NOEL. M. SWERDLOW
7 Galileo's discoveries with the telescope and their evidence for the Copernican theory
Galileo's researches in astronomy were more than original, they were unprecedented. He was not an astronomer in the sense of Copernicus, Tycho, and Kepler, making observations, devising models, and deriving parameters in order to compute tables and ephemerides for finding the positions of the Sun, Moon, and planets. Nor did he search for the physical principles governing the motions of the heavens as Kepler and later Newton did. Most of his work was concerned with two issues, the refutation of the Aristotelian and the defense of the Copernican “System of the World,” and his originality lies not so much in what he found as in how he interpreted his discoveries. Even his discoveries with the telescope, as interesting as they are in themselves – and it is hard to think of more surprising discoveries in the entire history of science – are of still greater interest for the conclusions that he drew from them, for nearly all of them could be turned to the criticism of Aristotle and the defense of Copernicus, and in his Dialogue on the Two Great Systems of the World that is just what Galileo did. Our concern here, however, is with his initial discoveries and his initial interpretations, which, although not as far-reaching as the conclusions he reached in the Dialogue, were upsetting enough to anyone who was not already a friend of Copernicus.
In late 1608 Galileo's friend Paolo Sarpi heard a rumor of an optical device, recently invented in the Netherlands, that made distant objects appear close, and by May of 1609 he must have alerted Galileo. It was not hard to make one of these things using spectacle lenses, a plano-convex lens as an objective and a plano-concave lens as an eyepiece. When placed in a tube, the result is a ‘spyglass’ giving an upright image of 3x or 4x magnification. Galileo did this much, and since he wanted something better, he learned to grind and polish lenses, and by August made an instrument of 8x or 9x. He called it a perspicillum, and he arranged through Sarpi a demonstration for the Venetian Senate, on whom its naval application for spotting distant ships was not lost. Galileo therefore donated sole rights to the manufacture of the instrument to the Republic of Venice – which is curious since he was not the inventor and Venice could hardly prevent manufacture elsewhere – asking in return only an improvement in his position at the university. This he received. His salary was nearly doubled to 1,000 florins, although not until the following year, after which it would be frozen. So Galileo promptly renewed overtures to his former pupil Cosimo de’ Medici for a court appointment in Florence, sending him a very fine telescope. He soon had a more splendid gift for Cosimo.
By the beginning of 1610 he had made a telescope of 20x, but even before that he began making observations of the heavens, in which it was not so much the magnification as the light gathering and resolving power of the telescope that allowed him to see what had never been seen before. In about two months, December and January, he made more discoveries that changed the world than anyone has ever made before or since. He began with the irregular surface of the Moon, went on to the uncountable number of the stars, and then in early January found the satellites of Jupiter, which made him resolve to publish quickly, before someone else had the bright idea of turning a telescope on Jupiter. In fact Simon Mayr later claimed to have observed the satellites in December of 1609, but he did not publish until 1614 and his claim to prior discovery is generally discounted. Galileo's latest observation is dated 2 March, and by 13 March the Sidereus Nuncius, the “Sidereal Messenger” (or Message) appeared in Venice, dedicated to Cosimo II de’ Medici, Fourth Grand Duke of Tuscany, after whom he named the four satellites of Jupiter the “Medicean Stars.” This is particularly appropriate, he points out in the dedication, since at the time of Cosimo's birth Jupiter occupied the midheaven, the royal planet in the tenth house of royal authority, and there are yet other pleasing astrological conceits to flatter the young Grand Duke's vanity. Within a few weeks Galileo's discoveries were known throughout Europe, and by June he had resigned his position at Padua to become Chief Mathematician of the University of Pisa, with no teaching responsibilities, and Philosopher and Mathematician to the Grand Duke of Tuscany. He continued his observations, and in the course of the year discovered the peculiar shape of Saturn, the phases of Venus, and irregular moving spots on the Sun, all of which he mentioned, along with the periods of Jupiter's satellites, in the preface to the Discourse on Bodies in Water in 1612 and then discussed in greater detail in his History and Demonstrations Concerning Sunspots, usually called the Letters on Sunspots, in 1613.
Within a year of publishing the Sidereal Messenger, Galileo was the most celebrated natural philosopher in Europe. In the spring of 1611 he visited Rome in what appeared to be a triumph. Cardinal Robert Bellarmine (1542–1621), statesman, theologian, member of the Congregation of the Holy Office, and head of the Collegio Romano, asked his mathematicians for their opinion of Galileo's discoveries, and they confirmed every one, with the proviso that Father Clavius believed that the surface of the Moon is not rough, but has denser and rarer parts. Christopher Clavius (1537–1612), with whom Galileo had earlier corresponded, then the most distinguished astronomer in Italy, had taken some time to be convinced of the discoveries and wished more time to interpret them properly, as he wrote in the last, posthumous, edition of his Commentary on the Sphere of Sacrobosco. Galileo met with Clavius and Bellarmine, and was feted by the Collegio with a dinner and speech in honor of his discoveries. He was also elected the sixth member of Federigo Cesi's (1585–1630) Accademia dei Lincei (lynxes), which published his Letters on Sunspots in 1613 and ten years later The Assayer. Galileo was very proud of this honor, and from this time he regularly signed his name Galileo Galilei Linceo.
Galileo's discoveries changed the world, but first they changed Galileo. Before, he was favorable to Copernicus and critical of Aristotle, but had published nothing on these subjects, at least under his own name. After, he became the strongest proponent of Copernican theory in Italy and the most hostile critic of Aristotelian physics anywhere, and for the latter distinction there was no lack of competition. And the transformation was immediate. In the Sidereal Messenger he states unequivocally that the planets move around the Sun and that in his System of the World he will show that the Earth is a planet. In the Letters on Sunspots, following the discovery of the phases of Venus, the heliocentric theory is treated as a fact, especially in the third letter. While it is true that Galileo's discoveries with the telescope do not by themselves prove the heliocentric theory – and he never quite claimed that they do, although he certainly believed they came very close – they did provide a great deal of evidence in its favor and remove a number of objections. Just as important as their evidence for Copernican theory was the evidence his discoveries provided against the Aristotelian theory of the heavens as perfect and unchanging – because they have only circular motions – and utterly unlike the Earth. And although the evidence for Copernicus now has the greater fame, it appears that to Galileo's contemporaries the evidence against Aristotle had the more disturbing effect. Here the Sidereal Messenger is not explicitly anti-Aristotelian, although Galileo had no doubts about the implications of his demonstrations of the similarities between the Earth and the Moon, while the devastatingly polemical Letters on Sunspots are in part a pointed attack on the Aristotelian perfection of the heavens. Truly, Galileo's discoveries changed the world, and it is not surprising that each one was received with everything from the greatest acclaim to the greatest hostility. On the one side was Kepler, who responded by May of 1610 with his enthusiastic and fanciful Conversation with the Sidereal Messenger, and Galileo's students and friends, who were soon to be known as Galileisti. On the other, the philosophers and, yes, the astronomers, including at first the learned and refined Jesuits of the Collegio Romano, who either refused to believe the observations or sought ways of explaining away their troubling consequences.
We have touched upon Galileo's discoveries and their implications in general. Now let us consider them specifically, noting that Galileo did not discuss their full implications until the Dialogue of 1632.
THE MOON
Galileo first turned his telescope on the Moon. He found that it had a rough surface with mountains and plains, which was especially evident by examining the terminator between the illuminated and dark portions. For bright points of light were seen in the dark that gradually extended toward the terminator, just as the light of the rising Sun first strikes the tops of mountains and then gradually extends down to the surrounding plain. He drew and had engraved five illustrations of crescent and quarter phases, two of which are shown in Figure 7.1 – seven of his hand drawings also survive – of remarkable realism if not altogether accurate, showing the points of light in the dark part, clear distinctions between the lunar seas and highlands, as they are now known, and a number of circular features that we know to be craters. The one of exaggerated size in Figure 7.1b is Albategnius, and others are also identifiable: the large dark region to the left is Oceanus Procellarum, and the roughly circular feature in the upper part Mare Imbrium with part of the illuminated rim of Mare Serenitatis extending into the dark half. Of course these large features are also visible without a telescope, but not in such detail. Estimating the distance of a lighted point from the terminator as 1/20 the diameter of the Moon, he determined that the height of a mountain exceeded four miles. Thus, in Figure 7.2, with the Moon at quadrature, suppose a point of light at B in the dark part projected to the limb at D. Let the radius of the moon CE = 1,000 miles and the distance DC = (1/10)CE = 100 miles. Then DE = (CE2 + CD2)1/2 ≈ 1,005 miles, and the height of the mountain DA= 5 miles, although Galileo gives DA > 4 miles. To explain why such mountains do not give the Moon an irregular edge, like a toothed wheel, he suggests that the ranges of mountains overlap to form a smooth curve, and further, that the Moon, like the Earth, is surrounded by a vaporous orb.
Figure 7.1.
Figure 7.2.
Galileo also used the opportunity to discuss a problem he had solved several years earlier, the secondary light of the Moon. When the Moon is in its crescent phase, the dark part of its body is also faintly lighted, sufficiently to detect the large spots with a good telescope, an effect that disappears around quadrature. The nonuniformities of shading in the dark part of Figure 7.1a may be intended to show the effect of the secondary light. After refuting a number of incorrect causes, as the intrinsic light of the Moon, or light imparted by Venus or the stars, or sunlight passing through the body of the Moon, he explains the secondary light as reflected light from the Earth. Just as the Moon when nearly full illuminates the Earth at night, so the nearly full Earth illuminates the Moon. He adds that he will explain this in more detail in his System of the World, where he will show with many reasons and experiments that there is a very strong reflection of sunlight by the Earth; and against those who exclude the Earth from the choric dance (corea) of the stars because it is without motion and light, he will confirm by demonstrations and countless reasons drawn from nature that the Earth is a planet (vagam, wandering) and surpasses the Moon in light. This is the most direct statement concerning the motion of the Earth in the Sidereal Messenger, and it is significant that it is in connection with the secondary light of the Moon, which Galileo thus takes as very important evidence that the Earth may be regarded as a heavenly body.
What is to be inferred from all this is that the Earth is like the Moon, a body shining by reflected light from the Sun, and the Moon is like the Earth, a solid body with a rough surface made, not of some fifth element of the heavens, but of the same solid stuff as the Earth. This in itself was not new. There had been speculation since antiquity that the Moon was like the Earth and also inhabited. In the Considerations of Alimberto Mauri, a controversial work on the new star of 1604 published pseudonymously in 1606, Galileo had noted the irregularity of the terminator at quadrature as evidence that the Moon has large mountains and flat planes. Kepler believed the curious circular features were built by the inhabitants to shelter themselves from the scorching Sun – they lived in caves along the rims – and some years before the telescope Michael Maestlin thought he saw rain clouds on the Moon. But these were just fancies. Galileo would have none of them, but he knew that the Aristotelian theory of the heavens was finished, or at least in serious trouble, and that if the solid and earthlike Moon could move about the Earth, the bright and moonlike Earth could move about the Sun. None of Galileo's discoveries provoked more hostility and more preposterous attempts at refutation than the rough surface of the Moon and the explanation of the secondary light, and with good reason because for none were the stakes as high. The controversy even extended to the depiction of the Moon in the iconography of the Immaculate Conception, drawn from Revelation 12.1–2, showing a pregnant woman with a crown of twelve stars standing on a crescent Moon with its horns downward that may be either smooth, immaculate, even translucent, according to traditional opinion, or rough, maculate, and opaque, according to Galileo's description.
THE STARS
In observing stars Galileo found that their enlargement was much less than that of the Moon and planets, which appear as globes, like little moons. The telescope, he concluded, removes the stars’ extraneous rays and shows them to be much smaller than previously thought, although so much brighter that a star of the fifth or sixth magnitude appears equal to Sirius. The removal of the stars’ “irradiation,” as he later called it, which he found to apply also to planets, was one of Galileo's most important discoveries, to which he returned in his later works, refining its explanation and extending its implications. Still more strikingly, countless fainter stars were seen, amounting to more than six additional magnitudes of brightness. Within a space of one or two degrees in Orion, he found more than five hundred new stars, and to illustrate this he showed eighty new stars around the nine original stars in the belt and sword and thirty-six within half a degree of the six Pleiades. The head of Orion and Praesepe in Cancer, listed in Ptolemy's star catalogue as “nebulous,” were found to consist of many small stars very close together, and the most spectacular of all, the Milky Way, whose nature had provoked endless discussion, turned out to consist of vast numbers of stars beyond all counting grouped into clusters.
The small apparent size, large range of brightness, and immense number of the stars were Galileo's most ambiguous, and potentially most important, discoveries. Were stars now to be very small objects at a single small distance, say, just beyond Saturn, or objects of indeterminate size distributed over many large but indeterminate distances? The latter interpretation makes the diurnal rotation of the celestial sphere implausible to the point of impossibility, and removes the one purely astronomical objection to the motion of the Earth about the Sun: the absence of any detectable effect on the positions of stars. However, after the speculations about an infinite universe filled with innumerable inhabited worlds by the unfortunate Giordano Bruno, the subject was, let us say, rather sensitive, and Galileo approached it cautiously even in the Dialogue. Nevertheless, there can be no doubt that Galileo's observation of the stars was the first step toward the universe of vast numbers of stars and systems of stars at vast distances of modern cosmology.
THE SATELLITES OF JUPITER
On 7 January 1610 Galileo observed Jupiter and found two small bright stars to the east of the planet and one to the west in a straight line parallel to the ecliptic. On the 8th all three stars were equally spaced in a line to the west. He wondered if perhaps Jupiter could be moving to the east, although by computation, from tables or an ephemeris, it was moving retrograde to the west. The 9th was cloudy, but on the 10th two stars were to the east and the third, he guessed, was hidden behind Jupiter. At this point he realized, with astonishment, that the motion must belong, not to Jupiter, but to the stars. By the next night, 11 January, he says that he reached his conclusion: the three stars were moving about Jupiter just as Venus and Mercury move about the Sun (although Stillman Drake has presented evidence that this conclusion was not reached until the 15th). On 13 January he observed a fourth star and noted that none of them twinkle like stars. That all four were moving around Jupiter was confirmed by nightly observations, continuing until 2 March, with measurements of their distances from Jupiter and each other in apparent diameters of Jupiter, taken as one arc minute, along with estimates of their size or brightness, and from 26 February their passing of a nearby star (see Figure 6.3 in previous chapter). Since Galileo wished to demonstrate beyond doubt that these four stars were indeed moving around Jupiter, he published sixty-five illustrations of the configuration at each observation showing stars aligned about an open circle to indicate their distances, with the sizes of the stars distinguishing their apparent size, and in the last five showing the nearby fixed star. Their variation in size or brightness he assumed was due to Jupiter's being surrounded by a vaporous orb, like the Earth and Moon, which dimmed the light of the stars when they were seen through it.
The satellites of Jupiter were a total surprise, first to Galileo, then to everyone else (except Kepler who immediately concluded that they must exist for the inhabitants of Jupiter as our Moon exists for us). Because the reliability of the telescope itself was suspect, and the satellites could only be seen with a fairly good telescope, there was some skepticism about whether they were really there even after the evidence of Galileo's observational reports and sixty-five diagrams. Galileo says he did an excellent job of convincing the entire University of Padua of their existence at public lectures – although the noted Aristotelian Cesare Cremonini refused even to look through a telescope – but when he tried to show them to Giovanni Antonio Magini in Bologna, he did not do as well, for Magini failed to see them even with Galileo's telescope. By the end of 1610, however, there had been a number of independent confirmations, including those of Magini and the astronomers of the Collegio Romano, and the existence of the satellites was well established. The term “satellites” (from satelles, an attendant upon an important person), incidentally, was introduced by Kepler in 1611; Galileo called them “planets,” “stars,” and “little stars” (stellulae). The significance of the satellites, aside from their own interest as the very first additions to the planetary system since the most remote antiquity, was that they showed that a planet could move and have satellites, since Jupiter was obviously moving, answering a perfectly reasonable objection to Copernican theory that it seemed odd that the Earth could have the Moon moving around it while it moved about the Sun.
After the publication of the Sidereal Messenger, Galileo continued to observe the satellites and set about determining their synodic periods. He did so in an “Atlantic labor,” as he called it, that remains his most important contribution to mathematical astronomy. Kepler thought the task to be nearly impossible because of the difficulty of distinguishing the three inner satellites. In fact the order of brightness is III, I, II, IV, but all are variable, especially when close to the planet, and the whole problem nontrivial. The most obvious way of distinguishing the satellites is by their characteristic greatest elongations from the planet, identifying first the outermost IV, then III, then II, and last the innermost I. But the moment of greatest elongation is not well defined since the satellite is sensibly unmoving for some time, so these are useless for finding the periods, without which it is impossible to keep track of any one of them and continue to distinguish it from the others. A precarious way of estimating the periods without necessarily distinguishing the inner satellites is to look for identical or nearly identical configurations. Galileo found something like this on 3 and 10 December of 1610, seven days less one hour apart, in which IV had moved nearly from one greatest elongation to the other, completing about half a revolution, and the inner satellites occupied the same positions, presumably completing integral numbers of revolutions. Hence, one might guess that the period of IV was two weeks – in the Sidereal Messenger it was “semimonthly” – III one week, II one-half week, and I one-quarter week, which is nearly correct for all but IV. On 11 December Galileo wrote to Giuliano de’ Medici, the Tuscan ambassador in Prague, that he had found a way of determining the periods of the Medicean planets, and that he should give his regards to Signor Kepler!
However, this was only a rough indication, by itself not very helpful without identifying the inner satellites. Galileo next turned to observations in which a satellite was hidden by conjunction with Jupiter, either at apogee above or perigee below the planet – now called occultation and transit – which could be distinguished by the direction of the satellite's motion, west to east with respect to Jupiter near apogee, east to west near perigee, as a means of establishing an epoch, a location at a known time. This too was precarious for a number of reasons, the first being that the brightness of Jupiter could well conceal a satellite separated from the planet by more than one diameter, a problem made all the worse by spherical and chromatic aberration in Galileo's telescope, enlarging Jupiter's image with a colored halo. His observational records show that on 29 December satellite I was at perigee, on 24 January 1611 III at apogee, on 13 February II at perigee, and on 7 March IV at perigee. Then on 15 March, after two observations showing three satellites very close to the planet, no satellite could be seen from three hours after sunset until the setting of Jupiter four hours later. He took this “great conjunction,” as he called it, as his fundamental epoch and, estimating times that II, III, and IV were at apogee and I at perigee, used earlier observations to derive provisional periods and mean motions. On 23 March he left Florence for Rome, continuing his observations each night, and after he arrived in Rome on 29 March for his great visit began the “Atlantic labor” of correcting the periods by calculating backwards to compare with earlier observations. In the preface of the Discourse on Bodies in Water (1612), he gives periods for the satellites that he says he worked out in Rome in April of 1611. It is, however, certain that these were not reached so early, for there were still problems in the method of determining periods. Also, it would not be characteristic of Galileo to wait a full year to publish, or at least report in correspondence, periods in which he had confidence, since he was not the only one trying to find them and he wished to be the first.
When he returned to Florence in June, he made two extended series of calculations to examine and refine the periods, probably worked out in Rome, forward from 15 March to 15 June and backwards from 10 March to the preceding 15 November, each containing drawings of the configurations to compare with the observations. The satellites were located in the drawings by means of a graphical analogue computer, called a giovilabi on the analogy of astrolabi, by which motion in a circle around the planet in degrees from apogee could be converted to an elongation in radii of Jupiter by means of a perpendicular to the diameter of the circle. But the results were inconsistent, particularly when the satellites were close to the planet, and for this there were two sources of error. The first is that he forgot to take into account that the Earth was moving around the Sun, which changes the direction of the apogee and perigee of Jupiter's satellite system by as much as ±11½°, the angle subtended by the radius of the Earth's orbit at Jupiter. Of course this does not mean that Galileo had any reservations about the Earth's motion, and the same effect would occur if the Earth were fixed and Jupiter moving on an epicycle, it is just that the problem of the satellites was so new and complex that he only gradually comprehended all that had to be done to solve it correctly. But in the worst case, in which two observations or calculations were made at the maximum positive and negative parallactic corrections, the difference in direction could amount to 23°, producing errors in the epochs and any subsequently calculated positions. Thus in Figure 7.3 in which the Sun is at S and Jupiter at P, when the Earth is at O1 or O2 the apogee and perigee will be A1 and B1 or A2 and B2 respectively, differing by π ≈ 23°, which can produce a difference of three hours in the time of apogee or perigee for I and of more than one day for IV. By late 1611 or early 1612 Galileo had introduced a correction into his calculations, angle SPO, under the name prosthaphaeresis (addition-subtraction), the term for the same correction in computing a planet's position, used by Ptolemy for the correction due to the motion of the planet on its epicycle and by Copernicus for the parallactic correction due to the motion of the Earth. He later carried out a series of calculations for 17 March to 16 July of 1612 using this correction, but the periods in the Discourse on Bodies in Water were already found with it not long before the manuscript was delivered to the printer in late March, for tables of mean motions implying periods from which these were rounded were either derived or confirmed by Galileo in notes using the correction. The published periods, the periods implied by the tables in Galileo's notes, and the modern values from Sampson's tables (1910) are as follows:
Figure 7.3.
Hence by March of 1612 Galileo had reached periods accurate to a few minutes. However, a second problem remained, which he had earlier noted, that at times a satellite remained invisible at apogee for an excessively long time. A note on the calculation for 18 March shows that he had found the solution: “It is clearly certain that IV was in the shadow of Jupiter, for it had not yet appeared at the sixth hour.” He had discovered that a satellite could be invisible somewhat before or after it was behind the planet because it was eclipsed. In Figure 7.4 the satellite is in occultation from Oc.D to Oc.R and in eclipse from Ec.D to Ec.R, the excess time of invisibility being from Oc.R to Ec.R, and in the same way the eclipse may also occur before occultation. This was the last piece of the puzzle to be discovered by Galileo – recognition of the latitudes and inequalities of the satellites, transits of the satellites’ shadows across the disc of Jupiter, and the equation of light came only in the second half of the century – and he again set to work refining his periods and epochs. He now had another device to aid his observations: a micrometer of sorts consisting of a grid ruled in radii of Jupiter attached to the side of his telescope. When an observation was made with one eye looking through the telescope and the other eye looking at the grid, the image of Jupiter and the satellites was superimposed on the grid and elongations could be found very precisely by simply counting lines of the grid. This device also allowed him to improve his measurements of the greatest elongations of the satellites and of the apparent diameter of Jupiter s by taking the diameter of the image i on the grid divided by the focal length f and magnification m of the telescope, s = sin−1(i/fm). In this way an estimate of o;o,50° for the diameter of Jupiter as a fraction of the elongation of IV was reduced using observations in January and June to o;o,41,37° and o;o,39,24°. The modern mean value is about o;o, 38°; Galileo's slightly larger results are due to the enlargement of Jupiter's image by spherical and chromatic aberration. On the night of 27–28 December of 1612 and on 28 January 1613 he made measurements of the distance of Jupiter from a star that it passed twice in direct and retrograde motion. These have turned out to be the first sightings of Neptune. Still more remarkably, on 28 January he noted the location, in a straight line with Jupiter and a fixed star, of the same star, “which was also observed the preceding night, but they (the stars) appeared more distant from each other” (sed videbantur remotiores inter se)!
Figure 7.4.
By early 1613 Galileo had worked out the theory of the satellites to his own satisfaction, and as a demonstration he prepared diagrams showing their elongations from Jupiter from 1 March to 8 May, the first of which is shown in Figure 7.5, published as an appendix to the third of the Letters on Sunspots, which appeared by late March. In a postscript he discussed the difficulties of observing the satellites when close to Jupiter because of its “irradiation,” and he explained and gave the dates of four eclipses, remarking that whether eclipses occur and their durations depend upon the annual motion of the Earth, the latitude of Jupiter, and the distance of the satellite from Jupiter. Evidently he now took the distinction of eclipses
Figure 7.5.
and occultations as evidence of the Earth's annual motion – as well he should – for, although possible, it is exceedingly cumbersome to attribute the distinction to Jupiter's motion on its epicycle in the Ptolemaic theory or the Sun's motion about the Earth in the Tychonic. There was also a practical purpose to Galileo's Atlantic labor on the theory of the satellites, namely, the determination of longitude, a proposal for which he sent to the government of Spain in September of 1612. The principle is that if identical phenomena of Jupiter's satellites, as occultations or eclipses, are observed from different locations, the difference in local time will correspond to the difference in geographical longitude. Thus tables and diagrams of the phenomena computed for the meridian of, say, Florence, would allow the difference in longitude from Florence to be determined from wherever the phenomena were observed. Negotiations with Spain and work on this project were to occupy Galileo for years – about 2,000 observations and calculations survive among his papers from 1613 to 1619 – and in 1636 he made the same proposal to the Netherlands. Again nothing came of it, but the idea was to occupy the attention of astronomers into the eighteenth century and was responsible for much of the study given to the great system of Jupiter and the four Galilean satellites, to this day, it should be noted, along with the Moon the most interesting satellites in the planetary system.
SATURN
On 25 July 1610 Galileo observed Saturn and found that it looked like a large star with two smaller stars on each side that nearly touched it and never moved. He announced his discovery to Kepler in an anagram, which Kepler assumed to refer to two satellites of Mars (since the Earth had one and Jupiter four). The first published report was in the preface to the Bodies in Water in 1612, but by late in the year the smaller stars had disappeared; Galileo predicted in the third of the Letters on Sunspots that they would reappear in 1613, and they did. In 1616 he noticed that their form had changed to what later came to be called “handles” (ansae). He now realized that whatever they were, they were not spherical, and he predicted another disappearance for 1626, which also happened. He suspected their changing appearance had something to do with the alignment of Saturn and the Earth – in this sense he regarded the changes as evidence for the Copernican theory – and possibly with a slow rotational period of Saturn and its two companions, but it was not until 1659 that Huygens gave the correct explanation, that Saturn was surrounded by a thin, flat ring, not touching the planet and inclined to the plane of the ecliptic.
VENUS
There was another discovery in 1610 that Galileo could explain completely: the appearance of Venus. If Venus were below the Sun, as in Ptolemy's theory, when observed from the Earth it would always appear as a crescent of greater or lesser size and width. If it were above, which is now seldom mentioned but was still a possibility, it would always appear as a disc. But if it moved around the Sun, as in the Copernican or Tychonic theories, it would change from a small round disc near superior conjunction to a large crescent near inferior. That is exactly what Galileo found between October and December, when he received a letter on the phases of Venus from his former student Benedetto Castelli (1578–1643), to whom he reported his observations. It has been suggested that Galileo did not understand the significance of the phases of Venus until he received the letter from Castelli, but that is to misunderstand the period required to see the succession of phases and eliminate two of the three possible arrangements. The significance was now apparent and conclusive, for it meant that Venus, and presumably Mercury, must move about the Sun. Even before he reached his final conclusion, on 11 December he sent Kepler an anagram, explained on 1 January as “The mother of loves emulates the figures of Cynthia” (the moon). Kepler later wrote Galileo that this came as a surprise to him for, as Venus is so bright, he had believed it to be self-luminous. To Father Clavius on 30 December Galileo wrote that Venus and all the planets shine only by the light of the Sun and that the Sun is “without any doubt the center of the great revolutions of all the planets.” The phases of Venus were also first mentioned in the preface to the Bodies in Water, and in the third Letter on Sunspots he reported the apparent diameter to vary from less than 1/200 the diameter of the Sun at greatest distance to more than six times as great at least distance, that is, from less than o;o,10° to more than o;1°, both quite accurate and far smaller than the traditional value of 1/10 the diameter of the Sun or o;3°. He probably measured them using the grid micrometer just as he did for Jupiter.
SUNSPOTS
Galileo was not the first to see sunspots with a telescope, nor was he the first to conclude that they were on the Sun and showed that the Sun rotated. Johann Fabricius had published a book on this in 1611. Galileo began observing them in 1610, showed them in Rome the following year, and made a careful study of their motions and changing appearance, later with help from Castelli, but kept his own counsel on a subject of such complexity. He mentioned them briefly in the preface to Bodies in Water as a strong argument either that the Sun revolves, or that there are other planets moving about the Sun with elongations smaller than that of Mercury, which only become visible when seen against the Sun, or both. In a paragraph added to the second printing, he reported that continued observation had convinced him that the spots are contiguous to the Sun's body and carried about by its rotation in about a lunar month, “a great event, and even greater for its consequences.”
What provoked him into serious publication was a pamphlet called Three Letters on Sunspots by one “Apelles hiding behind the painting” published by Marcus Welser in Augsburg early in 1612. The letters were sent to Welser in November and December 1611 by the Jesuit Father Christopher Scheiner (1573–1650), professor in Ingolstadt, who wrote under a pseudonym on instructions from his order lest he be wrong and prove a source of embarrassment; hence he used the name “Apelles hiding behind the painting” (the story is in Pliny 35.85), showing that he was willing to take correction. Scheiner thought it impossible that the Sun have on it spots darker than the dark parts of the Moon, and that the spots do not return regularly to the same positions shows that they are not carried around by a rotation of the solar body. Rather, he believed that the spots were many small planets moving about the Sun like Mercury and Venus, although much closer, the possibility that Galileo considered and rejected. One of his arguments for this was that the spots are broad near the center of the Sun but grow thin as they approach the limb where, similar to the crescent phase of Venus, part of the body of the small planet is lighted and not visible against the Sun. Thus, he was aware of the phases of Venus, but he also believed he had independent, and superior, evidence that Venus moved around the Sun. Magini's Ephemerides predicted that on 11 December 1611 Venus would reach superior conjunction with a latitude less than the semidiameter of the Sun; hence if Venus moved on an epicycle below the Sun a transit lasting no less than 40 hours should be visible, and this should be easily observable since Venus would be moving in the direction opposite to sunspots and Scheiner assumed the traditional apparent diameter of O;3°. Venus was not seen beneath the Sun. As he delicately put it: “She blushed, rushed forward, but we did not gaze upon her nuptials. What follows from this I do not say – it is clear in itself – even if we were deprived of all other arguments, from this one it would be proved that the sun is encircled by Venus.”
Galileo received Apelles's letters from Welser in late March with a request for his opinion, which Welser seems to have supposed would be favorable. Little did he know. Galileo answered in two letters in May and October and, following a reply to the first letter by Apelles, called A More Accurate Inquiry Concerning Sunspots and the Wandering Stars about Jupiter, a third in December. The History and Demonstrations Concerning Sunspots, published by the Accademia dei Lincei in March of 1613, is a masterpiece, of science and of invective. What aroused Galileo's ire was not so much Scheiner's incorrect explanation of sunspots, which was bad enough, as his smug insinuation that the absence of the transit was by itself the best evidence that Venus moved around the Sun. It is for this reason that he devotes so much attention to the phases of Venus, with a patronizing explanation as though Scheiner had never so much as heard of them, and to refuting the gross exaggeration of Venus's apparent diameter and with it the use of the absence of a transit as evidence. Venus could still, he points out, be entirely above the Sun or self-luminous, both of which possibilities are only refuted by its phases.
Sunspots, he says, cannot be dark bodies like planets or, as Scheiner believed, darker than the dark parts of the Moon, because they are not even dark, are in fact at least as bright as the brightest parts of the Moon and only look dark in contrast to the Sun. Galileo argued that, whatever they were, perhaps something like clouds, sunspots were on the surface of the Sun, as shown by their changing speed and separation as they move across the solar body and their foreshortening near the edge, all characteristic of motion on a sphere, as he then demonstrates. He noted that they all appeared within about 30° of the Sun's equator, moved with the same angular speed much too slowly for planets – he estimated the period of the Sun's rotation as about a month – and had irregular shapes that changed, appeared, and disappeared with considerable irregularity, and they could be of enormous size, much too large for planets. These were illustrated by thirty-eight plates in the second letter from drawings made in June through August 1612, using a method invented by Castelli of projecting the image of the Sun on to a piece of paper in a darkened room. Those for 3–4 July are shown in Figure 7.6, in which the motion, foreshortening, and change in appearance of the spots are evident. The implications of these discoveries for the Aristotelian perfection and immutability of the heavens need hardly be mentioned, but Galileo does so with scathing invective against philosophers who never raise their eyes from the pages of Aristotle. The letters are not confined to sunspots, for they consider his other discoveries with the telescope, including the predicted positions of Jupiter's satellites, are solidly Copernican, and contain discussions of scientific method that have become deservedly well known. They are scientifically unanswerable, brilliantly, and caustically, witty, and made Apelles look foolish. Galileo won hands down, which may have been a miscalculation because it made an implacable enemy for life of Scheiner, who was really quite a competent scientist, later writing the definitive work of the century on sunspots, the gigantic Rosa Ursina (1630), in which he decided that the spots were on the surface of the Sun after all.
Figure 7.6.
CONCLUSION
Even more so than 1604 when he discovered the law of the acceleration of falling bodies, 1610 was Galileo's annus mirabilis, and his discoveries with the telescope were to affect, perhaps even determine, most of his subsequent work. Although this point is certainly debatable, I believe that Galileo was an absolutely convinced Copernican years before he made use of a telescope. His reasons were: first, the sense of the heliocentric theory itself, how it determines the order and distances of the planets in a unified system and explains the behavior of geocentric planetary theory, but not vice versa, which has something close to an inevitability about it, at least for those who truly understood it, who were few; second, Galileo's explanation of the tides through the variable velocities of the seas caused by the Earth's annual and diurnal motions – never mind that it is incorrect by Newtonian mechanics and perhaps even by Galilean mechanics – which he reported to Paolo Sarpi by 1595, two years before he wrote to Kepler that he had arrived at the Copernican opinion “many years ago”; and, third, the explanation of the secondary light of the Moon, showing that the Earth and Moon are similar bodies – and the Moon most certainly does move – supported by the speculation that the Earth and Moon have similar rough surfaces, both conclusions reached by 1605. It is in connection with the explanation of the secondary light in the Sidereal Messenger that Galileo promised his System of the World, which he described in May of 1610 as “two books on the system and constitution of the universe, an immense conception full of philosophy, astronomy, and geometry”. This “immense conception” had surely been in the works for some time, certainly in Galileo's head and possibly also on paper; it was surely Copernican, and Galileo surely believed that the telescope had given him what he needed to bring it to completion, that is, to prove the Copernican theory, which, as evident from his correspondence prior to 1616, he believed he could do.
But it was not to be, at least not for another twenty years and not as Galileo had originally planned. The work was stopped dead by the prohibition against writing on Copernicus in 1616, lifted only conditionally in 1624. However, even before the prohibition something restrained Galileo's hand, which could have been no more than his work on sunspots and the satellites of Jupiter, to both of which he devoted a great amount of time, but it also could have been that he was still not ready to set out his full evidence and argument. It is difficult to know how much of the Dialogue of 1632 actually goes back to work, whether in his head or on paper, done by Galileo twenty years earlier in the way that much of the Two New Sciences of 1638 goes back to work done thirty years earlier. Most of Galileo's evidence, although not necessarily most of his argument, was in place by 1613, when he learned of the seasonal change in the motion of sunspots, but it appears that the argument from sunspots, which Galileo considered, along with the tidal theory, his best proof of the motions of the Earth, was not formulated until 1629, and it is possible, although in no way certain, that many of the arguments of the Second Day in refutation of Aristotelian criticisms of the diurnal rotation of the Earth were also formulated years after Galileo had reached the conclusions in mechanics that underlay them.
Nevertheless, it is the discoveries with the telescope and their interpretation that made the Dialogue possible, and whatever Galileo had previously written or thought about the System of the World must have been radically transformed by what he found in 1610–1613. Except for the sense of the Copernican theory itself and the theory of the tides, a physical theory that Galileo believed to prove the two motions of the Earth, all of the positive arguments for the heliocentric theory and all but one of the refutations of astronomical, not physical, arguments against it depend directly or indirectly upon what was shown by the telescope. (The exception is the refutation of Scipione Chiaramonti's large parallaxes of the new stars by a prescient application of probability, the first theory of errors.) Among these arguments are obviously the phases of Venus, showing that it must move around the Sun, extended by induction to all the planets since, aside from the superior planets reaching opposition, their motions do not differ from that of Venus; the removal of the “irradiation” of Venus and Mars, showing that their apparent sizes varied in proportion to their change of distance, which Kepler correctly pointed out was no argument since the change of distance is the same in the geocentric system, although Galileo seemed to think differently; the variation in the motion of sunspots, reasonably explained by the annual motion of the Earth and the rotation of the Sun, which is also evidence by analogy for the rotation of the Earth, and not reasonably explained in any other way; the similarity of the surfaces of the Earth and Moon, showing that if one can move, so can the other; the satellites of Jupiter, dark bodies that suffer eclipse just as our moon, showing that a planet can move and carry with it satellites; and the removal of the “irradiation” of stars, showing that they are much smaller than had been supposed and so can be sufficiently distant for parallactic effects to be negligible without their bodies being any larger than the Sun.
This is not a small list, and although philosophers may quibble over whether each point proves anything or not, as philosophers did and apparently still do, Galileo himself believed that together, by a preponderance of evidence, their force was overwhelming, and so apparently did anyone who read the Dialogue with an open mind, that is, without Aristotelian or theological prejudice that precluded appeal to empirical evidence and logical argument. If one wonders why the Copernican theory, with almost no adherents at the beginning of the seventeenth century, had pretty much swept the field by the middle, the answer, with no disrespect to Kepler, is above all the Dialogue – whether people actually read it themselves or not, it changed everything – and the Dialogue itself was grounded in a few months of telescopic observations that first established Galileo as the most celebrated scientist of his age and, with good reason, have kept him there ever since.
NOTE ON SOURCES AND FURTHER READING
Virtually all of Galileo's works, many writings of contemporaries concerned with Galileo, correspondence, and documents are published in Le Opere di Galileo Galilei, Edizione Nazionale, edited by Antonio Favaro, 20 vols., G. Barbèra, Florence, 1890–1909; reprinted with additions in 1929–39 and 1964–66. The earlier Le Opere di Galileo Galilei, prima edizione completa, edited by Eugenio Alberi et al., 15 vols., Società Editrice Fiorentina, Florence, 1842–56, is still valuable and contains some materials not included in the Edizione Nazionale.
The Sidereal Messenger (1610) has been translated by Edward S. Carlos, London, 1880; nearly completely by Stillman Drake in Discoveries and Opinions of Galileo, Doubleday, Garden City, NY, 1957; completely by Drake in Telescopes, Tides and Tactics. A Galilean Dialogue about the Starry Messenger and Systems of the World, University of Chicago Press, Chicago, 1983; and by Albert Van Helden in Sidereus Nuncius or The Sidereal Messenger, University of Chicago Press, Chicago, 1989. The two last are recommended. The Discourse on Bodies in Water is translated by Drake in Cause, Experiment and Science, University of Chicago Press, Chicago, 1981. Excerpts from the History and Demonstrations Concerning Sunspots (1613) can be found in Drake's Discoveries and Opinions of Galileo; a complete translation, including Scheiner's letters and contemporary correspondence, by Mario Biagioli and Van Helden is in progress and will be of great interest.
The Dialogue on the Two Great Systems of the World, Ptolemaic and Copernican (1632) was translated by Thomas Salusbury in Mathematical Translations and Collections, London, 1661, and has been revised by Giorgio de Santillana in Dialogue on the Great World Systems, University of Chicago Press, Chicago, 1953. Salusbury's translation is faithful but literal and archaic in language, and the freer modern translation by Drake, Dialogue Concerning the Two Chief World Systems – Ptolemaic and Copernican, rev. ed., University of California Press, Berkeley, 1967, has become the standard version. An abridged translation with an extensive commentary, mostly on philosophical issues, by Maurice A. Finocchiaro, has recently been published by the University of California Press, 1997.
There are many studies of various aspects of Galileo's astronomy. Of more comprehensive treatments, one must first note the works of Stillman Drake: the delightful presentation in dialogue in Telescopes, Tides and Tactics, Discoveries and Opinions of Galileo, and Galileo at Work, His Scientific Biography, University of Chicago Press, Chicago, 1978 (reprint Dover, New York, 1995), the finest book ever written on Galileo. The subjects of sunspots, comets, and the Dialogue are treated by William R. Shea, Galileo's Intellectual Revolution, Middle Period, 1610–1632, 2nd ed., Science History Publications, New York, 1977. A critical but nevertheless insightful survey is Willy Hartner, “Galileo's Contribution to Astronomy” in Galileo, Man of Science, ed. by Ernan McMullin, Basic Books, New York, 1967 (reprint The Scholar's Bookshelf, Princeton Junction, 1988), pp. 178–94.
Studies of the discoveries with the telescope include Van Helden, Measuring the Universe, Cosmic Dimensions from Aristarchus to Halley, University of Chicago Press, Chicago, 1985, Chap. 7, and “Galileo, Telescopic Astronomy, and the Copernican System” in Planetary Astronomy from the Renaissance to the Rise of Astrophysics, ed. René Taton and Curtis Wilson, The General History of Astronomy, vol. 2, Cambridge University Press, Cambridge, 1989, pp. 81–105; Drake, “Galileo's First Telescopic Observations,” Journal for the History of Astronomy (JHA), 7 (1976), pp. 153–68; and Shea, “Galileo Galilei: An Astronomer at Work,” in Nature, Experiment, and the Sciences, éd. T. H. Levere and W. R. Shea, Kluwer, Dordrecht, 1990, pp. 51–76, a fine study with particular reference to the work of Stillman Drake.
The lunar observations are considered by Ewan A. Whitaker, “Galileo's Lunar Observations and the Dating of the Composition of ‘Sidereus Nuncius’,” JHA, 9 (1978), 155–69, with discussion of papers by Guglielmo Righini and Owen Gingerich in Reason, Experiment and Mysticism in the Scientific Revolution, ed. by M. L. Bonelli and W. R. Shea, Science History Publications, New York, 1975, 59–88, and the paper of Drake just mentioned. Whitaker's excellent paper contains all of Galileo's drawings and engravings of the Moon compared with modern photographs, and his analysis of the dating of the observations appears definitive. See also Whitaker's “Selenography in the Seventeenth Century” in Planetary Astronomy from the Renaissance…, 119–43. The secondary light and the controversies following Galileo's lunar discoveries are treated by Eileen Reeves, Painting the Heavens, Art and Science in the Age of Galileo, Princeton University Press, Princeton, 1997, a highly original study of Galileo's knowledge of art and his influence on contemporary painting.
The manuscripts containing Galileo's observations and calculations for determining the periods of Jupiter's satellites, a sensational discovery in the Biblioteca del Palazzo Pitti by Eugenio Alberi, were first published by Alberi in 1846 in Vol. 5 of Le Opere di Galileo Galilei.; a more complete publication by Favaro with many facsimiles followed in 1907 in Vol. 3, Pt. 2 of the Edizione Nazionale with additions in the reprint of 1931. The principal studies are by Alberi in the volume just mentioned, by Pietro Pagnini in the introduction to the additions in the 1931 reprint, and by Drake, “Galileo and Satellite Prediction,” JHA, 10 (1979), 75–95.
The phases of Venus are treated in a series of papers by Drake, “Galileo, Kepler, and Phases of Venus,” Gingerich, “Phases of Venus in 1610,” and William T. Peters, “The Appearances of Venus and Mars in 1610,” JHA, 15 (1984), 198–214. Observations of Saturn and explanations of its curious appearance from Galileo to Huygens are treated by Van Helden, “Saturn and His Anses” and “’Annulo Cingitur’: The Solution of the Problem of Saturn,” JHA, 5 (1974), 105–21, 155–74. The observations and controversy concerning sunspots are discussed by Bernard Dame, “Galilée et les taches solaires (1610–1613)” in Galilée. Aspects de sa vie et de son oeuvre, Presses Universitaires de France, Paris, 1968, 186–251, in Shea's Galileo's Intellectual Revolution, and most recently by Van Helden in “Galileo and Scheiner on Sunspots: A Case Study in the Visual Language of Astronomy,” Proceedings of the American Philosophical Society, 140 (1996), 358–96.
It is only fair to mention that this paper is based in part upon a book in progress on Galileo's astronomy, treated in some detail, and his conflicts with the Church.