An Unblemished Success: Galileo's Sunspot Argument in the Dialogue

Soccorsi Filippo S.J. , Il processo di Galileo (Rome, 1947). Selections relevant to this paper are translated in Stillman Drake, Galileo studies: Personality, tradition, and revolution (Ann Arbor, 1970), 191–3.

Smith Mark A. , “Galileo's proof for the Earth's motion from the movement of sunspots”, Isis , lxxvi (1985), 543–51.

Hutchinson Keith , “Sunspots, Galileo, and the orbit of the Earth”, Isis , lxxxi (1990), 68–74.

Galilei Galileo , Dialogue concerning the two chief world systems, Ptolemaic & Copernican , transl. by Drake Stillman (Berkeley, 1967), 355.

Salviati is one of the three characters whose conversations constitute the text of the Dialogue. Salviati tends to speak for Galileo, Simplicio presents the Peripatetic point of view, and Sagredo is an educated and open-minded layman.

Galilei , Dialogue , 347–8. According to Stillman Drake, when Galileo was formulating his sunspot argument, he had not yet actually observed the annual changes in the path of motion of sunspots in any detail. Drake thinks that Galileo, who was aware that the axis of rotation of the Sun maintained a slight but apparently constant tilt with respect to the ecliptic plane, had deduced in a “thought experiment” the sorts of sunspot motions that would follow from that tilt in the Copernican system. See Drake , Galileo studies , 187. Indeed, when Salviati first describes sunspot motions in the Dialogue, it is as part of a thought experiment: He predicts the kinds of sunspot motions that would be observed if Galileo's modified Copernican hypothesis were true, and only later reveals that he and the “Lincean Academician” had tested these predictions and that after “… continuing to make very careful observations for many, many months, and noting with consummate accuracy the paths of various spots at different times of the year, we found the results to accord exactly with the predictions” ( Dialogue , 352).

Copernicus Nicolaus , De revolutionibus orbium coelestium (1543), Book I, Chapter 11. Actually, additional motions and structures were postulated by Copernicus to explain the inequality of the Sun's apparent motion. In his sunspot argument, Galileo ignores the these complications.

In Figure 1 and in subsequent figures of the kind, the period, orientation, and directional sense are listed for each postulated motion of Earth and Sun. The orientations are given relative to either the ecliptic or equinoctial plane. The ecliptic plane is fixed relative to the stars; it is the plane that contains the orbital path of the Earth around the Sun. The equinoctial plane is fixed relative to the Earth; it is the plane that contains the Earth's equator. The angle between these two planes is a constant 23.5°. The directional sense of a motion is considered positive if the motion is counter-clockwise as seen from the north celestial pole.

For Galileo's explanation of the modifications he introduces to the Copernican system, and of how the modified system accommodates sunspot motions, see Dialogue , 347–52. The passage quoted is from p. 347.

Galilei , Dialogue , 355.

Ibid. , 398–9.

I am grateful to Noel Swerdlow for the diagrams in Figures 3 and 4, and also for helpful discussions. In Figure 3, the diurnal rotation of the Earth is not shown.

Citations are from Aristotle, De caelo, 290a25. The translation is from Jonathan Barnes (editor), The complete works of Aristotle , i (Princeton, 1984), 478.

Later Peripatetics would be forced to correct Aristotle on this point, when the newly observed motions of sunspots made it apparent that a proper rotational motion should be attributed to the Sun. This would not have been impossibly difficult for empirically-minded Peripatetics to accept, since it was a correction not of a fundamental Aristotelian principle but only of an overly ambitious empirical generalization.

See Copernicus , De revolutionibus. Book I, Chapter 11. The Copernican system contains features repugnant to Peripatetic philosophy: The Earth rotates and is carried around the Sun as if it were a planet. But it seems fitting to designate the standard of axial motion employed by Copernicus as “Peripatetic”, since it is an obvious application of the more general Peripatetic conception of motion.

The distinction I have drawn between the Galilean and Peripatetic standards of axial motion was pointed out in different terms in Smith , “Galileo's proof”, 545–7. Smith's “fixed axis model” of motion corresponds to my “Galilean standard”, and his “variable axis model” to my “Peripatetic standard”. I will argue below that the question which of these two standards is the correct one is at issue in Galileo's sunspot argument. Smith's manner of designating his two “axis models”, fixed and variable, prematurely presumes and incorporates the settlement of this question in favour of the Galilean standard. Smith's designations mask the fact that, from the perspective of Galileo's Peripatetic opponents, the “fixed axis model” would have been considered variable and the “variable axis model” would have been considered fixed. For this reason, I have found it helpful to change Smith's designations to the more neutral “Galilean” and “Peripatetic” standards of axial motion. More will be said below about Smith's use of the distinction between the “fixed axis” and “variable axis” models.

Galilei , Dialogue , 353–4. The reasoning process by which it is determined which planetary motions must be introduced to accommodate sunspot motions in the Ptolemaic system has been spelled out here in greater detail than Galileo provides in the Dialogue. Galileo says little about this reasoning process because he was able to assume that his Peripatetic readers took certain concepts for granted, such as the Peripatetic conception of planetary motion. As far as Galileo's Peripatetic readers were concerned, his proposed modification of the Ptolemaic system would have appeared to be the simplest and most obvious way to accommodate the complexities of sunspot motions in that system. Galileo's proposal is the only Ptolemaic explanation of sunspot motions in which just one precessional motion is required; all other Ptolemaic explanations require two or more precessional motions, with at least one being a complicated precessional motion of a precessional axis.

Galileo's account of his Ptolemaic explanation of sunspot motions seems elliptical and inadequate to modern readers who do not share the tacit assumptions of his Peripatetic readers. By contrast, Galileo's account of his Copernican explanation of sunspot motions seems pedantic to modern readers, who take for granted the very feature of that explanation that would have seemed obscure and ad hoc to his Peripatetic readers: The assumption that it is natural for a planetary axis to maintain a constant orientation relative to the stars.

Since the motions in Figures 2.1 and 2.2 (and for that matter in Figures 1.1 and 1.2) are described according to the Peripatetic conception of proper motion, strictly speaking the orbital motions should be attributed to the carrying spheres, and not to the planets. I have listed them as motions of the planets for the sake of ease of presentation.

The diurnal motion of the Sun around the Earth is not shown.

Drake , Galileo studies , 195.

Galilei , Dialogue , 398.

Ibid. See Figure 1.1. For Simplicio, precessional motion is a species of rotation.

The objection might be raised at this point that the Peripatetics are inconsistent. It appears from Figure 2.1 that the Ptolemaic system contains incongruous motions: It attributes two orbital motions in opposite directions to the Sun. This objection is not warranted, however. For the Peripatetics, the two orbital motions in Figure 2.1 are proper motions of the two spheres that carry the Sun, not of the Sun itself.

Galilei , Dialogue , 398.

Ibid. , 355.

Ibid. .

An article by David Topper on the topic of Galileo's sunspot argument came to my attention only after I had completed this paper. Topper observes that Galileo rules out a Ptolemaic explanation of sunspot motions on the grounds that it would require incompatible motions: The Earth would have to rotate in one direction while its axis performed a conical motion in the opposite direction. Topper then notes that a similar combination of incompatible motions is required if Galileo's Copernican system is to be extended to accommodate the phenomenon of the precession of the equinoxes. Topper criticizes Galileo for making no mention of this inconsistency: “… Galileo dismisses as insignificant the very sort of contrary and conical motion, required for the Copernican system, that he argued falsified Ptolemy's system.” See Topper David , “Galileo, sunspots, and the motions of the Earth”, Isis , xc (1999), 757–67, p. 766.

Galileo is not guilty of any inconsistency. I have argued above that it is an unstated conclusion of the sunspot argument that at least one of two dearly held Peripatetic criteria of physical implausibility must be discarded: Either the incompatibility of motions or the mobility of the Earth. Galileo's preference for the Copernican explanation of sunspot motions was not based on either of these discredited criteria. His preference was based on simplicity: The Copernican explanation involves fewer motions and axes than the Ptolemaic. Pace Topper, from Galileo's perspective it is of no import that a Copernican explanation of the precession of the equinoxes requires motions that a Peripatetic philosopher would consider incompatible.

Soccorsi , Il processo , translated in Drake , Galileo studies , 191.

Ibid. , 192.

Drake , Galileo studies , 191.

Ibid. , 194.

Galilei , Dialogue , translator's note to p. 354, appearing on pp. 493–4.

It is difficult to determine whether Drake really held this position, however. In the above-cited translator's note, Drake mentions “both motions” of the Sun, but it is not clear whether he is referring to two precessional motions or to a precessional motion and an orbital motion. An additional complication is presented by the fact that in the same note Drake offers a sharp criticism of the same sort of analysis of the sunspot argument for which he praises Soccorsi in Galileo studies..

Smith , “Galileo's proof”, 550.

Ibid. , 543–4.

Hutchinson , “Sunspots”, 69.

As noted earlier, what I call the Galilean standard of axial motion corresponds to Smith's “fixed-axis” model, and what I call the Peripatetic standard corresponds to Smith's “variable-axis” model.

The planetary motions that are listed in Figure 5 are those which are required to accommodate sunspot motions in the various systems. My determination of these motions is at variance with Smith's in a couple places. First, in his “variable-axis” Ptolemaic model (P2 in Figure 5), Smith (following Drake) includes two distinct precessional motions for the Sun, one annual and one diurnal, bringing the total number of postulated motions to five. Second, Smith says that the precessional motion of the Sun's axis in his “fixed-axis” Ptolemaic model is counter-clockwise; this amounts to saying that the sense of the motion in G2 of Figure 5 is ‘+’ rather than ‘–’. See Smith, “Galileo's proof, 550, 548.

In Figure 5, the rows are numbered 2 and 3 (rather than 1 and 2) in order to accommodate the later expansion of the grid in Figure 6. Figure 1.2 corresponds to P3 in Figure 5; Figure 1.3 corresponds to G3; Figure 2.2 corresponds to P2; and Figure 2.3 corresponds to G2.

Smith , “Galileo's proof”, 550–1.

As is apparent from Figure 5, I disagree with Smith as to the number of motions required in explanation P2. See the note above.

Smith , “Galileo's proof”, 550.

Figure 6 is an expanded version of Figure 5. Rows 2 and 3 in Figure 6 are identical to Rows 2 and 3 in Figure 5.

Hutchinson , “Sunspots”, 70.

Galilei , Dialogue , 399–400. The section of interest in Gilbert's William De magnete is Book VI, Chaps. 3–4.