astronomical history (Cambridge, Mass., and Cambridge, 1992), #13, emphasis mine.

Edward Grant's discussion in Grant, Planets, stars, and orbs (ref. 14), 392ff.

Ibid. , 392.

Ibid. , 401.

Quoted in ibid. , 402.

Ibid. , 403.

Quoted in ibid. , 403.

The first theory, which Riccioli attributed to Macrobius, held that all stars (except the Moon) were self-luminous. Amongst the followers of this thesis, Riccioli quotes Cardanus and, more recently, Kepler (from the Astronomiae pars optica of 1604, in which Kepler discusses light phenomena regarding the heavenly bodies and concludes that since Venus remains visible below the Sun it must emit its own light). The second theory stated that all stars and planets shone because of the light received from the Sun. This he attributed to Plato's Timaeus and amongst the moderns to the Jesuit Father, Christoph Scheiner. The third theory was by a modern, Ismaël Boulliau. In the latter's Astronomia Philolaïca, according to Riccioli, the opinion was put forward that all stars and planets were partly lighted by the Sun and partly possessed their own light. The fourth theory was attributed by Riccioli to Giordano Bruno, Kepler, and Galileo. According to it, the planets were opaque bodies that shone because of the light received from the Sun, while the fixed stars emitted their own light. Riccioli himself favoured the thesis that the planets received their light from the Sun, i.e. the fourth one, although he did not concede that they were opaque bodies. He thought that their matter resembled that of metals, or rather that of precious stones of various colours. Thus, he concluded, planets are not opaque bodies similar to our Earth. Riccioli Battista Giovanni , Almagestum novum (2 vols, Bologna, 1651), i, 495ff.

Galilei Galileo , Dialogue concerning the two chief world systems , 2nd edn, ed. and transl. by Drake Stillman (Berkeley, Los Angeles and London, 1967), 334.

Rosen pointed out that Galileo, in his interpretation of Copernicus's ideas on celestial light, was actually misled by a misprint contained in the first edition of the De revolutionibus. Cf. Rosen Edward , “Copernicus on the phases and light of the planets”, Organon , ii (1965), 61–78. I have quoted the article from Rosen Edward , Copernicus and his successors (London and Rio Grande, 1995), 81–98. According to Rosen, Copernicus did not hold any personal opinion on this matter, but simply attributed to the followers of Plato the argument that all heavenly bodies are dark and shine because they receive light from the Sun, and believed that this argument was used by Platonists against Ptolemy's arrangement of the planets, which placed Venus and Mercury below the Sun. Copernicus therefore does not appear to have had any theory on celestial light and the phases of Venus. It was Galileo who attributed to Copernicus the explanation of the absence of phases based on the hypothesis that Venus was either self-luminous or made of such material that it could imbibe solar light and re-transmit it to Earth. But, according to Rosen , “that Venus was transparent or self-luminous was a theory imputed by Copernicus to the followers of Ptolemy”. Cf. ibid. , 93–97.

If, for example, Venus was only partially opaque and transmitted light both by reflecting some solar light and by irradiating some light that had been absorbed by its body, the appearance of the phases would consequently have been affected to such an extent as not to be predictable. This conclusion would be perfectly reasonable in the framework of what Grant, as we have seen, believes to have been the most popular of the medieval theories, the mixed theory. This mixed theory, in various forms, was still a plausible hypothesis in Galileo's time, especially before the advent of the telescope. Grant , Planets, stars, and orbs (ref. 14), 408–9. The author quotes a number of seventeenth-century authors on celestial light.

OGG , xi, 12.

“… sin qui dubbie tra i maggiori ingeni del mondo”, OGG , xi, 12.

Kepler Johannes , Gesammelte Werke , iv: Kleinere Schriften 1602/1611 , ed. by Kaspar Max Hammer Franz (Munich, 1941), 345–54.

Kepler , op. cit. (ref. 31), 350, my translation.

According to Galileo's theory of adventitious irradiation, it was the veil of humidity on the surface of the eyeball that was responsible for the formation of the adventitious luminous halo visible around bright objects. This theory, according to Galileo, explained why the luminous halo was not magnified by the telescope and why its shape and size practically remained the same for all objects (although he pointed out that by pressing the eyeball with a finger one could affect its appearance). Galileo concluded that if this halo was caused by humidity covering the eye, we should not marvel at its not being enlarged by the telescope, since it is formed behind the telescope, not beyond it. OGG , vi, 84–85.

OGG , xi, 61–62, my translation.

Kepler , op. cit. (ref. 31), 353, my translation.

Alan Chalmers noted that the telescope posed a threat to the teleological aspects of Aristotelianism and was perceived as such by some of Galileo's contemporaries. He reached the conclusion that “Galileo undermined in practice standards implicit in Aristotelian methodology”. This is confirmed by the case of Scipione Chiaramonti. Cf. Chalmers Alan , “Galileo's telescopic observations of Venus and Mars”, The British journal for the philosophy of science , xxxvi (1985), 175–84, p. 183.

OGG , xiii, 337.

Chiaramonti Scipione , Opuscula varia mathematica nunc primum in lucem edita (Bologna, 1653).

Chiaramonti Scipione , Difesa di Scipione Chiaramonti da Cesena al suo Antiticone, e libro delle nuove stelle dall’ oppositioni dell’ autor de’ Due Massimi Sistemi Tolemaico, e Copernicano (Florence, 1633). The book is not only a painstaking rebuttal of all the criticisms levelled at Chiaramonti by Galileo in the Dialogue, but contains critical comments on a number of other issues raised in the Dialogue. Cf. also Chiaramonti Scipione , De universo (Cologne, 1644).

Chiaramonti , Difesa di Scipione Chiaramonti da Cesena al suo Antiticone (ref. 39), 55, my translation.

Chiaramonti , De universo (ref. 39), 184.

Ibid. .

Ibid. .

As to the other planets, he adopted a teleological criterion whereby Nature granted different degrees of perfection to all bodies. Thus, he reasoned, on the celestial bodies Nature had bestowed light in ascending order of perfection from the Moon to the stars. But since the Sun was clearly the brightest object and yet not the highest one, Chiaramonti admitted that as regards the planets above the Sun the luminosity order was perhaps not respected by Nature and the question became one of religion rather than of philosophy. Chiaramonti , De universo (ref. 39), 185.

Cf. Ioannis Antonii Magini Patavini, Ephemeridum coelestium motuum continuatio, Ab Anno Domini 1608 usque ad Annum 1630 iuxta Copernici observationes accuratissime supputatarum , 2nd edn (Frankfurt, 1610), 168.

Cf. Galileo's letter of 25 February 1611 (ref. 10).

The ellipse can easily be derived by calculating the intersection between a plane (containing the origin of the frame of reference, parallel to the Y-axis, and forming an angle ε with the Z-axis) and a spherical surface (whose centre is the centre of the frame of reference) representing Venus's surface. The intersection is of course a circumference. By projecting this circumference onto the plane X = 0 one obtains the ellipse. An elliptical curve was derived for the line separating light from darkness in the case of the phases of the Moon by Scipione Chiaramonti. Cf. Chiaramonti , Opuscula varia mathematica (ref. 38).

The Home Planet package is in the public domain and available at the following internet address: http://www.fourmilab.to/homeplanet/homeplanet.html. The Help file contains references to the mathematical literature on which the software is based.

Galileo hoped that since Venus was so “high” he could eventually observe it even at its inferior conjunction with the Sun. Cf. OGG , xi, 53.