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GALILEO'S OBSERVATIONS OF THE MOON

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GALILEO'S OBSERVATIONS OF THE MOON

The purpose of this page is to bring together Galileo's surviving observations of the Moon, and the speculation regarding how and when they were made. An immense amount has been published on this subject, most of it inconsistent, and some of it obviously wrong. Please excuse the untidiness of our presentation while we, along with you, attempt to make some sense of it.

Frequent reference will be made to certain images published by and thought to have been drawn by Galileo. Particular emphasis is placed on a set of wash drawings appearing in a copy of the January 7, 1610 letter in which Galileo first announced his discovery of the moons accompanying Jupiter, on the engravings appearing in various editions of his book Sidereus Nuncius (first printed in Venice in mid-March 1610), on a sheet of wash drawings bound with Galileo's handwritten manuscript copy of Sidereus Nuncius at the National Library in Florence (BNCF), and on a brief series of perspective sketches of lunar features appearing on an undated sheet of calculations (also preserved at the BNCF). In the following we will show reduced size images of each of these with numbers assigned for identification. You may open the full-size original images on which these were based by clicking on the links in the following table. The selected image(s) should open in a new window from the host site (IMSS or BNCF). To the best of our knowledge, high resolution versions of the images in the recently discovered hand-illustrated possible printer's proof of Sidereus Nuncius are not yet available.

Links to High-Resolution Originals
Jan. 7, 1610 Letter (IMSS) L1 - L3 C1 - C4 & L4 L5
Engravings (IMSS, Venice ed.) E1 E2 E4 E3 & E4
Wash Drawings (BNCF) F1 - F6 F7
Perspective Sketches (IMSS) M1 - M5

For the engravings published in Sidereus Nuncius the links will direct you to the copies appearing in the IMSS's electronic version of the National Edition of Galileo's works, which are presumably photographs of the versions appearing in one of the first copies printed in Venice. Because printing quality is never perfect, the appearance of these plates varies slightly from copy to copy; and greatly in later editions, such as those later published (probably without authorization) in Frankfurt and London. Several places where you can view other copies of Sidereus Nuncius over the internet are indicated on our Additional Information and Accessing Manuscripts pages. Several of the other versions are as good as the IMSS copies linked to above. They also show more clearly how the images were placed on the printed page, something that is not obvious from the electronic transcription at the IMSS.

The topics addressed on this page include:

Introduction

It is by now well known that Galileo was not the first to examine the Moon through a telescope. Human curiosity being what it is, the idea of turning the early telescopes towards the sky had occurred to many. For example, in his article on the invention of the telescope, Albert Van Helden reprinted selections from a French newsletter published in October 1608 mentioning a telescope recently demonstrated in the Hague. Not only was it said to be useful for military operations, but when pointed at the sky it revealed stars too dim to be seen by the unaided eye. It is also now well known that the English mathematician and adventurer Thomas Harriot produced primitive drawings of the Moon as seen through a telescope dated as early as July 1609; and others later claimed to have made astronomical observations during that year and before.

Although Galileo carefully recorded the date and time of his observations of Jupiter's moons and, later, of sunspots; few, if any, of his surviving lunar observations are dated. This is a little surprising since it must have occurred to him that things in that new uncharted world might change with time; yet it appears that he did not date them. There is no real scientific purpose for assigning dates to them now; yet it is a topic that has stimulated considerable interest and debate. Many believe that the Earth's Moon was the first celestial object Galileo observed, and hence the date of his first observation of it might pinpoint the start of the remarkable sequence of discoveries by this most famous of early astronomers.

The possibility of assigning dates to the lunar engravings printed in Sidereus Nuncius on the basis of their appearance and historical context seems to have first occurred to Guglielmo Righini, a noted solar astronomer, and longtime director of the Arcetri Observatory in Florence. Righini had close ties to Galileo, for not only is the Arcetri Observatory adjacent to Galileo's final home, but Righini's wife, Luisa Maria Bonelli Righini, was the longtime and much beloved director of the museum (the IMSS) where most of Galileo's artifacts have been collected. Righini came to the conclusion that what he believed to be the first of the four distinct engravings in Sidereus Nuncius must represent an observation made shortly after sunset on October 2, 1609. His finding was challenged almost immediately by Owen Gingerich, and later by Ewen Whitaker, a prominent selenologist (lunar astronomer) at the University of Arizona's prestigious Lunar and Planetary Laboratory. Whitaker, with equal confidence, assigned a date of November 30, 1609 (two months later than Righini's date) to the same engraving, which he also felt represented the first evening of Galileo's celestial observations.

Whitaker's work, perhaps because of his more substantial credentials in the field of lunar science, seems to have attracted more attention than Righini's, and has led to the rather romantic notion that Galileo, paintbrush in hand, first turned a newly made 20-power telescope on the night sky on the evening of November 30, 1609, instantly recognizing the topography of craters and mountains written in the ragged pattern of light falling on the crescent Moon. This is certainly the impression it gave to an anonymous reviewer of Whitaker's article writing in the March 1979 issue of the popular and widely-circulated astronomy magazine Sky and Telescope.

Lest the reader imagine that the anonymous reviewer had added something for dramatic flair, the following are Whitaker's own words from a 1984 review of Selenography in the Seventeenth Century in the Cambridge General History of Astronomy:

"[Galileo] first directed one of his home-made telescopes (the 20-power) towards a non-terrestrial object during the evening of 30 November 1609, the object being the four-day-old crescent Moon. The fact that he observed that body until almost moonset, describing the progress of sunrise on what has since been identified as a group of mountain crests in the Janssen area of the lower cusp, as well as making three separate sketches of the Moon, shows that he immediately grasped the importance of what was revealed."

Yet, it is fairly clear from Galileo's letters that he must have looked at, and understood, the Moon considerably before this. In an August 29, 1609 letter to his brother-in-law, Galileo mentions both his pleasure at receiving a lifetime professorship at the University of Padua in return for his recent demonstration of the telescope in Venice, and also his disappointment that such a position would mean he could visit Tuscany at most during the university recesses. In a January 30, 1610 to Belisario Vinta, acting as a secretary to the Tuscan court in Pisa, Galileo describes some of the many wonders to be announced in his forthcoming book (Sidereus Nuncius). According to the translation published by J. J. Fahie in 1903, Galileo notes that his observations of the Moon will be somewhat old news, since he "had already ascertained that the moon was a body very similar to the earth, and had shown our Serene Master, the Grand Duke, as much, but imperfectly, not then having such an excellent spy-glass as I now possess." Since Galileo was living in Padua, some 120 or more miles from Tuscany, this demonstration of the Moon to the Grand Duke evidently occurred on one of those rare visits alluded to in the August 1609 letter. Fahie guesses the visit took place in October 1609 and quoting we know not what document says that the Grand Duke "to his great surprise and delight was able to see that the moon was a body very similar to the earth." The January 30 letter demonstrates not only that Galileo was curious enough to look at the Moon with telescopes less perfect than the one used to obtain most of the observations reported in Sidereus Nuncius; but also, if the date of his demonstration to the Grand Duke can be determined with more certainty, that he was aware of the earth-like nature of the Moon considerably before the November 30 date suggested by Whitaker.

Gingerich and Albert Van Helden, are among the very few professional scholars who acknowledge that Galileo may have looked at the Moon and even made sketches pre-dating any of those that survive. But even they believe Whitaker correctly dated all the surviving drawings and engravings, except one. Yet it is hard to believe that everyone is so sanguine about the accuracy of Whitaker's dates, or even the possibility of dating lunar drawings. Such dating requires the exact identification of features portrayed in the drawings. Manchester University's Zdenĕk Kopal, a noted astronomer of Whitaker's era, and author/editor of several definitive 1960's books on the Moon, including the Pic du Midi Photographic Atlas, repeatedly expressed his opinion that the engravings in Sidereus Nuncius were purely schematic and qualitative, and that there was no definite correspondence between any of the features depicted and real features on the Moon. Unfortunately we do not know if Kopal was aware of Whitaker's 1978 article or ever expressed an opinion about it. Similarly, Righini published a very slightly expanded version of his own datings in a 1978 compilation of his works about Galileo; in which he mentions (in note F) being aware that Whitaker had a similar article in press; but we do not know Righini's opinion about Whitaker's paper. Moreover it appears that none of these early researchers has bothered to check very carefully the claims of the others. In particular, no one seems to have investigated the extent to which two different people could independently arrive at the same identifications for the features shown along the terminator; nor whether the Moon would have actually looked the way these experts claim on their stated dates.

As to the identification of features we have been unable to find a single instance in which Whitaker and Righini claimed that a object on one of Galileo's engravings represented the same feature on the real Moon. As to the prediction of what the Moon would have looked like from a particular place at a particular time, modern computer technology has made this, if not necessarily any more accurate, at least much easier than it used to be. This a luxury that was not available to Righini, Gingerich or Whitaker in the 1970's; and it has brought accurate predictions within the range of non-experts like ourselves. The man in the street can now look at a photograph (or make their own observations) under circumstances very close to those that should have existed on the days the experts claim Galileo's images were made, and ask themselves whether the resemblance of the features is enough closer at those times (as opposed to some other) to assign a definitive date. As non-experts, we find considerable reason to be skeptical about all the dates to Galileo's lunar drawings, with the possible exception of one showing a star emerging from occultation. In the case of Righini, we find no resemblance between Galileo's engravings and the way the features he claims to have identified would have looked on the dates he mentions. In the case of Whitaker, there sometimes seems to be a vague resemblance, but the number of features in Galileo's images that cannot be plausibly accounted for on those dates, and number of ones that would be expected to be prominent but cannot be found in Galileo's images so far exceeds the others as to make one wonder if the occasional resemblance might be caused by nothing more than chance. This is not to say that the dates assigned by the experts are necessarily wrong (if they are true images of the Moon at a particular moment then there are, after all, only a very limited number of possible dates on which they could have been based), but only that the means by which those dates were determined seem highly suspicious to us. We find nothing in the visual or historical record definitive enough to justify so supremely confident and unequivocal a conclusion as that of Whitaker quoted above. Indeed, the number of inconsistencies in the interpretation, and in the drawings themselves, are so great that we are led to suspect with Kopal and others that the surviving images are much more impressionistic than realistic. We would be happy to be proven wrong, but we suspect, for that reason, that attempts to match the images in detail to the actual appearance of the Moon at any particular moment will ultimately prove futile.

Whether exact dates can be assigned to a particular drawing or not, we find it extremely hard to believe that Galileo's understanding of the nature of the lunar topography sprung (as Whitaker claims) full-blown into his mind on a single evening. It seems far more likely to us that, like the anonymous observers mentioned in Van Helden's 1608 newsletter, Galileo would have had the curiosity to look at objects in the sky, including the Moon, even with his very first telescopes in the summer of 1609. The January 7 letter suggests that Galileo must have been able to make reasonably detailed observations of the Moon, and to have had some understanding of what he was seeing by at least December 11, 1609. But this understanding was probably the culmination of a program of observing that had started some time before that, in a process to which no precise starting date can be assigned.

Drawings in a Copy of Galileo's Letter of January 7, 1610

Galileo's most famous letter is undoubtedly that in which he announced his discovery of three tiny stars near Jupiter, which later proved to be moons orbiting the planet. The story of this letter has been told at some length by Galileo scholar Stillman Drake, who includes a translation in his 1976 article. According to Drake, the original, which once belonged to Galileo's son, Vincenzo, seems to have been lost. The most complete copy is in the Vatican Library, and it includes the copies of Galileo's drawings of the Moon reproduced below. A second copy, in Florence, lacks both the drawings and the final page. Ironically, this famous letter, apparently written in response to a request for information about his telescopic observations, may never have been sent. Drake regards Favaro's assignment (in the National Edition) of Antonio de Medici as the intended recipient as without basis (he favors Galileo's fellow mathematician/astronomer Enea Piccolomini). Drake believes that the second of the letter's two sheets, containing the announcement of the stars near Jupiter (not yet recognized as moons), the signature and date, was written some days after the lunar observations; and that instead of sending the letter Galileo used the second sheet to record additional observations of Jupiter on subsequent nights. These, according to Drake, he copied into a new journal, discarding the original page; although it seems difficult to understand how this scenario could be consistent with the existence of the Vatican copy, ending with Galileo's signature and the January 7th date. In any event, Drake believes there was a lapse of time between when Galileo completed his description of his lunar observations and when he signed and dated the second page. The quality of the original drawings, and exactly what they depicted can only be guessed at from the anonymous copies, and from Galileo's description of the originals in the text of the letter, which has been likened by many to a first draft of Sidereus Nuncius.

![Galileo's First Drawings of the Moon](/web/20070601182754im_/http://www.pacifier.com/~tpope/Moon_Drawings/Galileo_MoonDrawings_Jan7_Letter.jpg "Drawings of the Moon appearing in a copy made from a letter dated January 7, 1610")
Adapted from original images © IMSS

Because of their apparent crudeness, these little copies of Galileo's drawings seem to have attracted almost no attention from professional Galileo scholars. Drake dismisses them as being copies of such poor quality that they serve only to indicate "what diagrams were included with the letter." He does not bother to reproduce them in his article. Whitaker also does not discuss or reproduce these drawings because, he says, "none of these displays any recognizable surface features." Yet, for the most part, they correlate quite well with the verbal descriptions in the letter, and, to us, seem to have important implications as to the reliability of dates which have been proposed for the other extant drawings and engravings. This is because the lunar features described in the letter seem to be the same as those described in Sidereus Nuncius; yet the copies of the drawings from the letter suggest that at least some of those features may have been observed at lunar phases quite different from what one would gather from the published engravings.

To make it easier to discuss the individual drawings, we have adopted Whitaker's procedure of assigning a Letter-Number designation to each. The drawings we call L1-L5 are sketches of the complete Moon, while C1-C4 depict the play of light across a single crater.

In his letter, as in Sidereus Nuncius, Galileo called the reader's attention to a particular feature illustrated by each of his sketches. In the following we attempt to extract and rearrange, but without change or embellishment, Galileo's description of each picture as given in Drake's translation of the letter [any comments added by us are in square brackets]:

  • L1: the Moon, four or five days after New. The boundary separating dark from light is rough, broken and confused. Light points protrude into the dark, and vice versa.

  • L2: [apparently an alternative version of L1] luminous peaks appear in the dark area, well separated from the light part. Over a period of some hours the luminous points grow and merge into the light area.

  • L3: shows the many dark spots visible in the lighted area. The dark spots have partially illuminated rims "facing the Sun". The spots are most frequent near the boundary between light and dark and, especially, in the lower [southern] horn of the crescent [the area we now call the Southern or Lunar Highlands]. In this area the spots are so numerous that they resemble "ice glass" [crackle ware]. The spots get smaller and fade at Full Moon, but return as the Moon wanes. Like a valley on Earth surrounded by mountains, the side of each spot towards the Sun is dark and the side towards the dark part of the Moon is light.

  • C1..C4: [Drake refers to these as "four schematic illustrations of different phases without any detail (and of smaller size than the other drawings)." We are unable to fathom his reason for believing they show the entire Moon. In the National Edition they are printed next to a sentence clearly stating they depict the changing pattern of illumination expected as the Sun shines at different angles on a particular crater with which Galileo was particularly impressed. Drake's own translation of that sentence is given in full below.]

    The spots come in different shapes, usually very irregular. There is one of particular interest that is:

    1. Near the middle of the Moon.
    2. Perfectly circular.
    3. Quite large compared to the others.Galileo observed this crater both at the moment when the Sun began to light the far rim, and later as the Sun rose and began to illuminate the bottom. It gave him the impression of an amphitheater on Earth, or, more precisely, the province of Bohemia: a circular plain bounded by very high mountains. Galileo, referring to this Bohemia-like crater, describes drawings C1..C4 as follows [Drake's translation]:

    "And its appearances before and after Full Moon are similar to these, noting that the shady part is always on the side of the Sun and the bright part opposite thereto, a positive indication that this is a perfectly round cavity surrounded by a high boundary."

    [The drawings, apparently impenetrable to Drake, appear to us to show: in C1, with the Sun rising to the right, a thin sliver of light is first seen illuminating the extreme left edge of the crater. In C2 and C3, as the Sun continues to rise to the right the illuminated area spreads across the floor of the bowl from left to right. Finally, in C4, with the Sun setting to the left, the shadow of the crater's left rim has begun to spread across the floor, extinguishing the bright part.]

  • L4: the Moon near its quarter. In the south there is an immense dark gulf that digs into the lighted part. As the sun rises, within this gulf a triangular prominence spreads into the form of promontory. Later, other bright points emerge, initially isolated in the dark, but growing and merging with the lighted part, like the tops of mountains on Earth which are lighted by the rising Sun before the valleys to their east. Such effects are seen only in the lighter parts of the Moon; the large dark patches visible to the naked eye appear smooth and do not change in appearance as the angle of illumination changes, although here and there are little patches brighter than the rest of the area. The contrast between the light and dark parts of the Moon is similar to what Galileo believes would be the appearance of the rough continents versus the smooth seas of Earth as viewed from space.

  • L5: the Moon, five or six days old. One of the large dark naked eye spots has long, brightly illuminated prongs at its top and bottom. The prongs converge toward the east [i.e., to the left, opposite to the current IAU convention for east and west on the Moon], and extend into the dark side of the Moon as shown.

These drawings place a definite limit on the latest date at which Galileo could have begun his telescopic observations of the Moon, because in his comments on drawing L3 he mentions he knew that the crackleware effect in the Southern Highlands was hard to distinguish at Full Moon. In Padua, where Galileo was living at the time, the most recent Full Moon occurred on the morning of December 11, 1609, the New Moon was early on December 26, and at the time the letter was signed was not yet quite full again. With the exception of the little diagrams of the Sun rising and setting over a bowl-shaped depression, all the drawings appearing in the letter could have been made, judging from the phase depicted, between about December 29 and January 1 or 2. However, they could be older for Galileo must have been observing longer, since he indicates he had seen craters illuminated both from the east and the west. Such observations of the Sun rising and setting over craters in various areas of the Moon could have been made between December 11 and December 26. Finally, the illustration L1-L5 themselves indicate phases from a little after a New Moon to a little before a first quarter. From Padua, the New Moon immediately preceding the date of this letter occurred in the early hours of the morning of December 26, 1609. The drawings indicate phases that could have been observed between approximately December 29 and January 2. It is, therefore, conceivable that Galileo could have started his telescopic observations of the Moon as late as December 11, 1609 and still seen everything reported in the letter of January 7, 1610. However, as we mentioned previously, it seems likely to us that he would have started much earlier, even though the views through his earliest telescopes would have likely been very imperfect. Galileo may have heard about the telescope as early as May 1609, but he says he did not try constructing one until he received a letter about it from the French nobleman Jacques Badovere (the letter does not seem to have survived); hitting upon the method of constructing it a short time later; and demonstrating a working version of about nine power to various dignitaries in Venice between August 21 and 24 (see Rosen, 1951). Although Galileo might well have looked at the Moon through this instrument, its power was, by his own admission, insufficient to see most of the things reported in Sidereus Nuncius, including clear images of the lunar craters. On the basis of the preceding reasoning, the date on which Galileo began to correctly understand the nature of the lunar topography based on observations with his telescopes seems to fall after August 24 and before December 11, 1609; trying to place a more precise date on it than that is probably futile.

This letter (which is written in Italian) seems to be the source of the commonly held belief that Galileo began his astronomical observations with a sighting of the four to five day old crescent Moon. The letter actually says, by way of introduction to figure L1:

Et le apparenze da me nella luna osservate, sono queste.
Prima, cominciando a rimirarla 4 o 5 giorni dopo il novilunio, vedesi il confine ...
come nella figura apresso si vede.

which Drake translates as:

And the appearances observed by me in the Moon are these.
First, commencing to look at it four or five days after New Moon, the boundary is seen ...
as seen in the adjoining figure.

It seems to us that Galileo has to start his description somewhere, and he may simply be saying that he will begin it with a drawing showing what one sees if one looks carefully at the Moon when it is 4 or 5 days past New. We are certainly not experts on Italian usage, but Drake's translation seems ambiguous enough to be read this way; particularly since, according to Drake, Galileo says he is showing how "the boundary is seen" rather than how "the boundary was seen". That is (if Drake's translation is correct), Galileo is presenting drawing L1 as a representation of a typical 4-5 day old Moon, not as a recollection of some particular one seen on a definite past date. He seems to be saying "If we commence our description with a careful examination of how the Moon looks when four or five days past Moon, we will see ..." Yet Drake unambiguously states his own belief that an observation of a five day old Moon on December 1, 1609 was Galileo's very first lunar observation, resulting in two "not very accurate" drawings.

Galileo was capable of writing in a direct and forceful way. If he had wanted to say "When I commenced my observations, the Moon was four or five days past New, and I saw the boundary as shown in the first figure ..." it would seem he could have easily done so. But he did not, either here or in Sidereus Nuncius (which appears to have been composed directly in Latin). Indeed, in Sidereus Nuncius Galileo used virtually the identical phrases to begin his detailed description of the Moon and introduce the first engraving, but chose to completely delete the words "first" and "commencing to examine," leaving no particular impression that this was his first observation:

The things I have seen by which I was enabled to draw this conclusion are as follows.
On the fourth or fifth days after New Moon, when the Moon is seen with brilliant horns, the boundary ...
as shown in the figure below.

The experts also allude to the passage towards the beginning of Sidereus Nuncius where Galileo says that after completing his 30 power telescope "forsaking terrestrial observations, I turned to celestial ones, and first I saw the moon from as near at hand as if it were scarcely two terrestrial radii away" (compared to what he believes is the normal 60 radii). This would seem to imply that viewing the Moon through a 30 power telescope was his first celestial observation. However, not only does he not mention what phase the Moon had, but this is clearly an unreliable description of his first celestial observations, since we know from the January 7th letter that he had already thoroughly observed the Moon before ever completing the 30-power instrument, for he says (in the letter) he is "about to finish" making it. So the passage may merely mean that the Moon was the first celestial object on which he tested his new 30-power telescope and he was gratified by how near it looked; not that this was his first celestial observation ever.

To emphasize that things may not be as tidy as many seem to think, it should be noted that in the January 7 letter Galileo most definitely describes a vast gulf with a triangular peak as having been observed in connection with drawing L4, in which the Moon is both shown and said to be near its first quarter. Yet in Sidereus Nuncius Galileo attaches virtually the identical words to a gulf and triangular peak illustrated in his first engraving: of a four to five day old crescent Moon (see engraving E1 below). The only thing lacking here is the statement that the merging of the promontory with the lighted portion of the Moon became complete just as the Moon has about to set. In dating engraving E1 to November 30, 1609 (at 8 pm Padua time), Ewen Whitaker attaches considerable significance to this triangular peak and the three surrounding points of light, all of which he claims to have conclusively identified. But if Galileo was drawing a feature he had seen not on a four day old crescent Moon, but rather much closer to the first quarter, as he says in this letter, then Whitaker's identifications, and hence his date and time, would be incorrect.

Engravings Appearing in Sidereus Nuncius

![Galileo's Engravings of the Moon](/web/20070601182754im_/http://www.pacifier.com/~tpope/Moon_Drawings/Galileo_MoonEngravings.jpg "Engravings of the Moon from Sidereus Nuncius as numbered by Whitaker")
Adapted from original images © IMSS

Galileo's best known images of the Moon are five engravings (one of which is a duplicate), that appear in his book Sidereus Nuncius, published in mid-March 1610. The four unique engravings are shown at left. The red numbers E1-E4 are those assigned by Ewan Whitaker. The dates assigned to these engravings by Whitaker, Righini, and others, are given in a table later on this page.

The two things that have most attracted modern readers' attention are the identification of the large crater shown on the terminator in engravings E2 and E4, and the date on which engraving E1 was made.

The special interest in engraving E1 is because many read the text of Sidereus Nuncius to imply that a sighting of the four to five day old Moon was the first of Galileo's astronomical observations, and that the other lunar drawings followed in sequence. As we have indicated in the previous section, this interpretation is by no means obvious to us and seems to have very little basis in the text. Galileo may have felt that if one begins with the New Moon, the first phase in which the unusual, jagged nature of the terminator is strikingly obvious is when it reaches this age; and that he could go on from there to describe how the appearance of the Moon changes during the remainder of the lunar cycle. In other words, he may have chosen the order of his descriptions for literary effect and clarity of exposition, rather than as a literal transcription of the sequence of his observations.

In the text it is also not always clear which words go with a particular illustration, and a number of comments are repeated many times. We believe, however, that the points Galileo wishes to make about these four engravings can be summarized as follows [again we try to repeat his words as accurately as possible and place explanatory comments in square brackets]:

  • E1:
    • This illustrates the horns of the Moon as they appear four to five days after each New Moon.
    • The terminator is wavy and jagged, with portions of the light area protruding into the dark, and vice versa.
    • The illuminated crescent is scattered with innumerable dark spots [what we would now call craters] having bright rims on the side away from the Sun and dark on the side towards it. The pattern can be likened to a summit on Earth illuminated by the rising Sun while the valley to its east remains in shadow. Like the earthly valleys, the darkness of the lunar spots diminishes as the Sun rises over them.
    • The small craters are rarely seen in the large darkish areas visible to the naked eye [which Galileo calls the "large and ancient spots"].
    • Bright points of light continuously sprout up in the dark portion of the Moon, initially completely separated from the illuminated part. These points grow slowly in size and brightness, then merge with the expanding illuminated part of the Moon an hour or two later [The total time from appearance to merging is not clear from Galileo' sentence. Galileo later mentions that the greatest observed distance from an isolated bright point to the terminator is about one-twentieth the diameter of the Moon, quite similar to what he shows in his illustrations. It would take the terminator more than 10 hours to move that far; however the merging might be expected to occur a bit before the terminator got to the peak.].
    • A particularly prominent example of this was observed as the Moon approached first quarter, and involved a triangular peak emerging in the great dark gulf shown near the lower cusp [note: Galileo says this event is illustrated in E1, but he is not clear about which of the several steps he is showing. The large detached bright object near the lower cusp is presumably the triangular peak surrounded by the three points of light; but the large bright pointed projection above it might also depict the appearance of "vast promontory of light" seen after it had merged with the lighted part of the Moon.]:
      1. For two hours the gulf appeared completely dark.
      2. At the end of the two hours, a bright peak began to emerge a little below the center of the dark gulf.
      3. As the peak grew, it assumed a triangular shape, but remained completely detached from the lighted part of the Moon.
      4. As it grew, three detached points of light became visible in the region around it.
      5. The peak continued to grow and thicken. Just before the Moon set it merged with the bright side of the Moon forming a vast promontory of light. However, even as the main peak merged, the other three points of light remained detached from it.
    • Points of light, completely detached from the illuminated crescent, are also seen beyond the tips of the crescent, both in the north and in the south [such polar dots certainly occur and are illustrated in the wash drawings shown in the next section; but even though Galileo says they are illustrated in E1, we are unable to see any examples of them].
    • The spots [craters] are most prominent when they are nearest the terminator, and fade the further they are into the illuminated part.
    • The spots are very numerous in the horns of the crescent, especially the southern one. The spots in the southern horn are so numerous they resemble the spots on a peacock's tail [Note: in the January 7th letter, the Southern Highlands "crackleware" effect was illustrated in Figure L3, showing a much wider crescent than E1. In Sidereus Nuncius, even though Galileo mentions it in connection with engraving E1, the effect seems to be better illustrated in E2].
  • E2 and E4:
    • The large dark areas visible to the naked eye are smooth and uniform, interrupted only by an occasional bright patch [Galileo later also mentions that his illustrations show darker "holes" within these regions, gently connected to the larger area. The intensity and apparent shape of both the bright and dark patches within the "ancient spots" varies only slightly with the changing angle of the Sun.].
    • The large dark areas are lower than the bright areas of the Moon. This is evident from the bright ridges seen around parts of them both when the Moon is waxing and waning.
    • The inner edges of these ridges, marking the outer boundary of the large spots, are relatively smooth and "uninterrupted by peaks or ruggedness."
    • None of the large ancient spots reaches completely to the edge [limb] of the Moon, all of which looks bright [This comment occurs in Galileo's explanation of why the limb does not look rough, and is not directed towards any particular illustration.]
    • The lighted limb appears to be of a larger diameter than the section in darkness [This comment appears in the same section, where Galileo attributes the effect to a sunlit atmosphere seen edge-on. This was also his explanation of why the dark basins can never appear to extend completely to the limb. The flat dark areas of the Moon's vast western sea, known as Oceanus Procellarum, do, in fact get extremely close to the limb when the libration is just right. Galileo evidently did not observe such an extreme case; but at a libration close to the maximum the thin band of sunlit peaks seen over the horizon could well create the impression of a shell of sunlit atmosphere hanging over a dark surface.].
  • E3 and E4 [E4 printed a second time]:
    • These two engravings illustrate the elevated bright ridges above and below a large dark naked eye region visible in the northern hemisphere.
    • E3: Before last quarter, the bounding ridge is seen dark on the side towards the Sun, and bright on the side towards it. This is opposite to the lighting effect seen in the cavities [and indicates a raised, rather than a lowered feature].
    • E4: Some time later the large dark spot fills with shadow and the bright ridges are seen protruding into the dark half of the Moon [Galileo actually says these ridges "emerge from the shade," as if he believes they were not visible until the terminator had moved past them].
  • E4 [referred to again after preceding discussion]:
    • Near first and last quarters there is an especially prominent cavity (crater) "represented as correctly as possible" in E4 [Galileo makes no mention of the crater also being shown in E2].
    • It is "almost in the center" of the Moon.
    • It is larger than all the rest and perfectly round in shape, with a pattern of light and shadow that resembles [in Galileo's mind] and idealized province of Bohemia.
    • Like the others, [the interior of] this crater is brightest on the side away from the Sun, and darkest on the side towards it.
    • The rim is so high that the peaks farthest from the Sun are bathed in light before the terminator [in the surrounding portion of the Moon?] reaches the midpoint of the crater.
    • In general, the small lunar spots are seen with the best contrast when they are closest to the terminator. The ones farther from it look smaller and last dark. At Full Moon they can be seen only very vaguely.

Galileo's description of the triangular peak illustrated in engraving E1 is so detailed and exact, that one would think it could be easily matched to some easily identifiable set of features on the Moon. However it is not totally clear if at the point illustrated by E1 the triangular peak is the large blob shown off the terminator, towards the bottom; or the sharply pointed promontory above it; or if he is possibly illustrating both facets at the same time. Righini was quite confident that Galileo was describing the Sun rising over the craters known as Baco, Breislak, Clairaut and Cuvier on the evening of October 2, 1609. Whitaker was equally confident that Galileo's triangular peak is "the illuminated centre of Janssen floor plus Fabricius west wall" as it would have appeared on the evening of November 30, 1609; and he identifies the three points of light as (1) the southwest wall of Janssen, (2) the west wall of Brenner, and (3) the west wall of Metius. Neither Righini nor Whitaker produced photographs of their proposed regions which look convincingly like Galileo's engraving, let alone photographs taken under the lighting conditions expected to prevail on the evenings they propose. In a later section of this page we will address the question of whether the features mentioned by Righini and/or Whitaker would actually have looked as they do in Galileo's engraving on the dates and times they suggest.

A more pressing question is whether Galileo actually observed this sequence of events along the terminator of a four to five day old Moon, as Righini and Whitaker assume; or if he has, for literary effect, interpolated into that discussion (and illustration) something he actually observed much closer to the first quarter. The reasons for thinking Galileo may have done this are first that he describes what appears to be the exact same sequence of events in his January 7, 1610 letter, and associates them there with drawing L4, which shows a completely different phase from E1, much closer to first quarter. Second, although Galileo introduces engraving E1 in Sidereus Nuncius as representing a four or five day old Moon, he begins the paragraph about the triangular peak illustrated in E1 with the statement that he is about to describe some striking events that he "observed when the moon as approaching first quarter". Whether Galileo regarded a four to five day old Moon as "approaching first quarter" is anybody's guess. If Galileo is indeed showing a composite illustration giving an impression of the appearance of the four day old terminator together with a detail of events occurring at the first quarter, and possibly even illustrating two different stages of the peak merging with the terminator in the same drawing, then dating that drawing by the methods of Righini and Whitaker (or any other method) is quite impossible since the engraving would represent no single date.

We are not alone in thinking it possible that the engravings shown in Sidereus Nuncius should not be taken entirely literally. Gingerich and Van Helden believe, for example, that Galileo produced the engraving of the first quarter Moon, shown as E2, above, by manipulating the watercolor drawing labeled F5 in the following section; copying the pattern of light and dark seen along the terminator at a rather different phase. Kopal, of course, is almost notorious for his claims that Galileo's drawings are only schematic impressions of the nature of the lunar surface.

As to the large crater shown on the terminator in engravings E2 and E4, Righini believes this is not a single crater, but an amalgam of the craters Purbach, Regiomontanus, Werner, Blanchnius and Lacaille -- a region, he says, that might, at low resolution, look as Galileo has depicted it. Whitaker followed Gingerich in identifying the large crater as Albategnius. Kopal once hazarded a guess that it might be Ptolemaeus. Many other opinions have been expressed as well.

Inferior copies of these engravings, sometimes even printed upside down, appear in pirated copies of Sidereus Nuncius published in Germany (see the web exhibit from the Linda Hall Library), and were later unwittingly reproduced by others. To add to the confusion, Galileo's Venetian publisher, Thomas Baglioni, reprinted the four distinct plates from Sidereus Nuncius and inserted them in some copies of Giulio Cesare Lagalla's 1612 book De phoenomenis in orbe Lunae (van de Vyver, 1971), causing some people to mistakenly attribute the observations to Lagalla.

In his 1998 book about the art of the printed book, Adrian Johns shows the complete set of lunar images printed in Venice (1610), Frankfurt (1610), London (1653) and London (1658) reproduced from copies of those editions in the archives of the California Institute of Technology. It seems unfortunate that the Frankfurt printers produced rather crude copies of Galileo's original plates, for it is evident from Johns' presentation that the London engravers, in 1653, copied the Frankfurt plates so carefully that it is almost impossible to detect any difference. Nonetheless, a comparison of the images in the various editions give us a realistic sense of how accurately a 17th century engraving can be expected to represent the artwork on which it was based.

In the following we compare engraving E1 as it first appeared in Venice in 1610, in the second volume of an early version of Galileo's collected works (the Le Opere printed in Bologna in 1656), and in two editions of Sidereus Nuncius printed in London.

Engraving E1 (Venice, 1610) Engraving E1 (Bologna, 1656) Engraving E1 (London, 1653) Engraving E1 (London, 1683)
![Engraving E1 from 1610 edition](/web/20070601182754im_/http://www.pacifier.com/~tpope/Moon_Drawings/E1_Gallica.jpg "Engraving E1 from 1610 edition") ![Engraving E1 from 1656 Le Opere](/web/20070601182754im_/http://www.pacifier.com/~tpope/Moon_Drawings/E1_Bologna.jpg "Engraving E1 from 1656 Le Opere") ![Engraving E1 from 1653 edition](/web/20070601182754im_/http://www.pacifier.com/~tpope/Moon_Drawings/E1_Wing_G291A.gif "Engraving E1 from 1653 edition") ![Engraving E1 from 1683 edition](/web/20070601182754im_/http://www.pacifier.com/~tpope/Moon_Drawings/E1_Wing_G293.gif "Engraving E1 from 1683 edition")
from Gallica IFN-2600224 from IMSS BD 300948_2 from EEBO Microfilm G291A from EEBO Microfilm G293

The London plates of 1653, as just mentioned, are virtually identical to the Frankfurt plates of 1610 (not shown here). The Bologna plates (we have only this very low resolution digitization from the IMSS Digital Library) appear to have been copied directly from the Venice printing. What strikes us is that although the various engravers differ considerably in their approach to representing the pattern of light and dark on the illuminated side of the Moon, they have all rather faithfully copied the shape of the terminator and carefully reproduced the points of light shown beyond the terminator in the dark part, both in number and placement. The appearance of the illuminated side was probably confusing and ill-understood by the engravers, but the stark black and white of terminator seems to have been easy to copy. Our conclusion is that the 17th century engravers were capable of very exact reproduction when they wanted to (as in the London plates versus the Frankfurt ones from which they were copied); and that even when they simplified shapes in the lighted part (as in the Frankfurt and Bologna plates versus the Venice originals from which they were copied), they retained with considerable accuracy the shape and pattern of bright dots along the terminator. It would seem to follow from this that in preparing the Venice plates, the engraver is likely to have quite accurately represented the lunar terminator as it was depicted in the original artwork given to him by Galileo.

Cherrington's Inversion Theory

In preparing the introduction to his popular 1968 book, Ernest Cherrington, a person very well experienced in observing the Moon with small aperture instruments, consulted a copy of Institutio Astronomica by Pierre Gassendi in the rare book collection of the Lick Observatory. This book, published in 1653, contained a reprint of Sidereus Nuncius with plates that Cherrington assumed faithfully reproduced the originals, and he included photographs of them in his own book. The book Cherrington refers to seems not to be the original of Gassendi's work, but rather a compilation put out by Jacobi Flesher in London. As well as the books by Gassendi and Galileo, the compilation includes the astronomical introduction to Kepler's Dioptrice, all in the original Latin. Four different copies of the 1653 printing (Wing G167, G167A, G291 and G291A - the last mislabeled in the catalog as being from 1643), may be viewed at Early English Books Online, along with a re-issue put out by Henry Dickinson in 1683 (Wing G293). The plates used for the lunar illustrations in the 1653 Sidereus Nuncius reprint are, in fact, extremely accurate copies, not of Galileo's originals, but rather of the degraded plates in the Frankfurt edition, and some were similarly printed upside down.

Cherrington correctly recognized that the version of E4 he was seeing in Flesher's reprint was a last quarter Moon printed upside down. Cherrington also decided that engraving E1 (printed right side up), was also upside down. After turning it around, Cherrington decided it represented a waning crescent, about 26 days old (that is, a view few days before the New Moon). He apparently thought he recognized the promontory around the crater Gassendi near the Moon's western limb, which does indeed, for a brief time around the 26th day, jut into the dark portion of the Moon much like the large pointed promontory Galileo shows above his triangular peak. However, this interpretation is quite inconsistent with Galileo's very clear statement that the engraving illustrates what he saw four or five days after the New Moon, and includes a depiction of sunrise over the triangular peak (as Cherrington would surely know, one sees only sunrise events as the Moon is waxing and only sunset events as it is waning). Cherrington also believes that engravings E2 and E3 (printed the same way they appear in "correct" copies of Sidereus Nuncius), are mirror images, inverted left-right relative to the view actually seen through a Galilean telescope. As he points out, such printing errors are not uncommon, even in modern times. His reason for suggesting this is that he believes the large basin near the top of E2 (with bright crab-link pincers extending into the dark side) to be Mare Imbrium, a huge lunar feature, readily visible to the naked eye, that is always to the left of center in the normal view. According to this theory, E2 and E4 are two different pictures of the same phase: an approximately 23 day old last quarter Moon.

Engraving E4 (London, 1653) E2 (1653 inverted)
![Engraving E4 from 1653 edition](/web/20070601182754im_/http://www.pacifier.com/~tpope/Moon_Drawings/E4_Wing_G291.gif "Engraving E4 from 1653 edition") ![Engraving E2 from 1653 edition (mirror image)](/web/20070601182754im_/http://www.pacifier.com/~tpope/Moon_Drawings/E2_Wing_G291A _reflected.gif "Engraving E2 from 1653 edition (mirror image)")
from EEBO Microfilm G291 from EEBO Microfilm G291A

As can be seen at left, given the information available to Cherrington, his inversion theory is not nearly as off-the-wall as it might seem. Viewed in this way, the plates do look remarkably similar, and the richly cratered region, now to the left of center, can be plausibly identified with the Moon's southern highlands. However, this seems to be the area Galileo refers to as the "peacock's tail" in his text, and mentions that as a sight visible as the Moon is waxing. Also, if Cherrington had had access to the original Venice engravings he would have noticed that the pattern of dark smudges in the upper left of the inverted view, only vaguely suggested in the 1653 reproductions, are, in the originals, unmistakably meant to represent the pattern of large lunar mare in the Moon's eastern hemisphere (that is, they should be on the right side as viewed from the northern hemisphere). So, although it is quite possible that the original engraving might have been faked in some way from an observation of the Last Quarter Moon, it was certainly meant to illustrate the First Quarter.

Our previous comments about the accuracy of the 17th century engravers notwithstanding, it is interesting to note that the engraver of the Frankfurt edition, apparently thinking such details unimportant, chose to show the shading inside the large crater at a 45° angle, rather than with a vertical boundary, parallel to the terminator, as had been the case in the original plates. All the later engravers followed his lead, copying the Frankfurt engraver quite exactly. On the real Moon, the boundary is, of course, vertical.

Cherrington believes the large crater on the terminator is Deslandres, which as we indicate on our homepage, is an attractive candidate as to size and position, but cannot be reconciled with Galileo's description of its floor as being bright on the side away from the Sun, and dark on the side towards it. Cherrington believes Mare Imbrium is also illustrated at a nearly opposite phase in E3 (which, as indicated, he also thinks is inverted left-right), with the shadowed sides of the large craters Clavius, Maginus and Plato causing indentations along the limb. To reconcile this interpretation of E3 with Galileo's clear description of this plate as being a representation of the Moon "before the second quarter," Cherrington suggests that Galileo means quarters of the lunar cycle, rather than the phases of illumination known to nearly everyone as first and last (or first and second) quarter; so that "before the second quarter" (of the cycle) actually means before the first quarter phase. This tortured explanation does not square with Galileo's use of the same terms (first and second quarters) in his discussion of the ashen light later in Sidereus Nuncius. So we find it hard to believe that E2 and E4 are really two different images of the last quarter Moon, one accidentally misprinted, making it look like the first quarter. Cherrington does not mention the large dark zones shown in E2 on the illuminated side of the Moon, which, even in the inferior copy in Flesher's reprint, resemble the naked eye markings seen on the east side of the Moon at first quarter, and have no obvious resemblance to the markings seen on the west side of the Moon at last quarter.

In fairness to Cherrington, it should be noted that it is only a guess that the lunar engravings were printed the way Galileo intended in the first edition of his book. As we observe on our Photo-Drawing Comparison page, his illustrations of star fields were printed in different orientations even in the "good" editions issued from Venice in 1610, and some are rotated both relative to the way he depicted them in his notebooks and to the way they would normally appear to an observer in the Northern Hemisphere. The printing of the lunar plates was similarly inconsistent. For example, the view of the first quarter Moon in the 1610 Venice edition at the National Library of France (see Illustration set IFN-2600224), reproduced on their Gallica website, is upside down. It has also never been obvious that the final lunar illustration in Sidereus Nuncius, where the printer has repeated plate E4, is the illustration Galileo intended. From the text one has the impression he was trying to illustrate something other than what was shown the first time E4 appears, and hence intended the printer to shown some other view.

The desire (and ability) to recognize familiar patterns in what we see is innately human. We describe Cherrington's unconventional views at such length only because they demonstrate the extent to which one can see what one wants to see. Somewhat like looking at an ink-blot test, Righini, Whitaker and others who have spent as much or more time than Cherrington puzzling over Galileo's engravings come to recognize different familiar patterns and thereby attach completely different interpretations to the same things. It is very difficult to know who, if anyone, is correct.

A Possible Printer's Proof of Sidereus Nuncius

On March 28, 2007, the University of Padua announced, with considerable fanfare, what they claim is the discovery of a previously unknown copy of Sidereus Nuncius. Simultaneous announcements were released in Italian, English, and Spanish-language newspapers, as well as on Italian language television. According to the story, the book belongs to a New York art dealer who claims he obtained it from an unknown source in South America. Apparently this copy is in all ways identical to the others except that in the places where the five lunar engravings are normally found, one finds instead hand painted watercolors, which resemble the long-known ones described in the next section. This is said to be a kind of proof or possibly a presentation copy, with the drawings having been executed by Galileo himself.

The following figure brings together the pages showing four drawings (P1-P4b) displayed in the University of Padua press releases, and places them next to the same pages as they appear in the normal copies of Sidereus Nuncius (E1-E4b).

![Images in Printer's Proof Copy of Sidereus Nuncius](/web/20070601182754im_/http://www.pacifier.com/~tpope/Moon_Drawings/SidereusProofWatercolors.jpg "Comparison of engravings in Sidereus Nuncius (left) to watercolors in alleged proof copy (right)")
E1-E4b © [U. of Oklahoma](https://web.archive.org/web/20070601182754/http://hsci.cas.ou.edu/images/pdf/Galileo-1610.pdf "Open PDF scan of Sidereus Nuncius in a new window"); P1, P2 © [_Corriere della Sera_](https://web.archive.org/web/20070601182754/http://www.unipd.it/stdoc/articolo_galileo_acquerelli_corriere.pdf "Open PDF article in a new window") ; P3, P4b © [_TGR_](https://web.archive.org/web/20070601182754/http://www.unipd.it/newsletter/galileo.qtl "Open QuickTime video of Italian language television broadcast in a new window")

As indicated elsewhere, one of the plates in the printed editions (E4) appears twice. The pages with E4b/P4b, shown here, are the ones on which engraving E4 is printed the second time. The proof copy presumably contains a separate watercolor (P4a) on the page where the first printing of plate E4 is normally placed. The press releases did not include an image of that page.

Left-hand panel, the image scale has been adjusted to make the layout of the printed text match in the two copies. It would appear that the diameter of the watercolors is very slightly larger than that of the engravings, making it appear unlikely that one was traced from the other.

At the present time, we know very little else about this.

Some interesting questions it raises include:

  1. Could this be a forgery?
  2. For what purpose was it created?
  3. Is the existence of such a proof or presentation copy consistent with printing practices of the day?
  4. Would the engravings have been made from these drawings, or were the drawings made from the engravings?
  5. Are the other illustrations in this copy also hand-drawn, or is it only the lunar ones?
  6. Why should we think they were drawn by Galileo?
  7. Is the watercolor corresponding to the first appearance of engraving E4 resemble the one corresponding to the second? Or is it of a different phase? (there has been some speculation that the duplication of a single plate in two places may have been an error on the part of the printer)
  8. Why does the orientation of P3 match neither the printed engraving (E3), nor the watercolor (F5 -- see next section) which it otherwise seems closely to resemble?
  9. What is the significance of the small difference in size relative to the text?
  10. When was this made? How did the page with drawing P1 come to be stamped with the insignia of the Academy of the Lynxes (Galileo did not become a member until after the publication of Sidereus Nuncius)?
  11. Would good copies of these watercolors show details that differ significantly from the details in the engravings? Would such differences affect our interpretation of the features they represent?

Watercolor Drawings Bound in the Manuscript Copy of Sidereus Nuncius

The National Library in Florence owns a heavily-corrected manuscript copy, in Galileo's handwriting, of the complete text of Sidereus Nuncius, referred to by Antonio Favaro in his introduction to Volume 3 of the National Edition of Galileo's works, as the first draft (there is apparently another manuscript in Germany; we do not know if it contains drawings). This document is bound in a folio along with other documents, including fragments of two other manuscript copies of Sidereus Nuncius, one apparently an Italian language translation by Galileo's assistant Viviani. The complete manuscript ends with a blank page. Sandwiched between that and the first page of Galileo's journal of Jupiter observations are following seven drawings of the Moon, executed in either watercolor or sepia ink. Owen Gingerich and Albert Van Helden suggest that it was Favaro himself who assembled these documents (something not entirely obvious from Favaro's own introduction), and that these drawings appear on "two single sheets of watercolour paper." However, we believe Gingerich's 1975 description (made shortly after examining manuscript) may be more accurate. At that time, he said the drawings, which he says were executed in brown ink wash, are on a single "stiff folded piece of drawing paper". The paper appears to have been folded in such a way that the inner surfaces are blank, while the outer surfaces contain the seven drawings, which face the adjoining pages of text. For clarity, we have taken the liberty of using Photoshop to unfold the images of these pages available on the BNCF website. Each page in the folio, including the blank one is numbered consecutively, without respect to the particular manuscript involved. Because of the fold, the sheet of drawings was assigned two numbers. The picture on the left shows what, in BNCF notation, is Page 29 verso in combination with Page 28 recto; while the image on the right shows Page 28 verso together with Page 29 recto. The Letter-Number we show in red next to each painting are the designations assigned by Whitaker in his 1978 article.

Drawing Side Reverse Side
![Galileo's Watercolors of the Moon](/web/20070601182754im_/http://www.pacifier.com/~tpope/Moon_Drawings/Galileo_MoonWatercolors_front.jpg "Watercolor drawings of the Moon on a sheet of paper bound in the manuscript copy of Sidereus Nuncius as numbered by Whitaker") ![Reverse Side of Galileo's Watercolors of the Moon](/web/20070601182754im_/http://www.pacifier.com/~tpope/Moon_Drawings/Galileo_MoonWatercolors_reverse.jpg "Reverse side of sheet of watercolor paper bound in the manuscript copy of Sidereus Nuncius")
Adapted from original images © BNCF

The rectangular diagrams with notes are horoscopes, one complete, the other incomplete. Owen Gingerich seems to have been the first to determine that the complete one corresponds to the date of May 2, 1590. Guglielmo Righini, who did not mention these drawings in his paper about dating the engravings in Sidereus Nuncius, later identified May 2, 1590 with the birth date of Cosimo de' Medici. Since Sidereus Nuncius was dedicated to Cosimo, this seems to strength the association of the drawings with that book. We are not entirely sure, however, whether these horoscopes are thought to be in Galileo's handwriting on not. In the National Edition, Favaro chose to edit out the horoscopes. Facsimiles of these pages (printed sideways in the print edition and upside down in the on-line IMSS version) appear after the text of the manuscript (as in the BNCF folio), after which Favaro has added facsimiles of two pages containing manuscript drawings of stars in the constellation Orion.

Our understanding of Latin and Italian is far too limited to understand the documentary evidence (if any) that links these drawings to Galileo and/or the composition of Sidereus Nuncius. Although there is a certain resemblance between the drawings and the engravings, in no case do the features shown along the terminator of a drawing exactly match the features shown in any of the engravings. Since there is a certain resemblance between all images of the Moon at a particular phase, we find it entirely possible that these drawings could have been made at a completely different time, and possibly by someone else. How and when they came to be inserted in the BNCF manuscript as pages 28 and 29, or what might be the significance of the numbers appearing near the Moon's north pole in the drawings Whitaker has numbered F1, F4, F5, F6, and F7 are both mysteries to us. We have no idea why drawings F2 and F3 are unnumbered (Whitaker says F3 is numbered "2", but we cannot see this -- perhaps he is looking at the "28" in the upper right corner, which is the page number in the manuscript folio), or why the numbers "6" and "7" were not used. The numbers were assigned roughly according to the sequence of the lunar cycle, but "5" (Whitaker's F5) is clearly an earlier phase than "4" (Whitaker's F6).

The best evidence we can adduce connecting these drawings with Galileo is the star shown to the left of the dark edge of the Moon in the drawing Whitaker labeled F7 (and someone else numbered 8). Although it is quite possible that someone simply put the mark there to indicate that this was a particularly fine illustration of the ashen light on the dark side of the Moon, Owen Gingerich suggested this might represent a conjunction of the Moon with a bright star, although he was unable to locate such an event. Ewen Whitaker later noticed that the Moon, as seen from Padua, occulted a 4th magnitude star in Libra on the morning on January 19, 1609. The star would have emerged from the dark limb shortly before sunrise at close to the position indicated, and the phase of the Moon would also have been extremely close to that shown. Occultations of 4th magnitude stars are not extremely rare (they would be expected, on average, perhaps once a month), but the coincidence of position angle and phase of the Moon is extremely unusual, and suggests that Whitaker is indeed correct regarding the date of this image. Since it would appear that Galileo did not share his astronomical observations with anyone before the publication of Sidereus Nuncius in March (Drake believes that to avoid being preempted by others, Galileo chose not to mail the January 1610 letter after discovering the moons of Jupiter), if this sketch was indeed made on January 19, 1609, then it would seem it must have been drawn by Galileo, and since the others are obviously executed by the same person, he must, therefore, have made the others sometime before or after that.

It should be kept in mind that in preparing Sidereus Nuncius, Galileo had nothing to go by but his memory and whatever images he had managed to commit to paper. In 1975, Gingerich declared that these were careful studio drawings adapted from an archive of original sketches, since lost, which had been made at the telescope; an opinion with which Whitaker strongly agreed. By 2003 he had changed his mind, and declared, along with Van Helden, that not only are these the original sketches prepared by Galileo while looking through the eyepiece of his telescope, but that they are the ONLY sketches that were available to him during the composition of Sidereus Nuncius. As a result, each of the four unique engravings appearing in Sidereus Nuncius must have been based on one of these drawings. In particular, since, according to this hypothesis, Galileo lacked a drawing of the first quarter moon, the engraving of that phase which appears in Sidereus Nuncius was achieved by distorting drawing F4.

Gingerich's Distortion Theory

In his 1975 comments on Righini's pioneering dating effort, Owen Gingerich noted what seemed to him a striking resemblance between engraving E2 and one of the wash drawings (F4) to be explained in the next section.

Engraving E2 Drawing F4
![Engraving E1 from 1610 edition](/web/20070601182754im_/http://www.pacifier.com/~tpope/Moon_Drawings/E2_cropped.jpg "Engraving E1 from 1610 edition") ![Watercolor F4](/web/20070601182754im_/http://www.pacifier.com/~tpope/Moon_Drawings/F4_cropped.jpg "Watercolor F4")
adapted from image © IMSS adapted from image © BNCF

Gingerich's comments are worth repeating for the extent to which they demonstrate the highly subjective nature of attempts to identify features in Galileo's drawings and engravings. He says:

"... although there is no manuscript drawing of the moon at first quarter, the drawing labelled "3" [F4, below] made a few days earlier than the first quarter yields a very close correlation between features on the terminator and the one purporting to be the first quarter in Sidereus Nuncius [engraving E2]. Furthermore, the dark maria are reasonably represented on the manuscript drawing, but bear only a grotesque approximation to reality in the printed drawing. I would like to suggest that the printed drawing is a highly distorted and derivative version or the manuscript drawing."

Although we would have to agree that engraving E2 may well have been derived from F4, or a drawing like it (for the sea shown straddling the terminator near the top of the E2 is never seen in that position); our reaction on comparing the drawing with the engraving is almost exactly the opposite of Gingerich's. We see no obvious correlation between the features shown along the terminator (the two terminators seem at least as different as in the comparison of E2 to E4, inverted, shown earlier) and the maria seem to us much more accurately represented in the engraving than in the drawing. In fact to represent the maria in the northeast quadrant as accurately as he did (see the corresponding image through the Galilean telescope on our home page), the engraver must have had some input other than vague blobs in the drawing. They are admittedly not perfect in the engraving, but they seem a lot closer to reality to us.

Hevelius (1644) Predicted Terminator
![Hevelius engraving Selonographia](/web/20070601182754im_/http://www.pacifier.com/~tpope/Moon_Drawings/Hevelius_cropped.jpg "Hevelius engraving Selonographia") ![Predicted terminator at time of Hevelius engraving](/web/20070601182754im_/http://www.pacifier.com/~tpope/Moon_Drawings/Gdansk_1644_3_15_17_55.jpg "Predicted terminator at time of Hevelius engraving")
adapted from image © Cambridge University Press  

The possibility that Galileo may have instructed the engraver to "improve" his drawing by straightening the terminator is certainly not to be dismissed. Even the later Polish astronomer Johannes Hevelius, who prided himself so much on the accuracy of his work (which he felt was much superior to Galileo's) that he made his own engravings, was not above doing this. In his Selenographia he printed at least one image in which the terminator appears to have been shifted for artistic effect. The example shown here, which appears on page 54 of Whitaker's 1999 book, is carefully labeled to indicate that it represents the 7 day old as seen from Gdansk at 7 hours after the meridian on March 15, 1644. According to a modern ephemeris, the Sun, as viewed from Gdansk, crossed the meridian at 10:55 UT, so this observation was, according to Hevelius made at about 17:55 UT (of course the drawing must have taken some time to complete, and he may be referring to mean solar time, which would be a few minutes different, rather than the literal meridian crossing; but this time should be close enough for the present purpose). A prediction of the position of the lunar terminator at that hour, based on the JPL lunar ephemeris, agrees very well with Hevelius' depiction of the features along it, including the prominent crater Albategnius, which he shows as the dark circle just below center. However, although the relation of the terminator to the features agrees with the engraving, it appears that the terminator should be significantly bowed to the left -- and not the perfectly straight line that Hevelius chose to show. Now, it is possible (although extremely unlikely at this scale) that the librations assumed in the JPL ephemeris do not extrapolate back properly to the 17th century -- that is, Albategnius might not have been precisely where JPL thinks it was relative to the Moon's limb; but the predicted shape of the terminator at 17:55 UT depends only on the relative positions of the Sun, Moon, and Earth, and those could not possibly be enough in error to account for the difference between the prediction and Hevelius' representation of it. Although the fudging is slight, it seems unlikely that Hevelius could have actually seen a straight terminator on this day: the exact moment of the terminator being a straight line would have occurred in the morning, some nine hours earlier, at around 9:00 UT, just as the Moon was rising with the Sun high in the sky. Hevelius, like Galileo, appears to have wanted a perfect First Quarter Moon for his book; and not having a perfect observation, he adjusted whatever he had.

In the captions to his figures, Gingerich invites us not only to compare engraving E2 to drawing F4, but also to make several other comparisons. Unfortunately, these directions are not elaborated in the text, so it is very difficult to know what he hopes for us to see.

Drawing F5 Engraving E3 Engraving E4
![Watercolor F5](/web/20070601182754im_/http://www.pacifier.com/~tpope/Moon_Drawings/F5_cropped.jpg "Watercolor F5") ![Engraving E3 from 1610 edition](/web/20070601182754im_/http://www.pacifier.com/~tpope/Moon_Drawings/E3_cropped.jpg "Engraving E3 from 1610 edition") ![Engraving E4 from 1610 edition](/web/20070601182754im_/http://www.pacifier.com/~tpope/Moon_Drawings/E4_cropped.jpg "Engraving E4 from 1610 edition")
adapted from image © BNCF adapted from image © IMSS adapted from image © IMSS

In looking at engraving E3, Gingerich's caption instructs us to "note the different placement of the bright points at the terminator compared to the drawing [F5]." We would certainly agree that the bright points along the terminator are different in these two images; but we find it puzzling that in comparing E2 to F4 we were told to note "the very close correlation between" the points. They look equally different to us in the two examples. Finally, Gingerich tells us to compare E4 to E3. We have no idea what we are supposed to see; nor why he doesn't mention drawing F6, which looks at least as much like engraving E4 as drawing F5 looks like E3.

It is of interest to note that Ewen Whitaker would later declare that drawing F5 and engraving E3 were made at the same hour, implying that to him the points shown along the terminator represent identical features, even though they looked different to Gingerich. In this case we would have to agree with Gingerich: they look quite different to us. Based on our earlier comparison of the engravings copied from one printing of Sidereus Nuncius to the next, we find it very hard to believe that a 17th century engraver given F5 as his artwork would produce E3. On the other hand, in comparing drawing F4 to engraving E2, Whitaker decided they were based on observations 24 hours apart, implying that to him there was no correlation between the points along the terminator in the two images, even though Gingerich had declared them closely correlated. In this case we have to agree with Whitaker: we see no correlation.

Whitaker's Sequencing of the Drawings

Gingerich and Van Helden's view that Galileo had only his seven wash drawings to go by in preparing the engravings for Sidereus Nuncius was evidently not shared by Ewan Whitaker, who assigned a unique day and hour to each drawing and engraving. In only one case does the date assigned to an engraving (Whitaker's E3) exactly correspond to the date of a drawing (F5). Whitaker's belief is that the other three engravings were based on drawings since lost, perhaps by the printer.

As to the surviving drawings, Whitaker asserts with great confidence that the four he labeled F1..F4 were copied in the studio based on observations made at the following dates and times in 1609:

F1 : Nov. 30; 15:00 UT F2 : Nov. 30; 17:00 UT F3 : Dec. 1; 16:30 UT F4 : Dec. 2; 16:00 UT
![Watercolor F1](/web/20070601182754im_/http://www.pacifier.com/~tpope/Moon_Drawings/F1_cropped.jpg "Watercolor F1") ![Watercolor F2](/web/20070601182754im_/http://www.pacifier.com/~tpope/Moon_Drawings/F2_cropped.jpg "Watercolor F2") ![Watercolor F3](/web/20070601182754im_/http://www.pacifier.com/~tpope/Moon_Drawings/F3_cropped.jpg "Watercolor F3") ![Watercolor F4](/web/20070601182754im_/http://www.pacifier.com/~tpope/Moon_Drawings/F4_cropped.jpg "Watercolor F4")
adapted from image © BNCF adapted from image © BNCF adapted from image © BNCF adapted from image © BNCF

This sequence is based solely on Whitaker's claimed ability to recognize features along the terminator. Now Whitaker is highly respected selenographer who has made many commendable contributions to his field based on detailed analysis of photos which he can undoubtedly date with great accuracy, but there seem to be some grounds for wondering whether he really has this ability when applied to Galileo's drawings. For example, to the man in the street, it would appear that the position of the terminator in drawing F2 (that is, its distance from the right-hand limb) is about mid-way between that shown in F1 and F3, if anything closer to its position in F3. Yet Whitaker would have us believe that the interval from F1 to F2 represents the change in just 2 hours, while that from F2 to F3 is 24 hours. Recognizing this problem, Whitaker came up with his "qualitatively correct but geometrically inaccurate" drawings. That is, he believes Galileo drew certain features with great accuracy but placed them in the wrong positions.

There is undoubtedly many an amateur artist to whom this theory will have great appeal, for they have themselves created drawings in which the various elements were incorrectly placed relative to one another. Indeed, nearly all 17th century astronomical drawings we have seen suffer from geometric inaccuracies. However there is another problem. Allowing that the difference in position of the terminator in F1 versus F2 might be an artifact of geometric distortion, we are unable to understand how a "qualitatively correct" pattern of dots on the Moon's surface could have changed so totally in two hours: dark craters that were present in F1 have disappeared in F2 while new ones have appeared; and the terminator is completely different. Now a few features on the Moon can change significantly in two hours, but we are unaware of such a total transformation, particularly in the appearance of the illuminated crescent. Once again to the man in the street, it would seem that if the drawings show a total transformation when the actual change is slight, then some of the features depicted must be qualitatively incorrect. How Whitaker can be so confident in his ability to distinguish the qualitatively correct from the qualitatively incorrect is unclear to us; especially since there are innumerable features for which he has no plausible explanation. If his identifications of lunar features are unreliable (not due to his lack of lack of experience in recognizing them, but rather due to their being depicted in an unpredictable way), then the dates he derives based on his supposed identifications are highly questionable.

It is particularly difficult to check Whitaker's work because although he gives a photo that he says corresponds to F1 he does not tell us when it was taken (even though he begins his article by scolding Galileo for failing to do the same), and does not bother to point out what features in the photo he believes correspond to patches in the drawing. He gives no photo corresponding to F2; that is, he provides no evidence that such a total transformation of appearance can occur in two hours at this phase of the Moon. For F3 he does give a photo with certain features labeled, but again (as with all the other photos) he gives no date or time, so it is impossible to confirm that the terminator position in his photo actually corresponds to that at 16:30 UT on December 1, 1609 (the date and time he assigns to drawing F3).

The illustrations from Whitaker's 1978 article were repeated, with slight modifications but without any further explanation of their datings, in his chapter on "Selenography in the Seventeenth Century" in the 1984 Cambridge General History of Astronomy as well as in his own highly-acclaimed 1999 book Mapping And Naming The Moon. The illustrations in the latter two publications appear to be identical, and differ from the former mainly in that all Galileo's drawings and engravings are printed against a uniformly black background to make them look more like the photographs. The photographs, still unidentified, seem to be the same as those shown in the original publication. The only substantive change we can detect is Whitaker's photographic comparison with Galileo's engraving E4. In the original article, Whitaker labeled four features along the terminator, one of which is the crater Albategnius (virtually invisible in the photo). In the two subsequent publications, Whitaker retained the photo, but deleted two of the labels along the terminator ("G" for the Ukert Hills in the 1978 article seems to correspond to "D" in the later illustrations, while "J", which referred to Albategnius in 1978 has become "E") and instead labels twelve new features which he claims are clearly visible in the illuminated half of Galileo's Last Quarter Moon. Unlike the 1978 article, where all labels are explained, Whitaker tells us what only five of the twelve new labels are pointing to (and then only in his 1984 publication). We show those, all located in the Moon's heavily cratered southern highlands, in the following panel.

Photo Labeled by Whitaker (1984) E4 Labeled by Whitaker (1984) Alternative Identifications
![Photo Labeled by Whitaker](/web/20070601182754im_/http://www.pacifier.com/~tpope/Moon_Drawings/Whitaker_Highlands_Photo.jpg "Photo Labeled by Whitaker") ![Engraving Labeled by Whitaker](/web/20070601182754im_/http://www.pacifier.com/~tpope/Moon_Drawings/Whitaker_Highlands_Engraving.gif "Engraving Labeled by Whitaker") ![Photo with Alternative Identifications](/web/20070601182754im_/http://www.pacifier.com/~tpope/Moon_Drawings/Tactile_Moon_Highlands.jpg "Photo with Alternative Identifications")
adapted from image © Cambridge Univ. Press adapted from image © Cambridge Univ. Press adapted from image © Project SEE

The arrows in the left-hand photo (which Whitaker has purposely de-focused) show what Whitaker thinks correlate with the corresponding arrows in the Galileo's engraving (center image). In the photo, Whitaker says the arrows are pointing at the craters Deslandres (d), Purbach (p), Regiomontanus (r), Walter (w), and Orontius (o). Although these identifications seem plausible at first glance, when looks more closely, any number of questions arise: why is Orontius shown so large when the photo shows it to be small? why is Deslandres depicted in the engraving when it is invisible in the photo? what is the large crater just the left of Whitaker's "E" in the engraving? As to the latter, is it Arzachel, the prominent crater just to the lower left of Whitaker's "E" on his photo? If so, why is it shown so much larger than Purbach when it is actually small? Why is it shown so close to the purported Albategnius? And what happened to Ptolemaeus and Alphonsus, the other two members of the prominent chain of which Arzachel is the southernmost member? To answer such questions one has to accept Whitaker's reasoning that Galileo's engraver has somehow shown certain craters in a "qualitatively correct" fashion (while, evidently choosing to completely omit others), but placed them in incorrect positions and grossly distorted their sizes relative to one another.

In the right-hand image we show what seem to us an equally plausible alternative set of identifications for four of these. We have placed the arrows on a typical photo of the southern highlands, this particular one being adapted from Project SEE's Tactile Moon display, which attempts to make the most prominent features visible at various lunar phases perceptible to the blind. Their photograph was taken on September 18, 2003. The arrows now point to the centers of the following craters: Longomontanus (d), Tycho (p), Maginus (w), and Clavius (o). In this identification, the very large walled plain Deslandres (above and to the right of "p" in the photo) occupies about the right position relative to "p" to be where Galileo puts the very large crater in his engraving. Although these features seem a bit too close to the Moon's south pole in this particular photo, their exact positioning depends on the lunar librations.

We do not mean to imply that our "identifications" are any more correct than Whitaker's. In this particular alternative scheme, without invoking geometric inaccuracy we have no clear candidate for the feature to the left of the "E" in the engraving, and the object pointed to by Whitaker's "r" could be several things. Our point is that the features represented in the engraving are so vague, and real features in this region of the Moon so numerous, that any number of plausible identifications can be proposed; yet none seems to work perfectly. We suspect that if the engraver drew a completely random impression of a cratered surface we would have about the same degree of success matching his imaginary features to the real ones.

Even if we accept Whitaker's identifications as definitive, the questions do not end. Galileo's engraving clearly shows the terminator butting up against the east wall of what Whitaker says is the crater Walter, and spilling over the east walls of Purbach and Orontius. Was the terminator really at this position at 4:00 UT on December 18, 1609 (the date and time Whitaker assigns to this engraving)? The position of the terminator in the engraving is distinctly farther to the left than in Whitaker's undated photograph. Since Albategnius had already nearly faded from sight when the photograph was taken, would it have been visible at all when the terminator got to the position shown in the engraving? Would the east wall of Goldschmidt, the Ukert Hills, and the north wall of Hipparchus (three features that Whitaker claimed to have identified in his 1978 paper) have actually been on the terminator when it got to the position shown here, and looked as depicted in the engraving? What are the dots of light shown in the shaded part of the Moon, well to the right of the terminator? Could exactly this phase have even been observed from Padua in 1609-1610? We will return to these questions in a following section after we have explained how the position and appearance of the terminator for any given date and time can be predicted with great precision.

Despite the vast resources of the Lunar and Planetary Institute, Whitaker was apparently unable to find a photograph more closely matching the phase he wanted to illustrate. Our own conclusion, based on terminator predictions and comparison of them to photos taken at known times, is that there is either something drastically wrong with the way the terminator is shown in the engraving or with Whitaker's identification of these craters: by sunrise on December 18th (6:00 UT), the terminator may indeed have been approaching the east wall of Walter, but it would have been full crater-widths away Purbach and Orontius. Our alternative "identifications" are no better in this respect: it is hard to see how the terminator could spill over into Tycho before it reaches the east wall of Maginus.

In addition to the major publications described above Whitaker published a 1980 letter in the journal Science which contains illustrations comparing wash drawing F4 and engraving E3 to a photograph. Labels superimposed on F4 claim to identify three features not mentioned in either his earlier or later publications. Whitaker does not say what these three new features are, implying that the correlation between photo and drawing should be self-evident even though "size reduction and further reproduction will undoubtedly cause loss of some of the finer points of correspondence along the terminators" (modern printing technology evidently being incapable of matching that of 1610). The times he assigns to these images are the same as those given in his 1978 paper, but again he offers no proof that his undated photographs "taken at similar phases" actually match the expected appearance of the Moon at those times. Even if they did, the "correspondence along the terminators" is not at all obvious to us, neither at the points Whitaker calls attention to with his labels no anywhere else. Indeed, to us, the number of mis-correspondences seems to far outnumber the number of correspondences; although in fairness Whitaker has chosen to print the terminator in his photographs in such a way that the terminator is dark and vague (as previously indicated, to make the appearance of the visual terminator clear in a photograph the gamma has to increased to a value far larger than the one normally used). Even Whitaker admits that the regions away from the terminator do not correlate well, and that must surely lead one to question whether the terminator was really rendered with that much greater care.

Finally, in his 1980 Science letter Whitaker makes the claim that the limited accuracy of Galileo's drawings was due among many other things to his using an unmounted 20-power telescope. This assertion seems more than a little odd, since in his January 7, 1610 letter (with which Whitaker was thoroughly familiar) Galileo goes to some length to warn the unknown recipient that the telescope needs to be fixed to a stable surface to escape "the shaking of the hand."

Gingerich and Van Helden's Page-turning Theory

Gingerich and Van Helden also express the opinion that, due to the low quality of Galileo telescope, only one feature (what is now called Albategnius) showed a clear enough pattern of shading to be definitely identified as a crater (i.e., a depression in the surface), and this led to Galileo to place a highly enlarged version of it on the terminator in engravings E2 and E4. We do not feel this opinion accords either with Galileo's other observations or with his written comments about all craters showing a distinctive pattern of light and shade.

In their recent paper Gingerich and Van Helden point out that if these watercolors were studio reproductions of original sketches made at the telescope, their placement on the page makes no particular sense: they are not arranged in sequence of increasing phase, and, more importantly, some are placed with the terminator horizontal and others vertical, for no obvious reason. They proceed to tell us that this all makes perfect sense when one takes Whitaker's dates and realizes that they were recorded directly on this paper at the telescope. We, for one, fail to see how the sequence makes any more sense when viewed in this way; but what we address here is Gingerich and Van Helden's contention that the orientation of the terminator was dictated by the appearance of the Moon in the sky, with the artist choosing to hold the paper either horizontally ("landscape mode") or vertically ("portrait mode"). We admit to a little confusion since Gingerich previously told us that all the drawings are on a single stiff sheet of watercolor paper; and now he seems to be telling us that drawings F1-F6 are on a separate rectangular sheet.

Jupiter's Moons Jan. 7; 16:30 UT Galileo's Record
![Predicted Orientation of Moon](/web/20070601182754im_/http://www.pacifier.com/~tpope/Moon_Drawings/Jupiter_1610_1-7_1630.gif "Predicted Orientation of Moon") ![Predicted Orientation of Moon](/web/20070601182754im_/http://www.pacifier.com/~tpope/Moon_Drawings/Jupiter_3-427.gif "Predicted Orientation of Moon")

We certainly agree that an artist will have a very strong inclination to record his subject in the orientation that he sees through the telescope. This contention is borne out by Galileo's recollection of the way the little stars next to Jupiter appeared on the night of January 7, 1610 as later recorded at the start of his journal page. Jean Meeus assigns a time of approximately 16:30 UT, and the angle he shows matches a modern prediction of how the moons of Jupiter would have appeared in a Galilean telescope at that time. The match would be exact if we guess Galileo was holding the paper rotated about 10 degrees counterclockwise.

The fundamental flaw in Gingerich and Van Helden's analysis is their apparent belief that the lunar terminator is always either horizontal or vertical. They say, for example, that drawings F1 and F2, made with the Moon low on the western horizon, is an accurate representation of how the lunar crescent looked when one assumes the artist was holding the paper horizontally (starting, for some unknown reason at the middle of the upper edge). In actual fact, the orientation of the lunar terminator in the sky is perfectly predictable at any given date and time, and it is rarely, if ever horizontal when the Moon is rising or setting.

In the following table we show accurate simulations of how the Moon would look as viewed by an observer with a Galilean telescope at the date and time assigned by Whitaker to each of the seven drawings. Below each simulation we give an updated version of Gingerich and Van Helden's presentation of how, on the assumption that the drawings were actually made at the telescope on these dates and times, the paper would have had to have been held for each night's work.

F1 Nov. 30; 15:00 UT F2 Nov. 30; 17:00 UT F3 Dec. 1; 16:30 UT F4 Dec. 2; 16:00 UT
![Predicted Orientation of Moon](/web/20070601182754im_/http://www.pacifier.com/~tpope/Moon_Drawings/F1_1609-11-30_15.gif "Predicted Orientation of Moon") ![Predicted Orientation of Moon](/web/20070601182754im_/http://www.pacifier.com/~tpope/Moon_Drawings/F2_1609-11-30_17.gif "Predicted Orientation of Moon") ![Predicted Orientation of Moon](/web/20070601182754im_/http://www.pacifier.com/~tpope/Moon_Drawings/F3_1609-12-1_1630.gif "Predicted Orientation of Moon") ![Predicted Orientation of Moon](/web/20070601182754im_/http://www.pacifier.com/~tpope/Moon_Drawings/F4_1609-12-2_16.gif "Predicted Orientation of Moon")
![Required Orientation of Paper](/web/20070601182754im_/http://www.pacifier.com/~tpope/Moon_Drawings/F1r.jpg "Required Orientation of Paper") ![Required Orientation of Paper](/web/20070601182754im_/http://www.pacifier.com/~tpope/Moon_Drawings/F2r.jpg "Required Orientation of Paper") ![Required Orientation of Paper](/web/20070601182754im_/http://www.pacifier.com/~tpope/Moon_Drawings/F3r.jpg "Required Orientation of Paper") ![Required Orientation of Paper](/web/20070601182754im_/http://www.pacifier.com/~tpope/Moon_Drawings/F4r.jpg "Required Orientation of Paper")
F5 Dec. 17; 4:00 UT F6 Dec. 18; 6:00 UT F7 Jan. 19; 5:50 UT
![Predicted Orientation of Moon](/web/20070601182754im_/http://www.pacifier.com/~tpope/Moon_Drawings/F5_1609-12-17_4.gif "Predicted Orientation of Moon") ![Predicted Orientation of Moon](/web/20070601182754im_/http://www.pacifier.com/~tpope/Moon_Drawings/F6_1609-12-18_6.gif "Predicted Orientation of Moon") ![Predicted Orientation of Moon](/web/20070601182754im_/http://www.pacifier.com/~tpope/Moon_Drawings/F7_1610-1-19_550.gif "Predicted Orientation of Moon")
![Required Orientation of Paper](/web/20070601182754im_/http://www.pacifier.com/~tpope/Moon_Drawings/F5r.jpg "Required Orientation of Paper") ![Required Orientation of Paper](/web/20070601182754im_/http://www.pacifier.com/~tpope/Moon_Drawings/F6r.jpg "Required Orientation of Paper") ![Required Orientation of Paper](/web/20070601182754im_/http://www.pacifier.com/~tpope/Moon_Drawings/F7r.jpg "Required Orientation of Paper")

The writing on the incomplete horoscope shown in the final illustration is, incidentally, upside down. That is, whoever labeled it seems to have turned the page once again. Also, if Gingerich's initial contention that the drawings are on a single folded piece of paper with drawing F7 "across the fold" then it is a little hard to understand why, with all the blank space available, the first six drawings were crowded, out of sequence, onto one half. Perhaps the paper was already folded at the time of the drawing?

It is unclear to us what to make of this result. There is a certain consistency in the way the paper might have been held for drawings F1-F5; however, if the journal entry for Jupiter's satellites correctly indicates Galileo's propensity to hold his papers a little counterclockwise, then only drawings F6 and F7 match this pattern. Also, as previously indicated, the sequence established using Whitaker's dates still makes no sense to us. One would think that the most artists would have filled the page in some orderly way: left-right and top-bottom, or clockwise (or counterclockwise) around the edge. But Whitaker's sequence follows no such pattern. The placement of drawing F4, with respect to the previous three drawings, as it would have to have been done if it was made on December 2nd, seems particularly illogical and inexplicable.

As a result, the page layout does very little to increase our confidence in the correctness of Whitaker's dates. As to whether these drawings were actually made live at the telescope or later copied in the studio, about all we can say is that if they were made live at Whitaker's dates and times the paper would have had to be held as shown. Someone more knowledgeable than us about painting might be able to tell from a careful look at the originals at the BNCF whether the brushstrokes are all consistent with an artist holding the paper as shown here. If they are, that would be fairly strong evidence in favor of the Whitaker-Gingerich-Van Helden theory of their creation. Such a person might also be able to make a judgment about the little detail of a crater that appears between drawings F1 and F2. To us this appears to be at a completely different scale (magnification) than the other images, and possibly of a different phase than any of the main drawings (it seems to show a crater partially illuminated by the Sun on a much larger radius dark limb). We have the impression that artists copying from nature usually draw things sight size, and have very little of the "zoom" capability illustrated here. The size of the image on the paper can, of course, be adjusted a little by moving the paper closer and farther from the eye, but the little cameo at a different scale makes one wonder if this was all really done live at the telescope.

The real question seems to be whether there is some other set of plausible dates for which the layout and orientation of the drawings would make better sense.

Pen and Ink Drawings from Folio Gal. 50

![Pen Sketches of Moon from folio Gal. 50](/web/20070601182754im_/http://www.pacifier.com/~tpope/Moon_Drawings/Gal50_Moon_Sketches.jpg "Pen Sketches of Moon from folio Gal. 50") ![Pen sketches of lunar features from BNCF manuscript folio Gal. 50](/web/20070601182754im_/http://www.pacifier.com/~tpope/Moon_Drawings/Gal50_Moon_Perspectives.jpg "Pen sketches of lunar features from BNCF manuscript folio Gal. 50")
Adapted from original images © IMSS

As explained on our Accessing Manuscripts page, many manuscript items related to Galileo are housed at the National Library in Florence (the BNCF). The items are bound in a series of approximately 350 folio albums. Many of the items are reproduced or transcribed in the National Edition of Galileo's Works; but there are also many that are not. There is an on-going project to make digital images of the manuscripts available via the internet, but to date only a small number of the folios are online. The five images of the Moon shown here appear on the front side of page 68 in folio Gal. 50, which happens to be reproduced on page 950 of the annex to Volume 3 of the National Edition. Gal. 50 has not yet been placed online, so the versions shown here are based on a new photo of this page released by the IMSS in connection with an article by Filippo Camerota in the inaugural issue of their new e-journal Galilaeana.

We know nothing more about these drawings other than that they appear among Galilean papers ascribed by the BNCF to the year 1610. Although very realistic depictions of lunar features, we do not know if they are based on actual observations, or a purely imaginary exercise to test how the play of sunlight over rugged topography might appear when viewed at various angles. They certainly indicate that Galileo, or whoever drew them, had both considerable artistic talent and a very good idea of that the Moon looks like through a telescope.

Lunar Librations and Predicting the Appearance of the Terminator

The attempts of Righini and Whitaker at dating Galileo's lunar drawings are based partly on the phase (the percentage of the side face the Earth that is illuminated) depicted in the drawings, partly on the features shown along the lunar terminator (the line dividing the lighted portion from shadowed portion), and partly (at least in the case of Righini) of the position of features relative to the lunar limb (the outer edge of the lunar disk). Although the cycle of changes in the Moon's aspect is extraordinarily complicated, its appearance at a given date and time is highly predictable, even back to the 1600's.

The phase is the easiest of the variations to understand. The illumination starts at 0% at the moment of the New Moon and increases to 100% at the following Full Moon. Righini felt that the phase depicted in engraving E1 of Sidereus Nuncius was depicted with sufficient precision that the Moon, at the time of Galileo's observation must have been 4.62 ± 0.08 days past the New Moon. Galileo also mentions in the text that engraving E1 represents what he saw a few hours before sunset, so Righini drew up a list of dates in the latter part of 1609 on which the Moon would have had this age shortly before sunset. He concluded that October 2, 1609 was the best, and only reasonable, candidate.

Righini's results were initially presented at a scientific meeting held on the island of Capri, and Owen Gingerich, who was present, immediately questioned Righini's finding, suggesting that the condition of Righini's measured phase occurring at sunset would equally well satisfied on January 29, 1610 and March 29, 1610.

Righini's conversion of his phase estimate to an equivalent "age of the Moon" is unfortunate, and exposes a flaw apparently understood by neither Righini nor Gingerich. What Righini could measure in the drawing was not the age, but rather the position of the terminator, or expressed in another way, the fraction of the Moon lit by the Sun. Righini probably estimated the percentage illumination shown in engraving E1 to be about 22±1%, which he converted to a solar angle, and then to an age assuming some average lunar cycle. Unfortunately, he gives us neither his estimate for the solar phase angle or the percent illumination. We ourselves would estimate the illumination at something like 21±3%, our larger uncertainty reflecting the difficulty of finding the center of Galileo's highly scalloped and non-elliptical terminator. However, even if we could determine the percentage illumination with absolute certainty we would not know the precise age of the Moon at the time of the observation.

Plot of Percent Illumination versus Age of Moon at Sunset The problem, as shown in this plot, is that not all lunar cycles are the same. One month a Moon of a given age will have a particular percentage illumination, but the next month it can be quite different. For, as the plot indicates, for a particular percentage illumination, say 20%, the age of the Moon having that illumination can actually vary, in different months, anywhere from nearly 4 to 5 days. In using an ephemeris to tabulate the age of the Moon at sunset, and rejecting those instances where the computed age differed by more than 0.08 days from his estimate, Righini may well thrown out the evenings on which the Moon looked most like engraving E1. For example, on the day he finally settled on, October 2, 1609, the age of the Moon at sunset was indeed close to 4.62 days, but the percentage illumination was less than 19%, considerably outside his probable target range. December 1, with 23% illumination would be a much closer match to the engraving (as interpreted by Righini), even though the age of the Moon happened to be 5.1 days, well outside the range he was looking for. Gingerich's alternative date of January 29, 1610 would also have been a better choice (also 23% illumination at sunset); but not March 29, 1610 with 27% illumination even though the age of the Moon is virtually the same as on October 2, 1609. However, Righini felt that the date of October 2, 1609 for engraving E1 was established not only by the phase, but also by the depicted orientation of features relative to the terminator and limb. This orientation would have been noticeably different on October 2 compared to January 29. To understand Righini's argument, and the later analysis by Whitaker, some rather technical background about what is called the lunar librations is required.

To the casual observer, the Moon appears to always present the same face towards the earth; but it actually rocks and swivels so that different features are pointed towards us at different times. These motions are referred to as librations. The easiest part of the libration to understand is the libration in latitude, caused primarily by the fact the Moon's axis of rotation is inclined slightly relative to the plane of its orbit about the Earth, as shown in the following diagram. The rotation axis has poles which are fixed relative to the topography of the Moon, and serve to define a system of latitude; each crater being assigned a position north or south of the Moon's equator, just as we describe the positions of cities on Earth by giving their (unchanging) latitude relative to the Earth's equator. Also like on Earth where an arbitrary point in Greenwich, England serves as the basis of the system of longitude; an arbitrary crater can be selected to serve as the origin of the system of lunar longitudes. The great circle through the poles and this arbitrary central crater is known as the Moon's Central Meridian. The Moon, acting something like a spinning top, tends to keep its axis always pointed in the same direction in space, independent of its orbital motion about the Earth. The result of this is that at certain times in the Moon's monthly orbit we see a bit more of its north pole (as when it is at the left-most position in this diagram); and at others we see more of its south pole (as when it is at the right-most position).

Moon's orbit as seen from side

The librations in longitude, which cause the Moon to nod in an east-west direction, are harder to explain. In theory, the Moon could spin about its own axis at any rate, but in practice it seeks the rate that minimizes the pull and tug of tidal distortions. This is accomplished by trying to keep a fixed orientation relative to the Earth. As the following diagram demonstrates, if the Moon moved about the Earth at a steady rate in a perfectly circular orbit, it would be possible (aside from a few complications introduced by the titled pole) to keep the Central Meridian (CM) pointed exactly towards the Earth if the rate at which it spins about its own axis was exactly equal to its rate of orbital rotation about the Earth. In the example shown, in going from the position labeled Moon 1 to the position labeled Moon 2 the orbital angle has increased by 45 degrees. If the Moon rotates about its own axis by 45 degrees during the same interval of time, then the Central Meridian will remain pointed exactly towards the Earth.

Moon's orbit as seen from top

Now the Moon does indeed rotate about its own axis at approximately this rate; and, like a top, the rate is nearly constant. However, the rate of orbital motion about the Earth is not constant. This is because the orbit of the Moon about the Earth is not a circle, but rather an ellipse. According to Kepler's Laws of planetary motion, the line from the Moon to the Earth has to sweep out equal areas in equal times. This requires the Moon to move significantly faster around its orbit when it is close to the Earth, and slower when it is far away. During the fast parts, the central meridian direction does not turn enough to match the orbital motion, so we see a little more of the eastern face of the Moon than normal; while during the slow parts, the central meridian direction turns faster than the orbital angle, and we see more of the Moon's western face.

Note: until relatively recent times, the side of the Moon that a naked eye observer standing in the Northern Hemisphere saw on his right hand side as the Moon crossed the meridian was known as the "west" side. In the 1960's, at the urging of NASA, the IAU reversed this convention for lunar and planetary maps, so that with north at the top the side to the right would be called "east" and the side to the left "west", just as on terrestrial maps. This is the notation we have used in labeling the preceding diagram which looks down on the lunar orbit from above the Earth's north pole. Oddly, the old system has been retained for referring to features on the Sun, where sunspots are still said to rotate from east to west.

In addition to this, the Earth's radius is a significant fraction of the distance to the Moon, so there is a measurable parallax effect as we spin about our own axis; allowing us to see more to the Moon's east when we first see it rise, and more of its west side in our last glimpse before it sets (an effect known as the diurnal libration). Add to this the facts that the Moon's axis is not permanently fixed in space, but rather precesses and wobbles (as does the Earth's); that the Moon's orbit about the Earth also precesses; and that all of this is compounded with the Earth's slightly irregular motion about the Sun. So the prediction of the apparent positions of lunar features, and their relation to the limb and terminator, is complicated indeed!

Fortunately greater minds than ours have worked out the details, and with modern computers precise predictions have become fairly routine. In addition, for checking the date of Galileo's observations, the thing that is most likely to be measurable in his drawings is the features that lie along the terminator, the line separately dark from light. As shown in the following two diagrams, the position of this line relative to the lunar craters is completely determined if we know the latitude and longitude of something called the "subsolar point".

Diagram of the subsolar point

For the Moon, the subsolar point is never more than about 1.5 degrees north or south of its equator, so the terminator (the transition from light to dark) is actually much more nearly vertical than we have shown it here. Lunar longitudes are measured from the central meridian with east positive. The angle equal to 90 degrees minus the longitude of the subsolar point is referred to as the Sun's selenographic colongitude. When the Sun is directly over the Moon's east limb (First Quarter Moon), the longitude of the subsolar point is +90 and the Sun's colongitude is 0. The Sun's colongitude, which is usually expressed on a scale from 0 to 360 degrees, increases at rate of about 0.51 degrees per hour, completing the circuit from one First Quarter Moon to the next in about 29.5 days. It can also be thought of as the longitude of the point where the sunrise terminator crosses the selenographic equator, but measured in the older system where longitudes increase westward from the central meridian. In his datings of Galileo's lunar images, Ewen Whitaker refers extensively to the Sun's colongitude, claiming he could estimate it to within 0.5 to 2 degrees by recognizing the unique pattern of features depicted along the terminator for each value. Despite what Whitaker implies, giving the Sun's colongitude (unlike giving the complete coordinates of the subsolar point), does not uniquely determine the position of the terminator. This is because the subsolar point varies in both longitude and latitude. The ±1.5 degree variation in the latitude, although it seems small, causes the terminator to twist significantly clockwise and counterclockwise relative to the central meridian. For a given solar colongitude it is quite possible for a particular feature north or south of the Moon's equator to be either in sunshine or in shadow depending on the latitude variation of the subsolar point.

When we look at the lunar lighting from the side, we see that the center of the dividing line between dark and shade is tipped very slightly towards the Sun due to the finite size of the Moon as seen from the center of the Sun; and, more importantly, has a finite width of about one-half degree (in lunar coordinates) due to the finite size of the Sun as seen from the Moon.

Diagram of the lunar terminator

The position of the sub-solar point on the Moon at any given instant can be found from such ephemeris services as JPL Horizons. From its longitude and latitude one can completely determine which craters (and other features) the terminator will pass through, something which is exactly the same for all observers, regardless of their location. The JPL ephemeris also gives the coordinates of the point at the Moon's apparent center as seen by an observer at any point on Earth (or elsewhere), taking into account all the effects of parallax, time delay, etc. The "sub-observer point" determines which crater will appear in the center, something that is different, at any given instant, for observers at different locations. The knowledge of these two parameters (the selenographic latitude and longitude of the sub-solar and sub-observer points) is completely sufficient to predict the visual appearance of the Moon to any level of detail for an observer at any location.

For predicting the appearance of the Moon at dates not too distant from the present time, Christian Legrand and Patrick Chevalley have produced the excellent freeware Virtual Moon Atlas. Their program not only plots the predicted position of the terminator, but includes a large clickable database for identifying craters and other features. Unfortunately, we found that, at least through version 3.0, when one enters dates from the 17th century the predicted lunar librations do not accord very well with those from JPL lunar ephemeris. To determine which was correct we examined several of the published lunar maps of Johannes Hevelius, which show the position of the terminator at carefully recorded dates and times. Not surprisingly, we found the JPL predictions agreed with Hevelius' maps, and the Virtual Moon Atlas predictions did not. We have therefore written our own program, much in the same spirit as the Virtual Moon Atlas, which shades a projected sphere according the same US Geological Survey texture map used by Legrand and Chevalley. However, for the center of the projection we use the latitude and longitude of the sub-observer point as determined by JPL, and then draw over that map the limits of the terminator as predicted using the JPL calculated sub-solar point. The terminator predicted in this way assumes a perfectly spherical moon of uniform radius. Because the actual Moon is not a perfect sphere, local variations in topography (in particular, variations in surface slope) will cause the actual terminator to deviate slightly from the predictions. However, these systematic errors can, in principle, be calibrated out. For example, if Ewen Whitaker tells us that the peak of a certain crater was in sunlight and another in shadow at 20 hours Padua time on November 30, 1609, we can generate a prediction for where the terminator would have been at that moment. We can then determine a modern date and time at which the terminator is predicted to be the same distance from those features, and examine a photo to see if they are actually in sunlight and shadow, as he says.

Note: beginning with Version 3.5, the errors mentioned here in the Virtual Moon Atlas (VMA) program of Christian Legrand and Patrick Chevalley have been corrected. The Basic Version, in particular, gives a clear graphic indication of the location of the terminator relative to the lunar features, and the series expansions it uses give results very similar to those found by look-up in the JPL files. Those who prefer the interface of VMA to that of LTVT can now use VMA with confidence. However they should be warned that in the Expert and Pro versions the theoretical position of the terminator is not as clearly shown as in the Basic one.

We make no claim that this approach is new. Many of the better photographic atlases of the Moon give the apparent azimuth and elevation of the Sun as seen from the center of the photo and the time of the observation; and the capability of making this calculation given the time and location of any observation has existed for a very long time. The modern computer-assisted graphic approach just seems a little simpler and more intuitive to us. Those interested in making their own comparisons between historic drawings and modern photos may be interested in our program, which allows you to prepare these graphic plots of the terminator position based on the sub-solar and sub-observer points given by the JPL database. A somewhat simplified version is freely downloadable on the website of Henrik Bondo, a Danish pathologist and moon enthusiast who helped in the development of a user-friendly version. The program works only on PC's running the Windows operating system.

Someday in the not to distant future the world will undoubtedly have a digital elevation model of the Moon accurate enough to predict the exact pattern of lighting that will be seen when the Moon is illuminated by the Sun at any given angle. The amateur of that day will simply be able to browse through a series of absolutely precise simulations of what the Moon would have looked like from Padua at each hour from July 1609 to March 1610, and will perhaps come across certain dates and times that exactly match Galileo's pictures (or perhaps find there are no such dates). If Galileo's pictures represent actual instantaneous observations, rather than merely illustrations of an impression build up from many observations, then we suspect the pattern of illuminated peaks shown on the dark side of the Moon, beyond the terminator will be the most telling feature. This Morse-code like pattern of dots and dashes is very specific to a particular moment: it lasts only a few hours and rarely repeats itself along the full length of the terminator. We, however, do not yet have the capability of generating such simulations, so the following is the best we can do.

The following computer-generated images are predictions of the appearance of the Moon, and the position of the terminator as seen from Padua (where Galileo lived at the time) shortly after sunset on various evenings in 1609-1610. As in Legrand and Chevalley's Virtual Moon Atlas, the background pattern of lunar features is meant only for orientation: it does not reproduce the expected pattern of light and shadow (for that, at present, as indicated above, you need to consult a photo taken when the terminator was at the same position). You may need to look closely to see the theoretical terminator, which is indicated by red and blue lines, marking its start and end. The scale has been chosen to match the reproduction of engraving E1, as shown above; and the evenings chosen are, for the most part, those suggested by Righini as possible dates for the observation on which E1 was based. We have adjusted the times slightly from those given in Righini's Table 1 so that in each case, to the nearest 5 minutes, the sun (uncorrected for refraction) would be exactly 6 degrees below the horizon (Righini may have used a slightly different definition of "sunset"). We have also listed November 30, 1609 in place of December 1, because November 30 is the date for engraving E1 later suggested by Whitaker. Below each picture we give the exact Universal Time and the Moon's phase. Righini expressed the phase in terms of the slightly ambiguous "age of the Moon" in days. The phase can be more precisely described in terms of either a phase angle or the percentage of the visible face that is illuminated (the two are mathematically equivalent, that is either one can be calculated from the other), which is also more directly related to the quantity Righini measured on Galileo's engraving. We give the percentage illumination as calculated by JPL. Righini apparently believed that Galileo drew the terminator on engraving E1 in a way showing approximately 22% illumination; but selected the sunset on October 2, 1609 as the most likely date because the Moon's age was 4.62 days, and he had the mistaken belief that an age of 4.62 days always corresponded to 22% illumination. As previously mentioned, the illumination at this phase increases by about 8% per day, and, in different months, correlates only loosely with the age of the Moon. Righini's preferred date of October 2, 1609 is especially atypical: the actual illumination at sunset is a little less than 19%. August 4 (too early historically), December 1, 1609 and January 29, 1610, all with about 23% illumination, would have been much closer to the value Righini thought he saw in the engraving. You may notice that Whitaker's preferred date of gives only 15.0% illumination, significantly lower than Righini's estimate. On December 1, the date considered more likely by Righini in his table, the predicted terminator position gives 22.8% illumination.

July 5, 1609

August 4, 1609

September 2, 1609

October 2, 1609

November 1, 1609
![Predicted terminator at sunset July 5, 1609](/web/20070601182754im_/http://www.pacifier.com/~tpope/Moon_Drawings/1609_07_05-19_40.jpg "Predicted terminator at sunset July 5, 1609") ![Predicted terminator at sunset August 4, 1609](/web/20070601182754im_/http://www.pacifier.com/~tpope/Moon_Drawings/1609_08_04-19_10.jpg "Predicted terminator at sunset August 4, 1609") ![Predicted terminator at sunset September 2, 1609](/web/20070601182754im_/http://www.pacifier.com/~tpope/Moon_Drawings/1609_09_02-18_20.jpg "Predicted terminator at sunset September 2, 1609") ![Predicted terminator at sunset October 2, 1609](/web/20070601182754im_/http://www.pacifier.com/~tpope/Moon_Drawings/1609_10_02-17_20.jpg "Predicted terminator at sunset October 2, 1609") ![Predicted terminator at sunset November 1, 1609](/web/20070601182754im_/http://www.pacifier.com/~tpope/Moon_Drawings/1609_11_01-16_30.jpg "Predicted terminator at sunset November 1, 1609")
19:40 UT; 20.5% 19:10 UT; 23.3% 18:20 UT; 17.5% 17:20 UT; 18.9% 16:30 UT; 20.4%
 

November 30, 1609

December 30, 1609

January 29, 1610

February 27, 1610

March 29, 1610
![Predicted terminator at sunset November 30, 1609](/web/20070601182754im_/http://www.pacifier.com/~tpope/Moon_Drawings/1609_11_30-16_05.jpg "Predicted terminator at sunset November 30, 1609") ![Predicted terminator at sunset December 30, 1609](/web/20070601182754im_/http://www.pacifier.com/~tpope/Moon_Drawings/1609_12_30-16_15.jpg "Predicted terminator at sunset December 30, 1609") ![Predicted terminator at sunset January 29, 1610](/web/20070601182754im_/http://www.pacifier.com/~tpope/Moon_Drawings/1610_01_29-16_45.jpg "Predicted terminator at sunset January 29, 1610") ![Predicted terminator at sunset February 27, 1610](/web/20070601182754im_/http://www.pacifier.com/~tpope/Moon_Drawings/1610_02_27-17_25.jpg "Predicted terminator at sunset February 27, 1610") ![Predicted terminator at sunset March 29, 1610](/web/20070601182754im_/http://www.pacifier.com/~tpope/Moon_Drawings/1610_03_29-18_05.jpg "Predicted terminator at sunset March 28, 1610")
16:05 UT; 15.0% 16:15 UT; 17.9% 16:45 UT; 22.8% 17:25 UT; 19.7% 18:05 UT; 26.8%

We also show three dates in 1610, not mentioned by Righini. Two of these (January 29 and March 29) are the ones on which Owen Gingerich correctly reported that the age of the Moon at sunset would be the same as that on Righini's favored date of October 2, 1609. The remaining date, February 27, 1610, is mentioned as a possibility by neither Righini or Gingerich.

You can check Righini's analysis (as corrected here to show illuminated percentages rather than age of the Moon) by using a ruler to measure the distance from the right hand limb to the predicted terminator on each evening, and compare that to the distance indicated in Galileo's engraving E1. Although the predictions for November 30 (15%) or March 29 (27%) certainly appear to show too little or too much illumination relative to engraving E1, we find it hard to understand how Righini could rule out with such confidence the possibility that the engraver might have been depicting the amount of illumination predicted on the other dates. The differences are extremely subtle, and the position of the terminator is not indicated with any great precision in the engraving.

Moreover, despite what Righini says, the predicted appearance of the lunar features on October 2 does not particularly well fit their depiction in the engraving. The one feature whose identification Righini is most confident about is the dark shaded oval at about 2 o'clock in engraving E1. Righini says that "the identification [of this feature] with the center of Mare Crisium is beyond doubt." Yet the engraver shows this feature comfortably situated in the middle of the illuminated crescent, midway between terminator and limb. Compare this to the JPL predictions for either October 2 (Righini's preferred date) or November 30 (Whitaker's preferred date). In both cases, Mare Crisium is far off center with one edge nearly touching the right hand limb. The position shown in the engraving is much more like that predicted for July 5, a date at which we believe Galileo had not yet heard of the telescope.

It should also be noted that Righini's predictions of the lunar at phase at sunset do not seem to be any more reliable than those of Gingerich. We find only a vague correlation between the ages of the Moon at sunset listed in Righini's Table 1 compared to the JPL predictions of percentage illumination at the same moment; and in some cases glaring discrepancies. For example, Righini lists September 2, 1609 at 18:30 hours as the oldest (that is, most fully illuminated) of all the moons he lists, yet in reality, according to JPL it is the second youngest (least fully illuminated) of those shown here. That is, Righini believed the terminator at sunset on September 2 was well to the left of his preferred position (for October 2), when it was actually a little to the right. We have no explanation of why his calculations were wrong.

As this page is completed, we will have more to say about Whitaker. His datings are all based on the identification of specific features along the terminator. Suffice it to say that examples can be found where Righini, Gingerich and Whitaker all, with equal extremely high levels of confidence, come up with totally different identifications for the same feature on a Galileo drawing. Each's confidence seems completely unshaken by the different opinions of the others. In view of this, it would seem to us that if the cases in which they disagree cannot be resolved, then the cases in which they agree may have less significance than is generally supposed.

Dating the Images

The following table lists the engravings in Sidereus Nuncius and the paintings on the sheet of watercolors according to the designations assigned by Whitaker, and then gives the dates assigned to them by Whitaker, Righini, Gingerich and Van Helden. Righini and Whitaker mention the local Padua time at which they believe certain of Galileo's observations were made. Whitaker defines this as Universal Time plus one hour. To avoid confusion we have converted all their results to Universal Time (formerly known as Greenwich Mean Time), the system most commonly used by modern ephemeris software.

Righini believed that from the phase depicted in E1 the age of the Moon at the time of the observation could be determined to within ±2 hours; a value accepted by Drake (1976) as having "an accuracy beyond the range of guesswork" (even though he rejects Righini's date and substitutes Gingerich's suggestion of January 29, 1610; also unaware that the "age of the Moon" is a poor predictor of anything measurable in the engraving). Righini based his other dates on the depicted libration of the lunar features, a method not accurate enough to give a specific hour.

Whitaker believed he could do better than Righini by identifying features along the terminator, which, he says, give the Sun's colongitude at the time of the observation to an accuracy of between ±0.5 and ±2 degrees (depending on the image). His measured solar colongitudes are summarized in the following table. Since the Sun's colongitude changes at a rate of about -0.51 degrees per hour, this corresponds to an accuracy of ±1 to 4 hours in time. In addition to measuring the Sun's apparent colongitude, in his Table 2 Whitaker assigned a specific date and universal time (to the nearest half hour) at which he believes the observation was made. In the second part of the table we have used the longitude and latitude of the subsolar point from JPL Horizons lunar ephemeris to compute the actual colongitude at the moment Whitaker assigned to the observation (we have subtracted the one hour correction Whitaker applied to convert universal time to Padua time). The colongitude is 180 degrees minus the selenographic longitude of the subsolar point.

Whitaker's Estimates of Solar Colongitude in Galileo's Moon Drawings

  Measured Assigned Subsolar Point
Image Colongitude Colongitude Longitude Latitude
E1 323 ± 1 323.2 126.8 +1.0
E2 358 ± ½ 358.2 91.8 +1.0
E3 162 ± ½ 162.0 288.0 +0.6
E4 174 ± ½ 174.2 275.8 0.5
F1 321 ± 2 321.2 128.8 +1.0
F2 322 ± 2 322.2 127.8 +1.0
F3 334 ± 2 334.1 115.9 +1.0
F4 346 ± 1 346.0 104.0 +1.0
F5 162 ± 1 162.0 288.0 +0.6
F6 175 ± 1 175.2 274.8 +0.5
F7 203 ± ½ 203.3 246.7 -0.3
F7* - 204.2 245.8 -0.3
*(Whitaker says that from the appearance of drawing F7 he determined the colongitude to be 203± ½ degrees and assigned to it a date and time of 4h UT on January 19, 1610\. However he also says it depicts a star emerging from occultation near that time. If this interpretation is correct, a recalculation with modern software puts the time of the event depicted at around 5:50 UT. The line labeled "F7" gives the expected circumstances of the lunar terminator at Whitaker's original estimated time of 4:00 UT; while the line labeled "F7*" gives the same information for 5:50 UT. For more on this see our section on [The Occultation of Jan. 19, 1610](#Occultation "Jump to this section").)

Examples of the appearance of the terminator within the range of nearly all Whitaker's measured colongitudes can be found in John Westfall's Atlas of the Lunar Terminator. Readers with access to that book are encouraged to check whether they can independently find the same "matches" that Whitaker claims to have found. It has to be noted, however, that just as the "age of the Moon" does not uniquely define the phase (percent illumination), stating the Sun's colongitude does not uniquely define the appearance of the terminator. The problem, as Westfall mentions, and illustrates in his Index Maps, is that for a given colongitude the latitude of the subsolar point can differ by as much as 3 degrees, causing a quite noticeable twisting of the terminator. This can significantly alter the appearance of the terminator to the far north and south. Since Whitaker does not give the dates or times for any of his comparison photos it is impossible to verify that they accurately represent the appearance of the terminator on his assigned dates. They also appear to have been printed too dark to give an accurate impression of how the terminator would have appeared to the human eye.

Galileo's drawings obviously do not represent photograph-like snapshots of the Moon as it appeared at a single instant. Using a modern spotting scope, Elizabeth Cavicchi took about an hour to complete similar, but somewhat larger (120 mm diameter), watercolors of the Moon. She suspects Galileo's smaller (55 mm) pictures could have been made faster; but the task of assembling the small views seen through the Galilean telescope into a coherent image is much more complex, so they could equally well have taken longer. Fortunately, the appearance of most lunar features changes slowly, and even with a camera it is difficult to demonstrate dramatic changes over times of less than several hours. Cavicchi, like Galileo, gives no dates for here published images. It would be interesting to know if either Righini or Whitaker could have correctly dated them. We have tried this experiment with some of the very few modern full disk drawings of the Moon available over the internet, and it is a very humbling experience. As with Galileo's drawings, many inconsistencies appear and these usually make the identification of particular features quite uncertain. When the true date is revealed, many of the features turned out to be something quite different from what one suspected them to be.

Incidentally, in dismissing out of hand Righini's earlier result for the date of E1, Whitaker makes what seems to us a completely erroneous argument about the impossibility of accurately dating a lunar image based on its phase. Whitaker correctly notes that, due to the librations in longitude, a terminator falling on the central meridian can be as much as 8 degrees to the left or right of the apparent center line of the Moon. We completely fail to see what this has to do with dating images based on the phase. If the observer shows the terminator as a straight line down the middle of the image (the phase corresponding to 50% illumination) he is showing a configuration that happens only once a month at a very specific hour. Similarly, every other phase, just the same as one of Whitaker's solar colongitudes, occurs only once, at a very specific hour, each month. The fundamental problem with Righini's dating of engraving E1 is that, for unknown reasons, he converted the measurable phase into an "age of the Moon". Unknown to Righini, Gingerich or Drake moons of a given "age" will have different widths in different months (and also in the same month as observed from different places on Earth). However, Righini's approach can easily be recast in terms of phase (the observable percentage illumination) rather than age. The real question is whether the phase is likely to be accurately depicted in a drawing. Despite Drake's enthusiastic endorsement, we find it very hard to believe that the phase shown in E1 is delineated to the accuracy of ±2 hours that Righini claims. With the possible exception of images showing a straight terminator down the middle of the picture, Whitaker's method seems intrinsically more accurate only because the artist seems more likely to correctly depict which features were seen along the terminator than to get their positions quite right. That is, in a drawing, particularly one made through a Galilean telescope, the artist may well show the terminator a little too far to the left or right, which will upset the apparent phase. But, as indicated above, there is no guarantee that the features the artist chooses to show along the terminator are what the person doing the dating believes them to be.

For a photograph, we can see no difference between determining the date using the apparent phase vs. the apparent solar colongitude, as they both require a very similar subjective judgment as to where these points lie. In fact, when working with photographs, which would seem intrinsically far more accurate, the apparent position of the terminator can move by many degrees depending on the exposure and contrast of the image. Anyone who does not believe this should try using photo processing software to alter the "gamma" of a full disk lunar photo downloaded from the internet. If the human eye had so much tolerance in choosing the point it calls the terminator, the dating methods of both Righini and Whitaker would be totally impossible. Fortunately, when we look at the Moon through a telescope we see the terminator at a fairly definite point, and that is what is depicted in most drawings. This point, corresponding roughly to the red and blue lines in our simulations, seems to correspond to what a camera sees when the photographic results are displayed at the highest possible gamma, giving a sharp transition from a solid white on one side to a solid black on the other.

With modern astronomical software it is possible to make a pretty good guess at what the Moon would have actually looked like from Padua at any of the proposed dates and times listed in the following table. Your opinion as to whether it matches the Moon shown in the drawings is probably as valid as theirs.

Proposed Dates and Times of Galileo's Moon Drawings

Drawing ID Phase "Age" [Righini (1975)](#Righini_1975 "Jump to citation to article") [Gingerich (1975)](#Gingerich_1975 "Jump to citation to article") [Drake (1976)](#Drake_1976 "Jump to citation to article") [Whitaker (1978)](#Whitaker_1978 "Jump to citation to article") [Gingerich and Van Helden (2003)](#Gingerich_2003 "Jump to citation to article")
F1 127° 4.3 - - Dec. 1, 1609 Nov. 30, 1609; 15 UT (Nov. 30, 1609)
F2 120° 4.9 - - Dec. 1, 1609 Nov. 30, 1609; 17 UT (Nov. 30, 1609)
E1 125° 4.5 Oct. 2, 1609; 16:48 UT or Jan. 29, 1610 Jan. 29, 1610 Nov. 30, 1609; 19 UT (Nov. 30, 1609)
F3 116° 5.2 - - - Dec. 1, 1609; 16.5 UT (Dec. 1, 1609)
F4 113° 5.5 - - Dec. 3, 1609 Dec. 2, 1609; 16 UT (Dec. 2, 1609)
E2 94° 7.1 Dec. 3, 1609 copy of F4 Dec. 3, 1609 Dec. 3, 1609; 16 UT Dec. 2, 1609
E3 -81° 21.4 shortly before E4 from F5? - Dec. 17, 1609; 4 UT (Dec. 17, 1609)
F5 -82° 21.5 - - - Dec. 17, 1609; 4 UT (Dec. 17, 1609)
E4 -90° 22.1 Dec. 18, 1609 - Dec. 18, 1609 Dec. 18, 1609; 4 UT (Dec. 18, 1609)
F6 -90° 22.1 - - Dec. 18, 1609 Dec. 18, 1609; 6 UT (Dec. 18, 1609)
F7 -120° 24.6 - - - Jan. 19, 1610; 4 UT (Jan. 19, 1610)

The second column of this table gives our estimate of the position of the terminator in each of Galileo's images, expressed as a phase angle. The phase angle of a solar system object is defined as the angle between the observer and the Sun as viewed from the center of the object (JPL refers to it as the Sun-Target-Observer angle and it is equivalent to the angle between the sub-solar and sub-observer points). It is closely related to the percentage illumination and easily inferred from the position of the terminator in the image. We obtained these values by using a computer to rotate the images so that we could fit an ellipse (symmetric about the vertical centerline of the image) to the drawn terminator. The ellipse represents the terminator that would be produced on an ideal sphere by the Sun at some angle to the left or right. For example, in Galileo's drawing F1, the middle of ellipse best approximating the sunrise terminator was about 0.60 of the lunar radius to the right of center. This is the sine of 37°. Neglecting very small corrections for the distance to the Sun, the sub-solar point is 90° away from the terminator along the same line for a total of 127°, the value listed in the table. A phase angle near 0° corresponds to a Full Moon, while the First and Last Quarters occur when the phase angle is 90°. We have arbitrarily added minus signs to distinguish the latter case (where the sunrise terminator is to the left of center) from the former (where it is to the right of center). The phase angle can be easily translated into a theoretical value for the percentage of the object that will appear illuminated by the Sun and vice versa. The formula is:

Percent Illumination = 50 x [ 1 + Cosine(Phase Angle)]

or

Phase Angle = ArcCosine(1 - [Percent Illumination]/50)

The true percentage illumination will, of course, vary depending on the surface slope and topography along the terminator, which can cause it to veer a little to the left or right of its theoretical position (a much bigger effect than the finite distance to the Sun, which has also been neglected). The percentage illumination can be estimated directly from an image without any trigonometry by drawing a line along a diameter perpendicular to the direction of the terminator. The percentage illumination is 100 times the fraction of the line that is in sunlight. The phase angle can then be determined using the second formula.

In the third column we have made an attempt to translate the phase angle measure into an "age" of the Moon. Normally, the "age of the Moon" means the number of days since the preceding New Moon. As already mentioned, this cannot be accurately inferred from the apparent phase in an undated photo or drawing. This is because the image shows only the percentage illumination, and the number of hours (and therefore days) it takes to go from New Moon to a particular percent illumination varies substantially from one month to the next. So if we don't know the month we can't tell the exact age. Nonetheless, it is useful to convert the angular measurement to a time scale so that one can get a feel for the likely interval between the observations. We have somewhat arbitrarily assumed that the phase angle starts at 180° when the age is zero and goes through a cycle of 360° in 29.53 days, the average length of the synodic month. In reality, the angular range is less since the phase angle rarely goes all the way to either 0 or 180° and the time taken to complete the cycle can vary by about ±0.3 days. Nonetheless, if the images were made during a single lunation, the assumption of an average rate of change of 12.2°/day in the position of the terminator should give a reasonable estimate of the likely interval between them. So for example, drawing F1 is 180 - 127 = 53° "past New," and assigned an age of 53/12.2 = 4.3 days.

Having done this, we see some obvious problems with the proposed datings. For example, Whitaker tells us, based on his identification of features along the terminator, that engraving E1 is based on an observation made after drawing F2, yet the terminator is shown as if E1 was made before F2. Similarly, the position of the terminator suggests that the interval from F2 to F3 (which Whitaker says are a day apart) is less than the interval from F1 to F2 (which Whitaker says are two hours apart). And F3 and F4, another pair which Whitaker says are a day apart, show the same very small change terminator as F2 and F3. In other words, if the drawings have been properly dated, it is very hard to see how the terminator could have moved, in two cases, by just 3° in 24 hours, while in another it moved 7° in just 2 hours.

Drake's conclusions about the dates of the drawings and engravings are somewhat cryptically given in the third paragraph on page 154 of his paper. Accepts Righini's contention that Galileo's first observation of the Moon was made when the Moon was four to five days old, but rejects Righini's date of October 2 as being too early. He also rejects Righini's next possible date of November 2, partly because he accepts Righini's dates of December 3 and 18 for the next observations, and does not like the idea of a lengthy period of inactivity between observations. This leaves December 1, 1609 as the next possible date to see a five day old Moon at sunset (Drake seems unaware of Righini's argument that the dates of November 2 and December 1 should both be rejected because the expected phase at sunset was two different from what he thought was depicted in E1). The result, according to Drake, was two "unpracticed" sketches on the evening of December 1st, presumably referring to the two wash drawings that Whitaker calls F1 and F2. Since, as Drake says, "it would be hardly credible" that on his first night of lunar observation Galileo could have achieved sufficient accuracy in his drawings to permit them to be dated by Righini's method, the unpracticed sketches were laid aside and engraving E1, representing the same phase, was made from a new observation on January 29, 1610. However, he says, Galileo's skill quickly improved and that the drawings made on December 3rd and December 18th were used for the engravings in Sidereus Nuncius. This implies that Drake is accepting Gingerich's theory that engraving E2 was derived from drawing F4 (even though the phases look very different); but is accepting Righini's date of December 3 for engraving E2 (and therefore for drawing F4) even though Gingerich argues this could not be a correct date since the engraving is a distorted picture of the Moon seen on any earlier day. By accepting Righini's date, Drake seems to be saying he thinks F4 is a distortion of the phase correctly depicted in E2. Drake also seems to be adopting Righini's date of December 18 for engraving E4, which he associates with drawing F6. Drake does not explicitly mention engraving E3, but seems to accept Righini's assessment that represents an observations made "shortly before" that used for E4. We can ourselves find nothing in the drawings themselves to suggest that F1 and F2, the ones Drake says were done on Galileo's first night of lunar observations and had to be replaced, are any less practiced than F4 or F6, the drawings Drake says were acceptable for preparing engravings.

Since the Gingerich and Van Helden article mentions a new date for only engraving E2, and says that Whitaker's dates for the other images are "definitive," we assume they are adopting them, and have listed them in parentheses.

Could Righini be Right About October 2, 1609?

Although we do not agree with Righini's assessment that engraving E1 must have been the first of Galileo's lunar observations simply because it is the first illustration shown in Sidereus Nuncius; considerable interest has attached to it, and it is the one Righini claims to have dated the most precisely. As described above, Righini dated this engraving based on a somewhat inaccurate argument about the age of the Moon depicted in it, an age which he believes would have been visible from Padua at around 15:18 UT (±2 hours) on October 2, 1609. The modern JPL ephemeris indicates that on that evening, from Padua, the Sun would have dipped below the horizon at about 16:50 UT, a value consistent with Righini's estimate, and the Moon would have followed at about 19:15 UT. As shown above, the phase shortly after sunset is indeed consistent with what Galileo seems to be showing in engraving E1, although it is probably a thinner crescent than Righini intended. However, if Galileo started observing the Moon around sunset, the interval of two and one-half hours from sunset to moonset seems uncomfortably short to contain all the events he described. Galileo says he saw the "immense gulf" near the southern tip of the Moon's crescent completely dark for two hours before the triangular peak (which would merge into the crescent at moonset) even began to emerge. Although it is certainly possible to observe the Moon during daylight, the contrast is not very good, and it seems unlikely Galileo would have been impressed by the blackness of the gulf while the Sun was still up. Yet if Galileo began his observations just as the Sun was going below the horizon, it is hard to see how he could have seen the complete sequence of events in the following two and one-half hours. For this reason alone, if Galileo's description applies to the engraving, as Righini supposes, his date seems unlikely.

Terminator on October 2, 1609 at 15:18 UT
![Predicted Terminator for October 2, 1609 at 15:18 UT](/web/20070601182754im_/http://www.pacifier.com/~tpope/Moon_Drawings/Baco_1609_10_02-15_18.gif "Predicted Terminator for October 2, 1609 at 15:18 UT")

Although Righini arrived at his date based on the phase, he also felt his proposed date was consistent with the features pictured along the terminator, which he says are accurately shown. In particular, Righini says the large detached bright feature that Galileo shows in the gulf near the south cusp (presumably the "triangular peak" mentioned in the text) represented the Sun rising over the craters Baco, Breislak, Clairaut and Cuvier. At left we identify these craters on the USGS texture map, and have used our program to plot where the terminator would have been at 15:18 UT (Righini's preferred time, even though it is well before sunset). As can be seen the terminator is far to the right of Righini's craters. They would have been far on the dark side, and would have remained so until long after moonset.

If Righini is correct about the date, he cannot, then, be correct about the cause of the bright patch shown in the engraving. On the other hand, at sunset the JPL terminator does seem to be approaching a possible triangular peak shown in the texture map between the craters Vlacq and Hommel. Is it possible that Righini, although mistaken about what caused the patch of light, was still correct about the date?

We show below a modern photograph taken when the terminator, in this region of the Moon, was very close to the position it had on October 2, 1609 at 18:00 UT. This time, a little more than an hour before moonset, would have been approximately in the middle of Galileo's brief nighttime lunar observing window for that evening. The photo has been purposely overexposed to show the appearance of the terminator, that is, to show as accurately as possible which bright points are seen as attached to, and which are seen as detached from, the Moon's illuminated crescent (a normal exposure does not show the terminator clearly). This photo was NOT taken with the Galilean telescope. It was taken afocally through a 4-inch reflector from Newport Beach, California. The dark lines are an azimuth-altitude grid used for calibrating pictures taken through it, and are irrelevant to the present discussion.

Terminator on Oct. 2, 1609 at 18:00 UT Photo on May 13, 2005 at 2:59 UT Terminator on May 13, 2005 at 2:59 UT
![Predicted Terminator for October 2, 1609 at 18:00 UT](/web/20070601182754im_/http://www.pacifier.com/~tpope/Moon_Drawings/Vlacq_1609_10_02-18_00.gif "Predicted Terminator for October 2, 1609 at 18:00 UT") ![Photo on May 13, 2005 at 2:59 UT](/web/20070601182754im_/http://www.pacifier.com/~tpope/Moon_Drawings/Vlacq_C87P0005.jpg "Photo on May 13, 2005 at 2:59 UT") ![Predicted Terminator for May 13, 2005 at 2:59 UT](/web/20070601182754im_/http://www.pacifier.com/~tpope/Moon_Drawings/Vlacq_2005_05_13-02_59.gif "Predicted Terminator for May 13, 2005 at 2:59 UT")

We find no obvious relation between the features shown in this photo and those depicted in Galileo's engraving E1. At this hour, which would have been well before moonset on October 2, 1609, the feature that looks like a triangular peak on the texture map is already thoroughly connected to the bright portion of the Moon, it is not located in an "immense gulf", and there are no obvious candidates for the three surrounding points of light (which should probably have emerged according to Galileo's timeline).

It is, of course, still possible that Righini was correct about the basic date for E1; but, as suggested above, Galileo may have chosen to interject both a picture and a description of events he had seen at some other phase of the lunar cycle.

Could Whitaker be Right About November 30, 1609?

Whitaker believes that watercolors F1 and F2, together with a now missing drawing that served as the basis for engraving E1 in Sidereus Nuncius, were executed, in that order, between about 15:00 and 19:00 UT on the evening of November 30, 1609. From Padua, on that evening, the Sun sat at around 15:30 UT and the Moon at about 18:45 UT. Although this interval of a little over three hours is slightly longer than that for Righini's proposed date, it is still uncomfortably short compared to Galileo's timeline of events he saw associated with the triangular peak. This problem notwithstanding, we will investigate here, as we did for Righini in the previous section, whether the features Whitaker claims to have identified in the two watercolors and in the engraving could actually have appeared the way Galileo shows them on Whitaker's proposed evening. Again we will conclude that there seem to be enormous problems with the claimed identifications of features.

The following images show the predicted position of the terminator for November 30, 1609 in the region near the south-east limb where Galileo reported seeing the immense dark gulf containing the triangular peak surrounded by three points of light (see Galileo's description earlier on this page), together with a fragment of the engraving (E1) referred to in Galileo's text, plus the two watercolors (F1 and F2) that Whitaker feels are based on observations made four and two hours before that of E1 on the same evening. Several features that Whitaker believes are illustrated in engraving E1 are labeled in the second and third images. According to Whitaker, the main triangular peak is the "illuminated centre of Janssen plus Fabricius w. wall" (indicated here by the arrowed "wall"), while the three points of light are "Janssen sw wall, Brenner w. wall, and Metius w. wall" (we believe the three points of light mentioned by Galileo are the dots marked with the red "1", "2" and "3" -- they are clearer on some prints than others). In addition, Whitaker identifies the prominent triangular projection marking the north end of the gulf as the "scarp north of Neander" (indicated here as "scarp"), the bright isolated patch of light above it as "mts east of Weinek" (indicated here as "mts"). (Note: our understanding is that Janssen is the large oval cavity around the "wall" especially evident in the lower right photo, below, with Fabricius lying entirely within it; so that the west wall of Fabricius is essentially in the center of Janssen)

Fragment of Galileo's Watercolor F1 Fragment of Galileo's Watercolor F2
![Same Area in Galileo's Watercolor F1](/web/20070601182754im_/http://www.pacifier.com/~tpope/Moon_Drawings/Galileo_F1_fragment.jpg "Same Area in Galileo's Watercolor F1") ![Same Area in Galileo's Watercolor F2](/web/20070601182754im_/http://www.pacifier.com/~tpope/Moon_Drawings/Galileo_F2_fragment.jpg "Same Area in Galileo's Watercolor F2")
Terminator at 15:30 UT (Sunset) Galileo's Engraving E1 at Same Scale Terminator at 18:45 UT (Moonset)
![Predicted Terminator for Nov. 30, 1609 at 15:30 UT](/web/20070601182754im_/http://www.pacifier.com/~tpope/Moon_Drawings/Janssen_1609_11_30-15_30.jpg "Predicted Terminator for Nov. 30, 1609 at 15:30 UT") ![Triangular Peak Area in Galileo's Engraving E1](/web/20070601182754im_/http://www.pacifier.com/~tpope/Moon_Drawings/Galileo_E1_fragment.jpg "Triangular Peak Area in Galileo's Engraving E1") ![Predicted Terminator for Nov. 30, 1609 at 18:45 UT](/web/20070601182754im_/http://www.pacifier.com/~tpope/Moon_Drawings/Janssen_1609_11_30-18_45.gif "Predicted Terminator for Nov. 30, 1609 at 18:45 UT")
Terminator on March 4, 2006 at 2:31 UT Photo on March 4, 2006 at 2:31 UT Photo on March 4, 2006 at 5:29 UT
![Predicted Terminator for March 4, 2006 at 2:31 UT](/web/20070601182754im_/http://www.pacifier.com/~tpope/Moon_Drawings/Janssen_2006_03_04-02_31.jpg "Predicted Terminator for March 4, 2006 at 2:31 UT") ![Predicted Terminator for March 4, 2006 at 2:31 UT](/web/20070601182754im_/http://www.pacifier.com/~tpope/Moon_Drawings/Janssen_C259P031.jpg "Predicted Terminator for March 4, 2006 at 2:31 UT") ![Predicted Terminator for March 4, 2006 at 5:29 UT](/web/20070601182754im_/http://www.pacifier.com/~tpope/Moon_Drawings/Janssen_C259P047.jpg "Predicted Terminator for March 4, 2006 at 5:29 UT")

In the final row we show portions of two photos of the Moon taken from Newport Beach, about three hours apart, on March 4, 2006. Again, the photos have been purposely overexposed to show the changes in the visual appearance of the terminator during this interval. And again, these photos were NOT taken with the Galilean telescope. The second photo is less sharp than the first, in part, because the Moon was low and the seeing poor (i.e., much atmospheric turbulence). These photos were selected because when the first was taken the terminator in the vicinity of the Janssen crater complex was near (actually slightly east of) its position at sunset on November 30, 1609. If you look closely at the predicted terminator for November 30, 1609 at 15:30 UT, you will see that the red line (marking the end of full sunlight) is very near the left (western) edge a small dark crater shown in the USGS texture map between Brenner and Metius. This crater is officially known as Brenner A. In the March 4, 2006 prediction the red line is near the right hand edge of Brenner A at 2:31 UT. It does not reach the left edge until about 4:00 UT. Similarly at 15:30 UT on November 30, 1609 the red line crosses the middle of jumbled feature labeled "mts" in the right hand texture map. On March 4, 2006 the red line was well to the east of this feature at 02:31 UT, and did not reach its center until about 05:00 UT (the fact that, even for features so close together on the Moon, there is a one hour difference between the times when the terminator position in 2006 matches that in 1609 demonstrates that a single parameter, such as the colongitude of the Sun used by Whitaker, is really inadequate to define the alignment of the terminator relative to the solar features).

In other words, the modern photo at 2:31 UT resembles what the terminator would have looked like an hour or two before sunset in Padua on November 30, 1609. By the time the sky grew dark, the terminator would have more closely resembled the situation shown in the 5:29 UT photo, and by the time the Moon set on November 30, 1609, the terminator would have swept still farther to the left; bathing all the features shown in the last photo in still more intense light, and revealing new bright features to the left.

Although our argument may be more than a little tedious, we feel this comparison demonstrates immense problems with Whitaker's interpretation of the engraving he attributes to November 30, 1609. The biggest problem is that the "wall" feature inside Janssen that Whitaker associates with Galileo's triangular peak would have been fully illuminated well before sunset. But Galileo describes having seen the basin dark for two hours before the peak even began to emerge. So Whitaker's identification of it cannot possibly be correct. Similarly, the first photo shows that the west walls of Janssen and Metius would have been fully connected to the illuminated portion of the Moon from well before sunset, so they could not possibly be (as Whitaker claims) two of the three points of light that Galileo describes as emerging well after the triangular peak, and still remaining detached from it at moonset.

If you are interested in making your own observations of the Janssen region, we have a page giving predictions of future dates on which the lighting will match that which Galileo would have seen at the times specified by Whitaker.

The pictures reproduced above demonstrate a more pervasive problem, as well. For Whitaker's method to work, one has to assume that the artist is faithfully representing the pattern of light and shadow along the terminator; otherwise attempts at identification are meaningless. The two modern photographs clearly indicate that the change in that pattern over a period of three hours is both orderly and rather subtle: the bright points that were detached from the terminator in the first photo have become a little large in the second, and a few new bright points have emerged to the left. We see no such orderly progression in going from F1 to F2 to E1, which Whitaker tells us, in his Table 2, are based on observations at intervals of two hours (earlier in his paper he tells us that F2 and E1 are so similar that they must have been copied from the same original observation, something that is not all obvious to us). In fact, to be frank, we can see no relation of any kind between the pattern of detached bright spots shown along the terminator in the three images. About the same degree of similarity would probably be found between any three randomly segments of the terminator taken from any of the drawings.

If we look at engraving E1 in isolation, compared to the modern photograph, the feature labeled "wall" in E1 might possibly correspond to the promontory above "wall" in the photo. This feature is the fully illuminated west wall of the crater Metius, but Galileo could not have seen it exhibit the sequence of events described in Sidereus Nuncius on the evening of November 30.

It would seem to us that either these three drawings do not represent the sequence Whitaker claims; or else the artist who made them was only trying to convey an impression of the presence of detached patches of light along the terminator, and not trying to faithfully represent the exact play of sunlight over any particular features.

The best clue as to which of these conclusions is correct is probably afforded by drawing F7. If Whitaker is correct that this represents the occultation of the star Theta Librae on January 19, 1610, then the time at which the observation was made is know with great precision, and one can ask if the terminator was faithfully represented (assuming the drawing was made at that time, and the star symbol not simply added to an earlier drawing).

Watercolor 8 (Whitaker F7): The Lunar Occultation of January 19, 1610

On page 162 of his 1978 paper, Ewen Whitaker says that, using his method of colongitudes, he arrived at the date and time of drawing F7 as being January 19, 1610 at 4 hours UT "give or take an hour or so" . Having done this, he consulted certain tables and determined that the 4th magnitude star Theta Librae would have emerged from occultation sometime between 4:30 and 5:00 UT, just as shown in Galileo's drawing. He regards this as a strong confirmation, both that the symbol on the page represents a star, and that he had arrived at the correct date for this image. In his 1984 and 1999 publications, for reasons unknown to us, Whitaker printed Galileo's drawings against a dark background, making the star is invisible, and made no mention of this remarkable demonstration of his ability to date the drawings.

We show below a chart of the Moon and its position relative to Whitaker's star at 5:50 UT, as prepared by Patrick Chevalley's excellent Cartes du Ciel sky mapping software. We have adjusted the time slightly because the model calculations, indicate that the star would have actually emerged from the Moon's dark limb about an hour after Whitaker's time: at about 5:45 UT (5:44 UT calculated using the JPL Horizons ephemeris with a perhaps slightly more accurate estimate of the star's position in 1609). We show it here 5 minutes later (during occultations, the Moon sweeps across the stars from right to left, in the diagram, so they disappear on the left, and reappear on the right). Although Cartes du Ciel quite accurately portrays the position of the star relative to the Moon, the indicated positions of the lunar features, and of the terminator relative to them, are a little misleading. Perhaps not surprisingly, the lunar librations are shown essentially the same as in the Virtual Moon Atlas, of which Chevalley is co-author. We show to the right a more accurate plot of the expected positions of the lunar features and terminator prepared, based upon the JPL data, using our own terminator prediction program.

Drawing F7 Predicted Positions of Moon and Star Jan. 19; 5:50 UT Predicted Lunar Terminator Jan. 19; 5:50 UT
![Star and Moon Prediction by Cartes du Ciel](/web/20070601182754im_/http://www.pacifier.com/~tpope/Moon_Drawings/F7_cropped.jpg "Star and Moon prediction by Cartes du Ciel") ![Star and Moon Prediction by Cartes du Ciel](/web/20070601182754im_/http://www.pacifier.com/~tpope/Moon_Drawings/Cartes-1610_01_19-05-50.jpg "Star and Moon prediction by Cartes du Ciel") ![Terminator Prediction](/web/20070601182754im_/http://www.pacifier.com/~tpope/Moon_Drawings/Terminator-1610_01_19-05-50.jpg "More accurate terminator prediction")
Adapted from image © BNCF Prediction by Cartes du Ciel Correct position of terminator

Although the time at which the star emerges is about an hour later than the time originally assigned to this drawing by Whitaker, the agreement between the predictions and the watercolor is quite amazing. Since the probability of finding a prominent star in the correct position at exactly the right phase of the Moon is quite rare, we agree that this result reinforces Whitaker's conclusion that the mark on the page does indeed indicate the presence of a star, and it represents an observation on January 19, 1609. Since the watercolors must have taken some time to complete, they cannot truly represent this exact moment, but must be based on observations some time before and/or after the event. The Sun rose at around 6:45 UT on January 19, so there would have been relatively little time to finish the painting after the event, put it certainly would have been possible.

Whitaker's ability to date this drawing to within two hours of the occultation (with no prior knowledge of when the occultation was expected to have taken place) is all the more remarkable given the huge apparent inaccuracies in how the grosser features of the Moon are drawn. Like all his other dates, Whitaker determined this one by identifying detailed features that he believes are visible along the terminator. Whitaker claims to be able to recognize seven features depicted along the terminator in this drawing. These include: the shadow of the Montes Juras (accounting for the prominent oversized-crescent shown in relief about three times larger than life near the top), Promontorium Laplace (accounting for the bright dot at the end of the arc), "Tobias Mayer and Gamma" (accounting for the detached point of light shown as a little above the center), and the two features labeled here (following Whitaker) as P and Q, which are explained as Palus Epidemiarum (P) and "Capuanus P and the low area to the south-west" (Q). In addition, he tells us that that the first bright projection from the limb above "P" is caused by Montes Riphaeus, and that the little dark blob at 8 o'clock from "Q" (and about halfway to the limb) represents the shadow in the crater Hainzel. He also shows an undated and purposely degraded comparison photo (a somewhat larger and better copy of which may be found in his 1999 book). The photo does indeed show features that might possibly correspond to all of these. However Whitaker offers no explanation, for example, for the prominent dark spot shown near the limb to the left of "P", nor for the two prominent detached patches of light shown near the southern cusp of the lunar crescent. The photo gives no hint of what might cause the two point of lights, but it does suggest that the dark spot near the limb might have been inspired by the crater Grimaldi. The dark floor of Grimaldi is one of the most prominent features of the waning crescent Moon, and Galileo later specifically mentioned it as a feature which could be used (in addition to the "ancient spot" of Mare Crisium on the opposite limb) to study the left-right rocking of the Moon. The problem is that Grimaldi is far above "P", and not below it as the drawing seems to show. So it seems fair to say that the drawing shows a number of features, just as prominent as any pointed to by Whitaker, that cannot be accounted for by the photo. Similarly, if we ask what are the most prominent features in the photo, many of these have no obvious counterpart in the drawing. For example, Whitaker's photo shows a good deal of variable terrain between Palus Epidemiarium and Montes Riphaeus, including the dark Mare Humorum, the crater Agartharchides with a prominent bright peak and the huge crater Gassendi, none of which seems to depicted in the drawing. Similarly, the photo shows the crater Kepler as a very prominent feature about 45° south-west of Tobias Mayer. It is seen as a prominent bright patch in the photo with the crater forming a dark pimple in its center. There is no obvious indication of this in the drawing. More importantly, Whitaker makes no attempt to identify the mare so prominently shown in the dark portion of the drawing (the part of the Moon lit by earthshine is not visible in his photo). They show no correspondence to their expected positions on January 19, 1610, or on any other date, being rotated far to the north or their normal positions. That is, if we take the dark oval closest to the limb to be Mare Crisium, it needs to be rotated 20 or 30° to the south. It is almost as if these features had been sketched in later, perhaps from an observation of the Full Moon, using the misplaced crater Grimaldi (which should have been at 9 o'clock on January 19) as a guide. As with every other comparison shown by Whitaker these many discrepancies make one wonder if the supposed identifications are really correct.

We will demonstrate below that if drawing F7 is indeed a snapshot of the Moon at the time of the reappearance of Theta Librae on January 19th, then the features Whitaker claims to have used to arrive at this date are incorrect: it does not seem they would have appeared as shown in the drawing at the time of the occultation. In particular, Whitaker says that the crater Capuanus and the wall around the tiny sea ("marsh") called Palus Epidemiarum account for the prominent bow-like arc of light extending out from the terminator towards the bottom of the engraving. In fact it appears to us that there are other features, farther to the east, that could have accounted for this appearance at 5:50 UT (the estimated time of the drawing if it represents this occultation). The features mentioned by Whitaker would have been in full sunlight during the occultation, and not had the appearance Whitaker ascribes to them until well after sunrise in Padua. Since he seems to have got the right date, this may seem like an extreme case of nit-picking, but we do not feel so. If the dots of light shown along the terminator in the other images are not the features Whitaker believes them to be, then the whole enterprise of deriving precise dates based on them is highly questionable.

As previously mentioned, Whitaker obtained his estimated time of 4:00 UT for this drawing, in part, by guessing that the bright B-shaped protuberance from the terminator, represents Palus Epidemiarum (P) and the crater "Capuanus P and low area to the south-west" (Q). To determine whether this is a plausible explanation of why a B-shaped arc is shown in the drawing, we generated a prediction of where the lunar terminator would have been at the moment Theta Librae emerged from the Moon's east limb, and then searched the internet for pictures taken when the terminator was at a similar position. The closest we could find was a fine photograph of this region taken by German amateur Peter C. Slansky at 3:46 UT on August 29, 2005. As shown in the center panel, the lunar terminator at that moment was predicted to be almost exactly where it was predicted to be at the moment of the occultation in 1610. Therefore Slansky's photo should show this portion of the terminator almost exactly as it would have appeared to an observer at 5:50 UT on January 19, 1610. We have altered the gamma of the original photograph to make the position of the terminator more apparent. We also show a standard photo of the terminator taken from the Lunar and Planetary Institute's on-line Consolidated Lunar Atlas. The red line of the predicted terminator corresponding to the time of this photo is tangent to the extreme east walls of the two moderately large craters it is approaching in the examples shown -- Capuanus (below) and Mercator (above). This corresponds to the predicted lighting situation on January 19, 1609 at about 7:00 UT. That is Slansky's photo shows the Moon as it would have appeared and the moment the star emerged from occultation, and the Consolidated Lunar Atlas photo shows it as it would have appeared about an hour later, just as the Sun was rising in Padua on that morning.

Predicted Lunar Terminator Jan. 19, 1610; 5:50 UT Predicted Lunar Terminator Aug. 29, 2005; 3:46 UT Photograph Aug. 29, 2005; 3:46 UT Photograph Jul. 12, 1966; 11:37 UT
![Lunar Terminator in Capuanus Region; Jan. 19, 1610](/web/20070601182754im_/http://www.pacifier.com/~tpope/Moon_Drawings/Capuanus_1610_1_19-5_50.jpg "Lunar Terminator in Capuanus Region; Jan. 19, 1610") ![Lunar Terminator in Capuanus Region; Aug. 29, 2005](/web/20070601182754im_/http://www.pacifier.com/~tpope/Moon_Drawings/Capuanus_2005_8_29-3_46.jpg "Lunar Terminator in Capuanus Region; Aug. 29, 2005") ![Photo of Capuanus Region by Peter C. Slansky; Aug. 29, 2005](/web/20070601182754im_/http://www.pacifier.com/~tpope/Moon_Drawings/Slansky_Capuanus.jpg "Photo of Capuanus Region by Peter C. Slansky; Aug. 29, 2005") ![Photo of Capuanus Region in Consolidated Lunar Atlas; Jul. 12, 1966](/web/20070601182754im_/http://www.pacifier.com/~tpope/Moon_Drawings/CLA_F22.jpg "Photo of Capuanus Region in Consolidated Lunar Atlas; Jul. 12, 1966")
    Adapted from [image](https://web.archive.org/web/20070601182754/http://www.lrz-muenchen.de/~slansky/bereiche/astronomie/mond/mondkrater/mondkrater_capuanus_29-08-2005_05-46.html "Open webpage containing this image in a new window") © Peter C. Slansky Adapted from image [F22](https://web.archive.org/web/20070601182754/http://www.lpi.usra.edu/resources/cla/info/f22/ "Open Consolidated Lunar Atlas image F22 webpage in a new window") in Consolidated Lunar Atlas © LPI

It would appear that Whitaker may have been using a slightly incorrect lunar ephemeris. Palus Epidemiarum is the large flat plain in which we have placed the letter "A" in the last two images. Capuanus is the large crater below the middle of the plain, with tendrils extending up towards the "A". The twin craters at the top edge of the plain are Campanus (top) and Mercator (bottom). The region Whitaker is referring to as "Capuanus P and low area to the south-west" is the long flattened valley to the lower left of Capuanus. The photograph Whitaker reproduces in his article, and which he says corresponds to Galileo's drawing, seems to show the terminator considerably more to the left, casting this valley into shadow and leaving the west wall of Capuanus as a prominent bright feature beyond the terminator. The floor of Palus Epidemiarum also seems to be in shadow in Whitaker's photograph making the craters above the "A" visible beyond the terminator (as previously indicated, these things are hard to confirm because Whitaker's published photographs are small, undated, purposely de-focused and printed rather dark). Indeed, Whitaker seems to be indicating that the terminator in his photo is about midway between Capuanus and Hainzel (a crater that is outside the present images -- just below the line of three tiny craters in the lower left), since he implies Hainzel is deeply shadowed with Capuanus visible as a dot beyond the terminator. Such a photograph corresponds to a solar colongitude of about 210 degrees, and to a time more like 17:00 UT on January 19, 1610: that is, the following evening when the Moon would have been far below the horizon in Padua. Why he is showing a photo at a colongitude so different from the one he associates with the drawing is unclear to us. Whitaker seems to be claiming that the features he labels "P" and "Q" on Galileo's drawing are produced by the west walls of the craters Campanus, Mercator and Capuanus being lit by sunlight as they lie slightly beyond the terminator. In Slansky's photo, which much more accurately represents how the terminator would have looked as the star emerged from occultation, these features are still fully bathed in sunlight; and, as shown by the Consolidated Lunar Atlas photo, they would still have appeared attached to the bright crescent of the Moon even an hour later at sunrise. An artist trying to depict the bright points visible beyond the terminator at the time of the occultation would more likely have been inspired by the features we have labeled "B" and "C" in Slansky's photo. Feature "B" is produced by the west wall of the crater Kies and the tiny crater, Kies A, below it. Feature "C" is the west wall of the crater Cichus and the ridge extending out of it to the northwest. Since Slansky's photograph covers only one very small piece of the terminator, we have no idea if "B" and "C" actually have anything to do with the features Whitaker labeled "P" and "Q" on Galileo's drawing F7, but they seem as plausible of possibilities to us as the ones offered by Whitaker. Another possibility is that the artist was wanting to create an impression of the brightness of the west walls of Capuanus and the two craters above the "A" (Campanus and Mercator). To do so, he may have artificially darkened the area to their left, making them appear detached from the terminator. So they might actually be quite similar to the features supposed by Whitaker, but it seems Whitaker obtained his date by comparing Galileo's drawing to the features visible in a photograph taken when the terminator was in quite a different position. Whether this was a result of skill and experience, or pure chance, is left to the reader to decide.

The Identity of the Large Crater

Prior to 1975 it would be fair to say that the most controversial question related to Galileo's lunar images was the identity of the huge crater shown straddling the terminator in his engravings E2 and E4. Zdenĕk Kopal (1969), to take a somewhat random example, guessed (with no great confidence) that it might have been inspired by the large central crater Ptolemaeus. But it is safe to assume that nearly every other large crater had been suggested by someone at some time.

At the Capri Conference where he first presented his pioneering effort to date the engravings, Guglielmo Righini suggested, with great conviction, that it represented not a single crater, but rather a broader region composed of the craters Purbach, Regiomontanus, Werner, Blanchnius and Lacaille; assuring his audience that is area of the Moon is actually a great depressed bowl, looking much as Galileo drew it. We assume there was some basis for this assertion, but we have been completely unable to find any photo supporting Righini's contention.

At the same meeting, in his rebuttal to Righini's dating effort, Owen Gingerich declared that it was most likely a somewhat exaggerated image of the single crater Albategnius. Three years later Ewen Whitaker said he agreed with Gingerich; and since then this identification seems to have been taken as a matter of settled fact.

Gingerich's initial conjecture was based on having looked at two photographs of the First and Last Quarter Moons taken at the Lick Observatory, both of which showed Albategnius on the terminator. One of them is shown on our page describing Claude Mellan's engravings of the Moon. We do not know if Gingerich, being more of a historian than an astronomer, had the impression that Albategnius is always on the terminator at First and Last Quarter. Due to the Moon's librations in longitude, this is, of course, not at all the case.

However that may be, Albategnius is indeed impressive when the phase is just right. But it is not perfectly round (there is a substantial crater in its southwest corner), it is not unusually large, and its bowl-like shape is not self-evident before and after Full Moon (all characteristics which Galileo attributed to the crater that he said reminded him of what the country of Bohemia must look like as viewed from above). More importantly, the fact that the Lick Observatory was able to photograph Albategnius prominent on the terminator does not in any way insure that Galileo would have had an opportunity to witness a similar phase from Padua or Venice in the few short months leading up to his publication of Sidereus Nuncius.

The sun rises over the lunar crater Albategnius only when the sun is at a definite altitude. Comparison of our terminator predictions with carefully timed modern photographs suggests that the peaks of the west wall first become visible when the sun reaches a colongitude of approximately 356.5° (more precisely, when the red line of the predicted terminator reaches the small central peak of the crater). The floor gradually becomes illuminated reaching a phase similar to that depicted for the "Bohemia" crater in Galileo's E2 (i.e., about 3/4 light and 1/4 dark) when the sun's colongitude gets to about 358.5° (more precisely, when the middle of the predicted terminator is roughly over, or very slightly past, the west wall Klein, the prominent crater within a crater in the southwest quadrant of Albategnius). For Albategnius, the entire process from the first visibility of the western wall to the stage depicted in Galileo's engraving takes about four hours.

This sequence of events happens every month, and, in theory, the entire four hour sequence should be visible from somewhere on Earth. However, the chance of seeing it from any particular place is not great. First, there is only a 50-50 chance that the Moon will be above the horizon at the moment of sunrise over Albategnius. Second, in roughly half those cases, the Sun will also be above the horizon, making the observation difficult or impossible. We are left with about a 1 in 4 chance of being able to see the sunrise, and the chance of being able to see the entire four hour sequence is even less. Finally, even in Italy clouds will interfere with some of those chances.

The following table lists the circumstances of the Moon and Sun, as seen from Padua, during each sunrise over Albategnius between August 1609 through March 1610. For each four-hour window of opportunity, listed in universal time, the elevation of the Moon and Sun above (+) or below (-) the horizon are given at the start and end of the four hour sunrise sequence. Only on the evening of January 31, 1610 was the Sun below the horizon and the Moon relatively high in the sky for the entire period. The only prior opportunity Galileo had to see the complete sequence was on December 3, 1609. However, at the start of the sequence, as the Sun began lighting the peaks of Albategnius' west wall, the Moon would have been just rising above the horizon with a Sun still up nearly twenty degrees in the sky. Under such circumstances, the sunrise, if visible at all, does not seem likely to have created a very vivid impression.

**Times of Sunrise Over Albategnius**
Elevation (deg)
Event Date Time (UT) Moon Sun
Start Aug. 7, 1609 08:30 -32 +45
End Aug. 7, 1609 12:30 +8 +57
Start Sep. 5, 1609 20:30 +6.5 -27
End Sep. 6, 1609 00:30 -32 -35
Start Oct. 5, 1609 09:00 -31 +33
End Oct. 5, 1609 13:00 +6 +33
Start Nov. 3, 1609 22:30 -15 -59
End Nov. 4, 1609 02:30 -54 -36
Start Dec. 3, 1609 12:30 +7 +19
End Dec. 3, 1609 16:30 +30 -10
Start Jan. 2, 1610 02:30 -40 -45
End Jan. 2, 1610 06:30 -43 -4
Start Jan. 31, 1610 17:00 +52 -8
End Jan. 31, 1610 21:00 +26 -48
Start Mar. 2, 1610 06:30 -24 +6
End Mar. 2, 1610 10:30 +6 +36

Weather permitting, there was an excellent opportunity to see the sunrise sequence over Albategnius from Padua on January 31, 1610, and it is conceivable he is referring to that observation in Sidereus Nuncius. However, Galileo already refers to having been impressed by an observation of sunrise over his Bohemia-like crater is his letter of January 7, 1610 it seems unlikely he could have been referring to Albategnius at that time. Another thing arguing against Albategnius is that in his letter Galileo mentions how the bowl-like shape of his Bohemia crater is evident from the pattern of shadows on it both before and after the Full Moon. Albategnius, even though it is exceptionally prominent for two brief intervals each month (when the terminator sweeps over it), is nearly invisible at the other phases. An large isolated crater like Copernicus would more plausibly be detectable and distinctly bowl-shaped throughout the lunar cycle. It seems quite possible that Galileo, in his early observations, may have seen different large craters at different phases of the lunar cycle that thought they were the same crater. Galileo obviously had no lunar atlas to guide him. He had to rely solely on his memory and whatever sketches he may have made to correlate what he was currently seeing with what he may have seen before.

Summary

In this section we bring together the opinions of the professionals about the four distinct engravings in Sidereus Nuncius, and our comments on them.

Engraving E1

Galileo's Moon Engraving E1

Ernest Cherrington (1968) believes this is a picture of the waning crescent Moon. He presumably suspects the printer either inverted it from left to right, or rotated it 180°.
Guglielmo Righini (1975) takes it to be an accurate representation of the waxing crescent Moon, as seen from Padua shortly after sunset on October 2, 1609 (sunset = 16:38 UT by Righini's calculation). He believes it represents Galileo's first observation of the Moon. He identifies a number of features. The one he is most certain about is the dark knob shown in the middle of the bright crescent at about 2 o'clock. This he takes to be Mare Crisium. The patch of light in the dark gulf at 5 o'clock is, he says, the craters Baco, Breislak, Clairaut and Cuvier; while the promontory above it, near 4 o'clock, is the "Continental Massif centered on the crater Rabbi Levi." The promontory a little above 3 o'clock is identified as the craters Capella and Isidorus; while the isolated dot of light between 1 and 2 o'clock is, he says, the crater Posidonius. Righini offers no photograph taken under similar lighting conditions to confirm his identifications. As an historical confirmation of Galileo's astronomical activities at this time, he offers a letter by Galileo to Belisaro Vinta, dated October 30, 1609. In the letter, Galileo is sending an Ephemeris to the recipient, saying he did not need it "being for some time already busy with other studies." Righini concludes the "other studies" could be none other than Galileo's telescopic observations of celestial bodies (we find this conclusion to be peculiarly illogical). Based on modern ephemeris calculations we are reasonably confident that Righini's lunar identifications are incorrect: none of the craters he mentions would have been visible from Padua on October 2. Moreover, his method of using the age of the Moon at sunset to select this date in preference to the other candidate dates seems flawed since the thickness of the crescent (which he measured) is only loosely correlated to the age.
Owen Gingerich (1975) questioned whether the width of the crescent shown in E1 defines the age as accurately as Righini claimed (±2 hours), and pointed out that a virtually identical age of the Moon at sunset would have occurred on January 29, 1610 (a date Righini did not consider). Gingerich was apparently, like Righini, unaware that the age of the Moon is a poor predictor of the width of the crescent, and, therefore, offered little reason to prefer one day over another.
Stillman Drake (1976), relying on the astronomical calculations of Righini and Gingerich, believes that the events Galileo described in connection with this engraving were observed by him on December 1, 1609; but that the engraving itself is based on a observation made on January 29, 1610. Drake believes that Galileo would not have had a sufficiently powerful telescope on October 2. Drake cites a letter dated December 4, announcing that Galileo would be in Florence the following summer "with some improvement in my spyglass and perhaps some other invention [the word, Drake says, could also be translated 'discovery']," as a historical indication that Galileo had commenced his astronomical observations by that date. Again, this seems something of an interpretive stretch to us.
Galileo's Moon Drawing F2 Drake believes that December 1 was Galileo's first ever look at the Moon. On that evening, according to Drake, he produced the wash drawings that Whitaker later labeled F1 and F2 (reproduced at left), but that they were too inaccurate to be used for making an engraving. We ourselves can see no difference in the apparent quality of these two drawings versus the others. We might also note that we can find no evidence of an immense dark gulf containing a triangular peak in either F1 and F2; and that from the phases depicted in them (the position of the terminator relative to both the limb and the dark mare), they appear to have been made on different nights. The position of the terminator at sunset of January 29 would have been quite different from that on October 2, but it still does not seem to match Righini's descriptions of the craters he claimed to have identified.
Ewen Whitaker (1978) believed that based on his identification of the features depicted along the terminator, and a check of the dates on which the terminator passing over those features would have been visible from Padua, the only possible date for this engraving is November 30, 1609. Whitaker also believes that this engraving depicts Galileo's first ever look at the Moon, and that wash drawings F1 and F2 are based on observations made on the same evening. In fact, he thinks E1 and F2 are so similar that they were "copied from the same original" (now lost). With all due respect to one of the world's greatest selenographers, if E1 and F2 are copied from the same original, the person(s) who copied them did not seem to have done much of a job. Other than as general depictions of a waxing crescent Moon, we can see absolutely no correspondence between the features depicted in the two images. The lunar features which Whitaker says he is able to identify in engraving E1 include the crater Atlas (creating the promontory at 1 o'clock), the crater Lyell (creating the bright region along the terminator just below the sea at 2 o'clock), the crater Lubbock Beta (responsible for the dot of light off the terminator at 3 o'clock), the crater Guttenberg (the promontory just below that, also at 3 o'clock), the mountains east of the crater Weinek (giving rise to the point of light above the pointed promontory between 4 and 5 o'clock), the scarp north of Neander (giving rise to the promontory itself), and the west wall of the crater Fabricius plus the surrounding area in the center of the crater Janssen (producing the triangle of light off the terminator at 5 o'clock). The three points of light surrounding the peak are identified as the southwest wall of Janssen and the west walls of the craters Brenner and Metius. Although these identifications sound very authoritative, Whitaker fails to indicate the corresponding features in drawing F2, even though he says it was copied from the same observation. He does offer an undated and purposely degraded photograph which he says (without proof) was taken under lighting conditions similar to those which would have prevailed at 18-20 UT on November 30, 1609 (the date and time he assigns to F2 and E1). Personally, we can see no correlation between the photo and the engraving. However Whitaker cautions that "smaller and more subtle" correspondences will probably be lost by reduction and printing (one wonders why he himself degraded them beforehand...). As an example of a major lack of correspondence not affected by the degradations, the area from about 2 to 3 o'clock, spanning what Whitaker says is Atlas at the top and Lyell at the bottom, is depicted as smooth mare in Galileo's engraving, yet it appears heavily cratered in Whitaker's photo. If Whitaker has identified these two endpoints correctly, it is hard to imagine how Galileo could have failed to see craters between them. Moreover, our attempts to recreate the lighting pattern on November 30, 1609 at 15-19 UT (sunset to moonset) make it seem unlikely that the craters around Janssen mentioned by Whitaker would have looked as they do in Galileo's engraving.
Gingerich and Albert Van Helden (2003) accept Whitaker's dating of this engraving to November 30, 1609 as "definitive," but they differ in two respects. First, they suspect Galileo had observed the Moon previously, possibly making rough sketches, now lost. Second, they believe the wash drawings were made directly at the telescope and that all the engravings appearing in Sidereus Nuncius were copied from, or at least, based on them. We are not sure if they think E1 was "copied" from F1 or F2. In either case, E1 would be a very poor copy, and we can find no evidence to suggest that 17th century engravers were such poor copyists. On the contrary, a comparison of the plates appearing in various editions (authorized and unauthorized) of Sidereus Nuncius suggests that they copied both the shape and location of features along the terminator with considerable accuracy. We find it very hard to believe that an engraver given F2 (or F1) would have produced E1.

Engraving E2

Galileo's Moon Engraving E2

Cherrington (1968), looking at a somewhat degraded re-copy of this engraving appearing in a later printing of Sidereus Nuncius believes it was derived from an observation of the Last Quarter Moon by inverting it left-to-right. He suspects this is a printer's error, and that it was intended to be shown the other way round. It is difficult to reconcile this interpretation with the engraving's context in Galileo's text.
Righini (1975) takes engraving E2 to be an accurate representation of the Moon as it appeared from Padua on the evening of December 3, 1609. Righini reached this conclusion based on his belief that it must have been made after E1; and an examination of the position of the large circular feature shown on the terminator in E1 compared to its position in E4. Righini assumes that both these circles represent a depression in the Moon's southern continental massif caused by the craters Purbach, Regiomontanus, Werner, Blanchnius and Lacaille. He attributes the fact that it is shown lower in E1 and higher in E4 to be a reflection of the Moon's libration in latitude. The difference, he says, is close to that expected between the First Quarter Moon on December 3 versus the Last Quarter Moon on December 18. Righini offers no photographic proof that his five large craters could ever be mistaken for the smooth, perfectly circular bowl-shaped object so lovingly described by Galileo in his text. We are similarly unable to find any indication of that.
Owen Gingerich (1975), based on looking at photographs of the First and Last Quarter Moons from a great distance, determined that the large circular feature must represent the crater Albategnius. He feels that its over-sized representation in the engravings is more symbolic than factual and that its position is not necessarily shown with any precision. He therefore thinks that the differences in its vertical position in E2 versus E4 is not necessarily an indication of the real difference in observed positions.
Galileo's Drawing F4 On the other hand, Gingerich thought he noticed a distinct similarity between E2 and wash drawing F4 (shown at left). In particular he sees "a very close correlation between features on [the] terminator." We personally see many more discrepancies than matches, and we are also unable to agree with Gingerich's assessment that "the dark maria are reasonably represented on the manuscript drawing, but bear only a grotesque approximation to reality in the printed drawing." However that may be, Gingerich feels that E2 was created by adjusting the terminator of F4 so that it would fall in the center of the Moon, then adding a symbolic image of Albategnius. Gingerich did not attempt to assign a date to drawing F4, from which he believes E2 was derived.
Drake (1976) seems to accept Righini's dating of engraving E2 to December 3, 1609, but says it is based on a drawing made that night. Whether he means one of the surviving drawings or a drawing now lost is unclear. Since he had just read the papers by Righini and Gingerich one might assume he is referring to Gingerich's theory that E2 is based on F4, but F4 represents a phase quite different from that which would have been seen on December 3. Drake expresses no opinion about whether he thinks Galileo's Bohemia-like crater was Albategnius, Righini's group of craters, or something else.
Whitaker (1978) accepts Gingerich's theory that the large crater is Albategnius, but rejects his theory that the remainder of the drawing on which it was based is derived from drawing F4. Whitaker believes instead that E2 is based on an observation for which no other drawing survives. Based on his identification of features depicted along the terminator, and a check of the dates on which the terminator passing over those features would have been visible from Padua, he says the only possible date for this engraving is December 3, 1609 at 16 UT (±1 hour). In addition to Albategnius, he claims to have identified five other prominent features. The detached patch of light at the north pole he says is the west wall of the crater Barrow; the detached point of light between the crab-like pincers is "Caucasus Beta, etc."; the dot below the lower pincer is "Manilius, etc."; the bright point off the pointed promontory in the center is Dembowki and Triesnecker; while the little round dot off the terminator midway between Albategnius and the south pole is Heraclitus. Whitaker offers an again undated and purposely degraded photograph which he says shows each of these features along the terminator as depicted in E2. The features visible in the printed photograph bear only a very faint resemblance to those shown in the engraving, and since the date is not given, it is impossible to verify that the lighting conditions correspond to those expected on December 3, 1609 at about 16 UT. The biggest problem, which we suspect must have bothered Whitaker, is that in his photo the circular mare corresponding to the one Galileo shows straddling the terminator is Mare Serenitatis, and the terminator in the photograph appears to pass more or less through what Whitaker calls "Caucasus Beta" -- the feature corresponding to the bright point between the pincers in Galileo's engraving. Whitaker's photograph offers no plausible explanation of why Galileo would have shown the terminator squarely down the middle of Mare Serenitatis. Indeed Whitaker's photograph seems to demonstrate that it would be impossible to see any of the other features when the terminator is at that position.
Predicted Terminator for Dec. 3, 1609 at 16 UT Our own calculation (shown at left), based on the current JPL lunar ephemeris is that at 16 UT on December 3 the terminator would have passed through the craters Aristillus and Autolycus, far to the left of Whitaker's Caucasus range, and Mare Serenitatis would have been fully bathed in light. In addition it is well to the left of the point at which, according to the lunar atlases, one is likely something like pincers with a dot of light between them. In addition, the terminator would have been distinctly curved to the right at this early hour of the evening. The terminator would have passed through the middle of Mare Serenitatis some 35 hours earlier, at about 5 UT on December 2, but not only would none of the features mentioned by Whitaker have been visible at that time, the Moon itself was not visible from Padua at that hour. We can readily accept the notion that Galileo would have cleaned up his observation by asking the engraver to make the terminator appear straighter than it actually was, but given the totally different lighting around Mare Serenitatis, we find it very hard to accept Whitaker's contention that E2 is a qualitatively accurate but geometrically distorted representation of how the Moon looked on his stated date.
Gingerich and Van Helden (2003) also rejected Whitaker's date for engraving E2, and maintain Gingerich's 1975 theory that it is derived from drawing F4 with an over-sized image of Albategnius added to the terminator for dramatic effect. Since Whitaker dated F4 to the evening of December 2, 1609 at 16 UT, this is the date they take for E2 (with the exception of the Albategnius "inset," which could not have been observed on that date). Our opinion is that even with "Albategnius" removed, it is not at all clear that this is a plausible picture of the Moon as it would have appeared on December 2. That is, we do not know what lunar features visible that night might have given rise to the dots shown along the terminator in either E2 or F4.

Engraving E3

Galileo's Moon Engraving E3

This engraving is actually the fourth lunar plate in the original edition of Sidereus Nuncius. It is designated E3 because Whitaker numbered them according to the sequence in which he thought the observations were made, and he thought E3 (the fourth plate) was based on an observation before E4 (the third plate).
Cherrington (1968) evidently believed this engraving had also been inverted left-right by the printer, for he identifies the prominent "spot" on the upper terminator as Mare Imbrium, but identifies the ring around it as the Alps, Caucasus and Apennine Mountain ranges, bounding it on the east. If the engraving is inverted in this way, it becomes a view of the Moon slightly after the First Quarter (rather than before the Last Quarter as it appears here). In this inverted world, Cherrington finds possible hints of indentations along the terminator caused by the shadowed floors of the large craters Plato, Clavius and Maginus.
Righini (1975) took this to be a properly printed image of the Moon a little before the Last Quarter. According to Righini "many features on this drawing are easily recognizable." Among these, he says are the craters "Maurilius" (apparently a misprint for Manilius) and Apianus. "Maurilius," he says accounts for the dot of light shown off the tip of the southern cusp of the ring of mountains around the mare; while Apianus is represented by the last, and brightest, of the dots shown off the terminator a little below center. From the deviation of these two points from their standard selenographic positions Righini deduced the libration in latitude. Without disclosing the exact answer, he tells us it is consistent with the librations that would have been present slightly before the Last Quarter of December 18, 1609. Since December 18 is already the date he had assigned to E4, he presumably thought that engraving E3 is based on an observation made a day or so before that. Our calculations with the JPL lunar ephemeris suggest than Manilius and Apianus would still have been parts of the illuminated half of the Moon on December 17, and not become separated points of light until long after that.
Galileo's Moon Drawing F5 Gingerich (1975) questioned whether Righini's estimate of the libration depicted in E3 could be at all accurate, noting that "the rather ambiguous features measured by Professor Righini in [E3] appear in quite different positions on the manuscript drawing [F5, reproduced at left], thus shattering any confidence in their reliability for quantitative argument." Gingerich evidently thinks that a similar set of bright points is shown in both images, but that there positions are unreliable. Our opinion is that although there is a certain similarity between the two images, when examined in detail, the patterns shown along the terminator, both on the lighted and on the dark side, are so different they may not even be depicting the same features at all. We again find it hard to believe that a competent engraver given F5 would have produced E3, or that they can be thought of as two different renderings of some now lost original. For example, to the lower left of the mare on the upper terminator, the engraving shows a bright highlands where the drawing shows a smaller dark mare. Similarly, the F5 shows a distinct fan-shaped wedge of craters extending out from the center between 6 and 7 o'clock. This feature is not at all clear in the engraving, which instead shows the craters clustered in an arc near the center.
Drake (1976), as near as we can tell, makes no reference to engraving E3.
Whitaker (1978) believed that based on his identification of the features depicted along the terminator, and a check of the dates on which the terminator passing over those features would have been visible from Padua, the only possible date for this engraving is December 17, 1609 at about 4 UT. Among the features he says he could identify are Aristoteles, responsible for the small projection in the terminator halfway between the upper cusp of the ring of mountains and the Moon's north pole; Eudoxus, responsible for the bright point at the eastern tip of the upper end of the ring; Promontorium Archerusia, responsible for the detached bright point opposite the lower tip of the ring; the Kant-Zöllner plateau, producing the upper bar of the E-shaped indentation in the terminator just below the Moon's center (and/or the tiny dot of light just beyond it in the Moon's dark half); and the east wall of the crater Maurolycus producing a feature we are unable to identify with certainty in Whitaker's reproductions, although he puts his label next to the second outward pointing prominence in the terminator, one-sixth of the way up from the bottom, where it bends from a slanting to a more vertical direction (he possibly means that the feature forming this corner is the crater Maurolycus, with its east wall on the terminator). Again, Whitaker offers an undated photograph which he says corresponds to this view. In the photo, Mare Serenitatis is vaguely visible on the upper terminator, but it is impossible to perceive what would have inspired Galileo to draw the boldly accented ring of mountains. We find it quite possible that the photo is poorly printed and/or that Galileo may have exaggerated the contrast of a feature that caught his fancy, but we are, unfortunately also unable to detect any of the other correspondences that Whitaker alludes to. It should also be noted that in the text of Sidereus Nuncius Galileo very clearly indicates that E3 and E4 represent two views of the same large northern "spot," yet, as we will see, in his photo comparisons Whitaker clearly identifies the large northern spot in E4 as being Mare Imbrium, a feature completely different from and much larger than Mare Serenitatis. Finally E3 and F5 form one of those pairs of images which Whitaker says are so strikingly similar they must have been copied from the same now-lost sketch of the same original observation. Although E3 and F5 look slightly more similar to us than E1 and F2, we find it ironic that Gingerich called particular attention to how different they are; and that Gingerich can see a similarity between E2 and F4, where Whitaker cannot. As usual Whitaker fails to point the features in drawing F5 that he thinks correspond to the features he has "identified" in engraving E3. The relationship is not at all obvious to us. In nearly every case there are multiple possibilities in the drawing that might correspond to the features Whitaker highlights in the engraving.
Gingerich and Van Helden (2003) make no particular comment about this engraving so they presumably accept Whitaker's dating of it to December 17, and its association with drawing F5. However, since Gingerich finds the placement of the dots on E3 quite different from those in F5 he evidently feels it is a rather inaccurate copy.

Engraving E4

Galileo's Moon Engraving E4

This engraving is actually the third lunar plate in the original edition of Sidereus Nuncius, and was also used as the fifth lunar plate. It is designated E4 because Whitaker feels it is based on an observation made after E3 (the fourth plate).
Cherrington (1968) examined an early reprint of Sidereus Nuncius in which a copy of this engraving was rotated 180° (printed "upside down"). Cherrington recognized it as a misprinted image of the Last Quarter Moon.
Righini (1975) also took this to be an image of the Last Quarter Moon, and dated it to the morning of December 18, 1609 based on the libration argument previously mentioned in connection with engraving E2 (the First Quarter Moon). He takes the oversized circular crater shown on the terminator to depict the same group of five craters as in E2. Again, we can find no evidence that they would ever look this way.
Gingerich (1975), as previously mentioned, rejected Righini's belief that the libration in latitude was shown accurately enough to permit dating of the engravings. He made no further comment about this engraving other than to print a copy of it and invite the reader to compare it to E3. He did not elaborate on what the reader was expected to see in the comparison. Gingerich did not reproduce wash drawing F6, which looks similar to E4. Nor do we know if Gingerich thought this was a "live" image of Albategnius, or if as he believes was done with E2, a symbolic image of this crater that "loomed large in Galileo's mind" was arbitrarily added "in disproportionate size to convey his wonder."
Galileo's Moon Drawing F6 Drake (1976), accepts Righini's date of December 18, 1609 for E4, and goes on to suggest that it is based on a drawing made that morning, presumably referring to F6 (reproduced at left).
Whitaker (1978) believed that based on his identification of the features depicted along the terminator, and a check of the dates on which the terminator passing over those features would have been visible from Padua, the only possible date for this engraving is December 18, 1609 at about 4 UT. Among the features he says he could identify are the east wall of Goldschmidt (causing the small projection in the terminator close to the north pole), the north wall of the crater Hipparchus (causing the first projection in the terminator above "Albategnius"), the hills near the crater Ukert (causing the projection above that), and Albategnius itself (the large circular crater). Whitaker does not identify the source of the prominent dot of light between Hipparchus and the Ukert hills. As usual Whitaker does not indicate what he believes to be the corresponding features in the drawing (F6), even though this is another of the pairs he says are so similar they must be different representations of the same observation. We can only guess that since the drawing shows, slightly below the Moon's center, a little crescent composed of four small craters with a dot of light to their right that this must be the feature Whitaker believes corresponds, in the engraving, to the little crescent along the terminator from the "Ukert hills" to "Hipparchus" (with a similar dot of light to its right). If this is correct, then, judging from the engraving, the feature corresponding to Albategnius in drawing would have to be the first of the several large dark blobs shown below the crescent of craters. Now, Whitaker's own (degraded) comparison photo shows a similar chain of small craters consisting of Ptolemaeus, Alphonsus and Arzachel with Purbach and Walter visible below them and perhaps a vague crater-like shadow visible above Ptolemaeus. The correspondence of the large dark blobs below the crescent of craters to features in Whitaker's degraded photo is much less obvious, but this is certainly not the region of the Moon where one would expect to find Albategnius. As we have shown earlier on this page, in his 1984 article Whitaker points out what he believes are further correspondences between engraving E4 and his comparison photo. This time he points to what he says are the craters Purbach, Regiomontanus, Walter, Deslandres, and Orontius as represented in engraving E4. Again he fails to point out the corresponding features in F6, even though he tells us it is another representation of the same observation. We are not selenographers, but the dark blobs below the chain of craters in Galileo's F6 (if it is truly Ptolemaeus, Alphonsus and Arzachel as Whitaker's photo suggests) would much more likely be inspired by such large craters as Deslandres, Maginus and Clavius, with Deslandres being roughly at the position (relative to the crescent of craters) that Whitaker ascribes to "Albategnius" in the engraving. In short, despite his great experience, we find Whitaker's identifications highly subjective, ambiguous, and open to question.
Gingerich and Van Helden (2003) make no particular comment about this engraving so they presumably accept Whitaker's dating of it to December 18, and its association with drawing F6. If they do so, then Gingerich must have at least a slight problem with his theory about how Galileo inserted Albategnius larger than life into the engravings because of how impressed he was with it. Albategnius is barely visible in drawing F6, which Gingerich and Van Helden say is the "live" image made at the telescope on December 18. Yet, if Whitaker's "unchallenged" sequence is correct this is presumably Galileo's second sighting of Albategnius near the terminator (the first having been, according to Whitaker, the now-lost sketch from December 3 on which engraving E2 was based). Perhaps Galileo featured Albategnius more prominently in that lost sketch; but based on the evidence before us it is a little hard to see how Galileo would, by the time of publication, have become so impressed by a feature that he scarcely noted (in F6) when he was actually looking at it, for a the second time, in the eyepiece on December 18.

If you wish to make your own observations of the Moon under lighting conditions similar to those which Whitaker ascribes to the four engravings (as well as to the seven wash drawings), please see our page giving predictions of future dates on which the terminator can be seen at the same solar colongitude.

Conclusions

  1. Despite their many detractors, the engravers who produced the plates appearing in the various editions of Sidereus Nuncius copied the material given to them with reasonable accuracy. In particular, the shape and position of features pictured along the terminator seem quite consistent from one version to another.
  2. The perspective drawings found among Galileo's manuscript papers demonstrate that he was able to perceive the structure of small lunar features quite accurately through his telescopes.
  3. Despite this ability of Galileo to see features accurately (possibly at a somewhat later time), the engravings published in Sidereus Nuncius seem more impressionistic than realistic to us; probably reflecting the material given by Galileo to the engraver. We find it hard to accept Whitaker's contention that, although geometrically imprecise, they are qualitatively correct. In particular, despite a diligent search both visually and through hundreds of photographs in atlases and internet postings, we have been unable to find any image of a waxing crescent Moon that seems qualitatively equivalent to engraving E1 (so different does it look from any real crescent that Ernest Cherrington took it to be a waning crescent rotated upside down). Similarly, since Mare Serenitatis is always to the east of the Moon's vertical centerline, we can find no plausible way to interpret engraving E2, with what appears to be Mare Serenitatis straddling the northern terminator, as a qualitatively correct representation of a First Quarter Moon.
  4. Whitaker's opinion to the contrary notwithstanding, the phase of the Moon depicted in a drawing can be used to date it. Looking at the positions of the terminator depicted in the images evaluated by Whitaker, we find them to be inconsistent with the dates he has assigned to them: the motion of the terminator shown in images Whitaker says are a day apart is often less than the motion shown in images he says are a couple of hours apart.
  5. We find the connection between the wash drawings bound in the manuscript copy of Sidereus Nuncius to the engravings published in that book less obvious than it seems to others. In particular, we can find no wash drawing with any obvious relationship to a published engraving. Also, although the drawings look more like the real Moon than the engravings, it seems similarly impossible to plausibly "correlate" more than a few of the features shown in any given drawing with real features on the Moon. We have been unable to find any case in which all the features shown along the terminator match a pattern to be expected for the real Moon. In fact, the number of mismatches seems to far exceed the number of "matches." This suggests that these drawings, like the engravings, are also more impressionistic than realistic and that the purported correlations are mostly random coincidences between similar appearing features.
  6. If the drawings and engravings are impressionistic rather than naturalistic, then it seems impossible to accurately date them based on the precise "identification" of the features depicted. Although the appearance of the Moon on any given date in the 17th century can be predicted with great accuracy, the proposed datings are only as good as the identifications of features, all of which seem questionable to us.
  7. Galileo's statement in Sidereus Nuncius (published in mid-March, 1610) that he is describing lunar observations made in the previous two months may be correct, but his letter of January 7, 1610 suggests that he had been observing (and understanding his observations of) the Moon since at least the preceding Full Moon (December 11, 1609). We would suspect he had looked at the Moon before that, as well, but perhaps without a clear understanding of its topography.
  8. We find nothing in Sidereus Nuncius to suggest that an observation of the four to five day old Moon was Galileo's first celestial observation. It is certainly the first he describes, but he nowhere says it was his first observation. In his January 7, 1610 letter Galileo describes observations "commencing" with the four to five day old Moon; but it certainly seems open to interpretation whether he is trying to say that his observations began at this phase, that his description begins at this phase, or that (to an observer starting at the New Moon) the raggedness of the terminator first becomes obvious at this phase.
  9. The identity of the large crater that Galileo shows so prominently on the terminator in engravings E2 and E4, and describes as reminding him of "the province of Bohemia," is unclear to us. No single crater seems completely consistent with Galileo's verbal description. Albategnius is a popular candidate, but at the time of his January 7th letter, Galileo would not have had an opportunity to witness the sunrise he describes over the peaks of its western wall. Similarly, Galileo says the bowl-shaped nature of the Bohemia-like depression was still evident, though faded, a little before and after Full Moon, when Albategnius is nearly invisible. The large walled plain of Deslandres has also been suggested, since it more closely matches the engravings in size and position, but it would hardly be described as strikingly bowl-shaped. The large isolated crater Copernicus matches the bowl-shaped description before and after Full Moon, but is not particularly "near the middle of the Moon," unless that phrase is taken rather loosely. Many other large craters seem possible candidates. Given the limited visual records available to him, it seems possible to us that Galileo may have confused observations of several different large craters, seeing them at different phases, weeks apart, and taking them to be the same.
  10. Despite all our criticism about the difficulty of assigning dates, the overall similarity (as discovered by Whitaker) of wash drawing F7 to the predicted appearance of the Moon as a fourth magnitude star emerged from its dark limb on the morning of January 19, 1610 is quite striking. However, the pattern of the large naked-eye mare shown in the portion of the Moon lit by earthshine has only a vague resemblance to the pattern expected that morning. In view of that, it seems unlikely to us that the patterns shown along the terminator would have been depicted with much greater precision.
  11. At some time in the future these conclusions can be rechecked when an accurate digital elevation model of the Moon permits scientists to precisely simulate what the entire Moon would have looked like during the periods Galileo could have observed it. We suspect that no times will be found when the pattern along the terminator precisely matches the pattern shown in Galileo's engravings. We also suspect that the patterns shown along the terminator in the wash drawings will not completely match any precise moment.
  12. In the meantime, those wishing, as has been done here, to investigate what Galileo and other early astronomers would have seen on different nights by studying modern photographs taken with similar predicted terminator positions are invited to download a free copy of the terminator-drawing computer program used in the present investigation. It may be obtained on the website of Henrik Bondo, a medical doctor and moon enthusiast who helped to develop a user-friendly version. It works only on Windows PC's, and is optimized for a 1024x768 display.

References :

  1. D. Alter, ed., Lunar atlas: prepared by the Space Sciences Laboratory of the Space Division of North American Aviation, Inc., (Dover Publications, 1968).
  2. Anonymous, "Galileo's Drawings of the Moon," Sky and Telescope 57, 222 (March 1979).
  3. H. Bredekamp, "Gazing Hands and Blind Spots: Galileo as Draftsman," Science in Context 14, 153-192 (2001).
  4. F. Camerota, "Galileo's Eye: Linear Perspective and Visual Astronomy," Galilaeana 1, 143-170 (2004). (available via the Galilæana Online page of the IMSS digital library)
  5. E. Cavicchi, "Painting the Moon," Sky and Telescope 82, 313-315 (September 1991).
  6. E. H. Cherrington, Exploring the Moon through Binoculars, (McGraw-Hill, 1968).
  7. S. Drake, "Galileo's First Telescopic Observations," Journal for the History of Astronomy 7, 153-168 (1976). (freely available from NASA's ADS)
  8. S. Y. Edgerton, Jr. "Galileo, Florentine "Disegno," and the "Strange Spottednesse" of the Moon," Art Journal 44, 225-232 (1984). (available on JSTOR)
  9. J. J. Fahie, Galileo, his life and work (John Murray, 1903; reprinted by W. C. Brown Reprint Library, 1967).
  10. O. Gingerich, "Dissertatio cum Professore Righini et Sidereo Nuncio," in M. L. Bonelli and W. R. Shea, eds., Reason, experiment, and mysticism in the Scientific Revolution (Science History Publications, New York, 1975), pp 77-88.
  11. O. Gingerich and A. Van Helden, "From Occhiale to Printed Page: The Making of Galileo's Sidereus Nuncius," Journal for the History of Astronomy 34, 251-267 (2003). (freely available from NASA's ADS)
  12. A. Johns, The Nature of the Book: print and knowledge in the making (University of Chicago Press, 1998).
  13. Z. Kopal, "The Earliest Maps of the Moon," The Moon 1, 59-66 (1969).
  14. Z. Kopal, A New Photographic Atlas Of The Moon with introduction by Harold C. Urey (Taplinger, 1971).
  15. R. J. M. Olson and J. M. Pasachoff, "Moon-struck: Artists rediscover nature and observe," Earth, Moon and Planets 85-86, 303-341 (2001).
  16. E. Reeves, Painting the Heavens : art and science in the age of Galileo (: Princeton University Press, 1997). (sample pages from this book may be viewed on Google Books)
  17. G. Righini, "New Light on Galileo's Lunar Observations," in M. L. Bonelli and W. R. Shea, eds., Reason, experiment, and mysticism in the Scientific Revolution (Science History Publications, New York, 1975), pp 59-76.
  18. G. Righini, "L'Oroscopo Galileiano di Cosimo II de Medici," Annali dell'instituto e Museo di Storia dela Scienza di Firenze I, 28-36 (1976). (freely available via the Nuncius Online service of the IMSS digital library)
  19. G. Righini, Contributo alla interpretazione scientifica dell'opera astronomica di Galileo (IMSS, 1978). (this special supplement is available online as the last item in the list of volumes in the Nuncius Online directory of the IMSS digital library)
  20. E. Rosen, "Galileo and the Telescope," The Scientific Monthly 72, 180-182 (1977). (available on JSTOR)
  21. O. van de Vyver, "Original Sources of Some Early Lunar Maps" Journal for the History of Astronomy 2, 86-97 (1971). (freely available from NASA's ADS)
  22. A. Van Helden, "The Invention of the Telescope," Transactions of the American Philosophical Society 67, 1-67 (1977). (available on JSTOR)
  23. A. Van Helden, "Moon Maps in History" (review of Whitaker, 1999) Journal for the History of Astronomy 33, 285-289 (2002). (freely available from NASA's ADS)
  24. J. E. Westfall, Atlas of the Lunar Terminator (Cambridge University Press, 2000). (sample pages from this book may be viewed on Google Books)
  25. E. Whitaker, "Galileo's Lunar Observations and the Dating of 'Sidereus Nuncius,'" Journal for the History of Astronomy 9, 155-169 (1978). (freely available from NASA's ADS)
  26. E. Whitaker, "Lunar Topography: Galileo's Drawings," Science 210, 136 (1980).
  27. E. Whitaker, "Selenography in the Seventeenth Century," in Michael Hoskin, ed., The General History of Astronomy Vol. 2, Pt. A, (Cambridge University Press, 1984).
  28. E. Whitaker, Mapping And Naming The Moon: A History Of Lunar Cartography And Nomenclature (Cambridge University Press, 1999). (Sample pages from this book may be viewed on Google Books)
  29. M. Winkler and A. Van Helden, "Representing the Heavens: Galileo and Visual Astronomy," Isis 83, 195-217 (1992). (available on JSTOR)
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