Time and the Analemmatic Sundial of Bergamo, Italy

Jeffrey La Favre

I find the subject of time and timekeeping interesting. It is a subject that falls within the disciplines of astronomy, anthropology and other fields within the humanities. Our concept of time is tied to the apparent movements of the Sun across our sky, during the day, and during the year. These apparent solar movements are actually the result of the spin of the Earth upon its axis and the orbital movement of the Earth around the Sun.

Today we rely on clocks and watches to meter the day and calendars to meter the year. We have lost touch with the Sun, even though its apparent movements are the basis of our day and year. In the past many people were involved in watching the Sun as a means of measuring time. Sundials of various designs were employed for accurate solar observations. The study of a sundial can reveal the astronomical knowledge of the builder as well as aspects of a culture. It is for these reasons that I find the sundial in Bergamo of interest.

While we were in Bergamo, I was able to examine the analemmatic sundial near the front of the cathedral, located specifically in the portico of the Palazzo della Ragione. This sundial was installed in 1798 and has undergone two major restorations, one in 1857 and the other in 1982. As currently configured, the sundial provides the following information regarding time:

  1. time of local noon, also 15 minutes before and after local noon
  2. time of mean local noon, determined by the analemma
  3. day and month of the year
  4. sign of the zodiac for the current sun

Before we examine the sundial in detail, it would be a good idea to review some terms and concepts regarding time. We are all aware that the unit of time called the day is related to the Sun. We are familiar with the system devised to divide the day into hours, minutes, etc. Before widespread availability of accurate clocks, people did measure time by watching the Sun. At the point of midday, between sunrise and sunset, timekeepers noted the time as noon, or in modern terminology, local noon. The term local noon must not be confused with noon, as we determine by our clocks, they are not the same thing.

Due to the nature of the Earth's orbit around the Sun and the tilt of the Earth's axis, the period of the solar day is variable throughout the year. We could manufacture our clocks to run at different rates, depending on the day of the year. Then they could track the real, or apparent Sun. A more practical solution would be to sum the amount of time for each solar day of the year and divide by the number of days in the year, thus obtaining the average or mean solar day. Then a clock running at a constant rate can track the mean solar day. Noon on our clocks is the mean local noon. Throughout the year the Sun is usually behind or ahead of the clock, but averages out to a position that matches our clock noon.

By allowing our clocks to track the mean sun, we have devised a simplified method of tracking time, but our time standard is still local. That is, every line of longitude on Earth has a unique time of local noon and mean local noon. Societies operating on a local scale can keep time by a local standard without any problems. With the development of industrialized societies, a standardized time is needed for an extended geographical area. For example, when the railroads were developed during the 19th century in the United States, there was a need to keep a standard of time for train schedules. This was done by establishing time zones. By convention, the Earth is divided into 360 degrees of longitude and our day is divided into 24 hours. Dividing the Earth into 24 time zones, we obtain each time zone at 15 degrees longitude wide. By adopting this standard, we have become even more estranged from the Sun. Now the mean local sun matches our clock noon only at the midpoint of each time zone. At all other points we must add or subtract time from our clocks to match the mean local sun.

The Bergamo Sundial

We are ready now to consider the sundial in Bergamo. In the photo below I have labeled the main components of the sundial with arrows. The red arrow points to the gnomon, a bronze disk that is perforated with a small hole near the center (see this photo and this photo). The purpose of the gnomon is to cast a shadow with a central bright spot, which is actually an image of the sun. Due to the relatively small size of the hole in the disk, it functions like a pin-hole camera, that is to say, the hole functions like a lens, which projects the image of the sun. At certain moments during the middle of the day, the image of the sun projected by the gnomon will intersect markings on the pavement.

The blue arrow points to a straight meridian line engraved in the inlaid marble pavement. This meridian line runs true north and south (that is it points to the true north pole of Earth in one direction and the true south pole in the other direction). The gnomon is aligned so that the image of the sun in the center of the shadow intersects the engraved meridian line when the Sun transits (crosses) the meridian. The meridian is an imaginary great circle across the sky, intersecting the horizon at true north and south and intersecting the zenith (the point directly overhead in the sky). At the moment that the center of the Sun intersects the meridian, that time is called local noon. At that moment, the image of the Sun will be centered on the meridian line engraved in the marble inlay. Thus, this sundial can be used to determine the time of local noon.

sun dial

A photo on this page shows the shadow cast by the gnomon and the image of the solar disk in the center. This photo was taken around the time of the summer solstice. Unfortunately, I neglected to take a similar photo at the time of our visit. However, in my photo below, you can see the shadow of the gnomon, which is covering a portion of the line to the left of the meridian line. The line to the left marks the time of 15 minutes prior to local noon, so my photo was taken at a time slightly less than 15 minutes prior to local noon.

shadow

There is ample evidence from many civilizations, even thousands of years ago, that time was accounted for by positions of the Sun. That is, time of day and day of the year. As the centuries passed, ancient solar observers came to notice certain peculiarities or variations in the movement of the Sun throughout the year. The Babylonians were aware that the length of a solar day varied during the year. This variation is known today as the equation of time.

Another variation in solar position is the variation in elevation of the Sun above the horizon at local noon for each day of the year. The Sun is high in the sky at local noon in the summer and low in the winter, due to the tilt of the Earth's axis. In fact, measuring the solar elevation above the horizon at local noon can be used to determine the day of the year. The Bergamo sundial can be used to determine the day of the year by observing exactly where the solar image crosses the engraved meridian line. At the winter solstice, the image of the Sun projected by the gnomon intersects the meridian line near its northern end and on the summer solstice, near its southern end. The days of the year are marked in increments of two along the engraved meridian line.

When we combine the two factors, the equation of time and variation above the horizon due to the day of the year, the Sun marks out an interesting pattern in the sky. The pattern is that of a skewed figure-8, known as the analemma. This pattern can be recorded with a camera with some patience. That is, take multiple exposures of the Sun at the same time of day by the clock (it does not need to be done at noon) on several days during the year. Here is a photo done just that way.

Below is a plot of the analemma for the location of the Observatory in Greenwich, England. The altitude of the Sun for the days of the year is plotted on the vertical axis and the difference between the clock time and the real Sun is plotted along the horizontal axis (for negative values the real Sun is behind the clock).

analemma

(source: http://upload.wikimedia.org/wikipedia/commons/archive/a/a6/20071118062415%21Analemma_Earth.png)

I know that some of you also observed the sundial in Bergamo. I hope that you noticed the figure-8 pattern engraved in the stone pavement. Below I provide some photos of portions of the figure-8 (see my photo above for a more complete image).

center

In the photo above you can see the central portion of the figure-8 pattern, where the lines intersect. Also note the days of the year engraved in the marble along the meridian line. Below the meridian line is the line that marks the time of 15 minutes prior to local noon and above the meridian line is the line that marks the time of 15 minutes after local noon. On the far right are two engraved symbols, representing the constellations Taurus and Virgo of the zodiac. The symbols (all 12) are positioned to indicate the day of the year when the Sun moves into that particular sign of the zodiac. For example, the Sun is usually in Taurus April 20 to May 20 and usually in Virgo August 23 to September 22. Note that the mark on the meridian line for April 20 lines up roughly with the sign of Taurus and that the line for August 22 falls just short of the center of the symbol for Virgo. Thus, the symbols for Taurus and Virgo on the sundial mark the entry points of the Sun into the constellations of Taurus and Virgo.

tauruvirgo

summer

In the photo above you can see the southern end of the figure-8 engraving, marking the summer solstice. The summer solstice occurs on June 20 or 21, depending on the year. The Sun is in Gemini May 21 to June 20, in Cancer June 21 to July 22, in Leo July 23 to August 22

geminicancerleo

 

winter

In the photo above you can see the northern end of the figure-8 engraving, marking the winter solstice (solstizio d'inverno), which occurs December 21 or 22 depending on the year. The Sun is usually in the constellation Capricornus December 22 to January 19 (I am not sure why the symbol for Capricornus is centered on December 26). Also note here the name G.(Giovanni) Albrici, who was the abbot responsible for construction of the original sundial and the date 1798. The last date of restoration, 1982, is also indicated.

capricorn

Now, with the inclusion of the analemma on the sundial, we can determine the time of local noon AND the time of mean local noon (mean local noon is the time of noon on our clock or watch - but must be adjusted for the fact that Bergamo is not at the center longitude of the time zone, but about 21 minutes to the west (behind - as the world turns), i.e., Bergamo mean local noon is 12:21 PM standard time). Thus, the image of the Sun projected by the gnomon crosses the analemma line at 12:21 PM each day. But which line of the analemma, the one west of the central meridian line or the one east? In order to select the correct analemma line, you must know if the Sun is behind or ahead of the clock, which can be determined from the equation of time. At the time of our visit on March 11, the Sun was behind the clock, thus the image of the Sun first crossed the analemma line on the west side of the meridian line at 12:21 PM. Then a few minutes later it crossed the meridian line at the time of local noon (remember that the Sun moves to the west during the day, thus the shadow it casts moves east). I was lucky to have been there as the the image of the Sun crossed the analemma line. Unfortunately, I did not record the time on my watch as I was busy discussing the impending event with Dr. Ferri and his family (and due to my poor memory, I don't remember the time on my watch - guess I will just have to go back another time).

Now lets take a look at another part of the sundial which indicates the longitude (I have a photo)

long

From the above photo we learn that the sundial is located at a longitude of 9 degrees 39 minutes 46 seconds (east of Greenwich, England). There are 360 degrees of longitude and there are 24 time zones, which means that each time zone is 15 degrees wide. Therefore, the border of each time zone is measured at 7 1/2 degrees from the central longitude (in practice many borders do not match these measurements, but that does not concern us for our calculations). Bergamo is located in the next time zone to the east of Greenwich and that time zone is centered on 15 degrees east of Greenwich. There are 60 minutes in one degree and 60 seconds in one minute. Therefore, the sundial is located approximately at 9.66 degrees east of Greenwich or 5.34 degrees west of the central longitude of the time zone. The mean sun moves through 15 degrees in 60 minutes of clock time, therefore, local mean noon at Bergamo is (5.34/15)(60 minutes) = 21 minutes behind local mean noon at the center of the time zone (i.e. the time on the clock).

I believe the figure for longitude given above was engraved as part of the 1982 restoration as it clearly represents the modern system which sets the prime meridian at Greenwich, England. As part of the 1857 restoration the longitude is said to have been engraved as 27 degrees 29 minutes, which I believe was with reference to the old prime meridian on the island of El Hierro (the "Meridian Island"), one of the Canary Islands. It was not until 1884 that an international conference settled upon Greenwich as the prime meridian, which has been maintained up to the present day.

The Science Behind the Sundial

I have completed my description of the Bergamo sundial and how it works. Now we should study some aspects of the relationship of the Earth to the Sun, specifically the orbit of the Earth around the Sun. It is by examining the orbit of the Earth and its rotation upon its tilted axis that we can appreciate why there is variation in the solar day.

If the Earth had a true circular orbit with the Sun in the exact center of the orbit, and if the axis of the Earth was not tilted with respect to the plane of its orbit, then the period of the solar day would be the same each day of the year. However, the orbit of the Earth is elliptical and the Sun is located at one of the focal points of the ellipse. With this arrangement, there are points in the orbit where the distance between the Earth and Sun is less than at other points. When the Earth is closer to the Sun, its orbital velocity is higher, which results in a longer solar day. Why is this the case?

I believe it is a common misconception that the period of the solar day is only due to the rotation of the Earth upon its axis. While this is the major contributor to the day, it is also necessary to consider the orbit of the Earth. In astronomy we have the terms sidereal day and solar day. The sidereal day is the day marked by the stars, that is the time between one transit of a star on the local meridian and the next. It is the sidereal day that is only the result of the rotation of the Earth on its axis. But outside of astronomy, we are usually concerned with the solar day. The solar day is longer than the sidereal day because the Earth must spin a little more than one rotation to bring the Sun back to the meridian on the next day. Why is this so?

As the Earth orbits the Sun in a westerly direction, the apparent position of the Sun in our sky moves to the east. If we could see the stars during the day, we would notice that the Sun was in front of different stars each day of the year. Keep in mind that the Sun is much closer to the Earth than the other stars (the Sun is also a star). Then try a mind game. You are standing in a field or large parking lot and looking at an object close to you (the Sun). There are also objects in the background, much farther away than the close object (the stars). Now you take a number of sidesteps to the right (west) while watching the close object and the background objects. The near object (Sun) appears to move to the left (east) against the background objects. You can also do this experiment for real to satisfy yourself of this effect. Thus, the apparent movement of the Sun to the east in our sky, against the background stars of the zodiac constellations, is due to the orbital movement of the Earth to the west.

earth orbit

Now if we add the complication of variable orbital velocity for the Earth, we can see why the length of the solar day varies. When the Earth is moving faster along its orbit, the apparent Sun moves a greater distance to the east in a day. Thus, the Earth needs to turn more on its axis to bring the Sun back to local noon, which consumes more time, resulting in a longer solar day.

Oh, if it were only that simple! Now we must consider the tilt of the axis of the Earth. This is more difficult to visualize in the mind. Due to the tilt of the Earth's axis, the yearly path of the Sun across our sky follows the ecliptic (where the constellations of the zodiac are located). When we trace the ecliptic out on our sky, it marks a great circle at an angle to the celestial equator (the celestial equator is an extension of Earth's equator into the sky). That angle equals the angle of the tilt of the Earth's axis. Thus, given even a constant orbital velocity of the Earth, the apparent solar movement in an EAST-WEST direction will vary depending on the position of the Sun on the ecliptic. Said another way, the orbital movement of the Earth will cause the Sun to move in a NORTH-SOUTH direction in our sky in addition to an EAST-WEST direction. And the magnitude of solar movement in each of these directions depends on the location of the Sun on the ecliptic. Furthermore, it is only the solar movement to the EAST that affects the length of the solar day.

ecliptic

(source: http://en.wikipedia.org/wiki/Ecliptic)

ecliptic

The image above depicts the apparent movement of the Sun throughout the year, the result of the orbital movement of the Earth. Note at the solstices in June and December that the Sun moves parallel to the Celestial Equator, thus strictly in a due east direction. However, at the equinoxes in March and September, the Sun is moving in both a north or south direction as well as an east direction. These differences are due to the tilt of the Earth's axis and its variable orientation with respect to the Sun for each day of the year. Therefore, due to this factor alone, the apparent Sun moves at a faster rate to the east in June and December then in March and September. The faster rate contributes to a longer solar day. But these movements are not to be confused with the variable rate of the Earth's orbital velocity, the other factor contributing to variation in the solar day. The Earth reaches its closest approach to the Sun about January 3, which astronomers call perihelion. It is at this time that the Earth's orbital velocity is maximum. Then about July 4 the Earth reaches aphelion, the farthest distance from the Sun and the slowest orbital velocity.

 

eartg orbit

(source: http://en.wikipedia.org/wiki/Earth%27s_orbit)

Then to summarize, the variation in the solar day is due to two factors:

1) variation in the rate of the Earth's orbital velocity due to its elliptical orbit around the Sun

2) variation in the rate of the apparent solar movement to the east in our sky depending on position of the Sun on the ecliptic

 

Some Aspects of the History of Astronomy that Relate to the Sundial

If we look back in the history of astronomy, we can find remarkable achievements by talented scientists who lived hundreds, even thousands of years ago. In keeping with the time periods that were touched upon in our trip to Italy, I would like to mention the work of two individuals in particular: Johannes Kepler (1571 - 1630) and Galileo Galilei (1564 - 1642).

Kepler was a German astronomer and mathematician who discovered that the orbits of the planets around the Sun are ellipses. He was able to make this discovery by painstaking analysis of positional data of Mars accumulated by another noted astronomer of the time, Tycho Brahe (1546 - 1601). Kepler developed three laws of planetary motion, of which the second is directly related to our discussion of the sundial in Bergamo: A line joining a planet and the Sun sweeps out equal areas during equal intervals of time. The results of this law include the fact that the orbital velocity of a planet increases as its distance to the Sun decreases, as we have already discussed. Kepler's achievement is to be greatly admired considering that his work was done 400 years ago.

kepler

Galileo Galilei was a contemporary and correspondent of Kepler. He has been called by some the father of modern science. I might also mention that he lived in Pisa and Florence and also had dealings with people in high places in Venice while he was a professor in Padua. I happen to be a fan of Galileo, which made our trip to Italy even more special.

In the summer of 1609 Galileo produced his first telescope, while he was a professor at the University in Padua, about 22 miles west of Venice. Galileo had heard rumors of a telescope produced by a man in Holland, which was being demonstrated with excitement in Venice at the time. This spurred Galileo on to produce his own telescopes, which were superior to those few others available during the early years of the 17th century. He started to use his telescopes for astronomical observations soon after manufacture. Galileo's observations in January and February of 1610 resulted in the discovery of the four large moons of Jupiter, now known as the Galilean Moons. Since I am such a fan of Galileo, I hope you will indulge me in some details of his work, which ultimately impinge on our understanding of the solar system.

Below I have reproduced the drawings of Galileo, published in his book Sidereus Nuncius (The Stellar Messenger) in March 1610. Along with his drawings, I have included the positions of the four moons of Jupiter as determined by computer software (I used the program RedShift2). I hope you will find the comparison of the results by computer and Galileo's drawings very interesting. Galileo's first observation was done January 7:

"Accordingly, on the seventh day of January of the present year 1610, at the first hour of the night, when I inspected the celestial constellations through a spyglass, Jupiter presented himself. And since I had prepared for myself a superlative instrument, I saw (which earlier had not happened because of the weakness of the other instruments) that three little stars were positioned near him -- small but yet very bright. Although I believed them to be among the number of fixed stars, they nevertheless intrigued me because they appeared to be arranged exactly along a straight line and parallel to the ecliptic, and to be brighter than others of equal size. And their disposition among themselves and with respect to Jupiter was as follows. That is, two stars were near him on the east and one on the west; the more eastern one and the western one appeared a bit larger than the remaining one. I was not in the least concerned with their distances from Jupiter, for, as we said above, at first I believed them to be fixed stars."

The computer verifies that the Galilean moons were positioned as Galileo drew them on January 7, 1610. With a modern telescope Galileo would have been able to see Europa and Io separately. However, his telescope was optically inferior by modern standards and so he viewed these two moons as one object due to their small separation and the relatively low magnification of his telescope.

image

 

"But when, on the eighth, I returned to the same observation, guided by I know not what fate, I found a very different arrangement. For all three little stars were to the west of Jupiter and closer to each other than the previous night, and separated by equal intervals, as shown in the adjoining sketch. Even though at this point I had by no means turned my thought to the mutual motions of these stars, yet I was aroused by the question of how Jupiter could be to the east of all the said fixed stars when the day before he had been to the west of two of them. I was afraid, therefore, that perhaps, contrary to the astronomical computations, his motion was direct and that, by his proper motion, he had bypassed those stars. For this reason I waited eagerly for the next night. But I was disappointed in my hope, for the sky was everywhere covered with clouds."

Now our computer generated diagram reveals three moons west of Jupiter just as Galileo drew them. However, on this day Galileo did not draw in Callisto, which had now moved farther to the east. Since Galileo saw only three moons the day before, he probably expected to see again three moons. He either missed Callisto on this day or he thought it was a background star and excluded it from his drawing.

At this point Galileo probably still thought the moons were fixed stars. However, he was confused because the astronomical tables, which were correct, indicated that Jupiter was in retrograde movement. If so, Jupiter should be moving to the west with respect to the fixed stars. If the moons were fixed stars, he should have seen them to the east of Jupiter on the 8th. But he saw them on the west. That is why he suggests that perhaps the "astronomical computations" may not be correct. If Jupiter was in direct motion (i.e. moving to the east) then one would expect to see fixed stars shift from the east side to the west side.

 

image

 

"Then, on the tenth, the stars appeared in this position with regard to Jupiter. Only two stars were near him, both to the east. The third, as I thought, was hidden behind Jupiter. As before, they were in the same straight line with Jupiter and exactly aligned along the zodiac. When I saw this, and since I knew that such changes could in no way be assigned to Jupiter, and since I knew, moreover, that the observed stars were always the same ones (for no others, either preceding or following Jupiter, were present along the zodiac for a great distance), now moving from doubt to astonishment, I found that the observed change was not in Jupiter but in the said stars. And therefore I decided that henceforth they should be observed more accurately and diligently."

Now the computer helps us understand again what Galileo observed. As he suspected, Io did move behind Jupiter on this day and so became invisible. At the same time Callisto had moved back closer to Jupiter and so Galileo sees it and places it on his drawing. But now Ganymede and Europa are very close to each other so they appear as one to Galileo. After observations on three different nights, Galileo still does not realize he has been observing four moons, not three. On the first and third nights, two of the moons were so close to each other that he saw them as one and on the second night he missed Callisto because it had moved very far to the east of Jupiter (Callisto's orbit is the outermost of the four moons). However, at this point he has come to a very important discovery: it is not the movement of Jupiter that has caused apparent shifting of the moons but rather the movements of the moons themselves. One does not observe Jupiter to be moving in a certain direction against the stars one night and then reverse suddenly and move the other way two days later. The change from direct to retrograde motion occurs over a longer time period.

image

 

"And so, on the eleventh, I saw the following arrangement. There were only two stars on the east, of which the middle one was three times as far from Jupiter than from the more eastern one, and the more eastern one was about twice as large as the other, although the previous night they had appeared about equal. I therefore arrived at the conclusions, entirely beyond doubt, that in the heavens there are three stars wandering around Jupiter like Venus and Mercury around the Sun. This was at length seen clear as day in many subsequent observations, and also that there are not only three, but four wandering stars making their revolutions about Jupiter. The following is an account of the changes in their positions, accurately determined from then on. I also measured the distances between them with the glass, by the procedure explained above. I have added the times of the observations, especially when more than one were made on the same night, for the revolutions of these planets are so swift that the hourly differences can often be perceived as well."

On the 11th Io and Europa were too close to Jupiter to be seen by Galileo and so he saw only Callisto and Ganymede to the east. He also mentions that Ganymede is brighter (larger) than Callisto, which is correct. However, he also says that the night before they appeared to be about the same brightness. This could not be since Ganymede is brighter and then Europa was seen also combined with Ganymede. Both of these moons are brighter than Callisto so we must view Galileo's judgements of brightness with some doubt. It may be that when Ganymede was closer to Jupiter, the glare from the planet made it difficult for Galileo to judge the true brightness of the combined Ganymede and Europa.

 

image

 

 

"Thus, on the twelfth, at the first hour of the following night, I saw the stars arranged in this manner. The more eastern star was larger than the western one, but both were very conspicuous and bright. Both were two minutes distant from Jupiter. In the third hour a third little star, not at all seen earlier, also began to appear. This almost touched Jupiter on the eastern side and was very small. All were in the same straight line and aligned along the ecliptic."

On this day Galileo first saw Ganymede to the east and Europa to the west just as our computer plot indicates. For the first time he estimates the angular separation between the moons and Jupiter which he puts at 2 minutes for each. Now on this day he continues to observe into the later hours of the night and he notes the emergence of Io from the back side of Jupiter. Io is the closest of the four Galilean moons to Jupiter and therefore has the fastest orbit, completing one orbit in only 1.77 days! This means that it is possible to note a change in its position after only a few hours. And so, on the first hour of night Io was very close to Jupiter and was not visible to Galileo. But just two hours later, Io had moved just enough to the east so that Galileo could now see it very close to the eastern side of the planet! Callisto at this time was very close to Jupiter and thus was not seen by Galileo.

image

 

"On the thirteenth, for the first time four little stars were seen by me in the formation with respect to Jupiter. Three were on the west and one on the east. They formed a very nearly straight line, but the middle star of the western ones was displaced a little to the north from the straight line. The more eastern one was 2 minutes distant from Jupiter; the intervals between the remaining ones and Jupiter were only 1 minute."

Now, on the sixth day of observations, Galileo happens to observe Jupiter when all the moons are fairly close to the planet but not so close that they can't be seen. Furthermore, they are all separated enough so that they can be seen as individuals. Galileo discovers the four largest moons of Jupiter!

image

Now we will jump to the end of Galileo's daily descriptions and examine part of his summary.

"These are the observations of the four Medicean planets [now we call them moons] recently, and for the first time, discovered by me. From them, although it is not yet possible to calculate their periods, something worthy of notice may at least be said.....It is further seen that the revolutions of the planets describing smaller circles around Jupiter are faster. For the stars closer to Jupiter are often seen to the east when the previous day they appeared to the west, and vice versa, while from a careful examination of its previously accurately noted returns, the planet traversing the largest orb appears to have a semimonthly period."


After two months of observations, Galileo has a good handle on the motions of Jupiter's large moons. He realizes that the inner moons, Io and Europa, have orbital periods of a few days while Callisto has a period of about two weeks. Modern figures for the orbital periods are: Io 1.77 days; Europa 3.55 days; Ganymede 7.15 days; Callisto 16.69 days. Galileo was an extraordinary observer.

These observations provided evidence against the old geocentric model of the universe, where all heavenly bodies were said to orbit around the Earth. Many have been the times that I have marveled at the sight of the Galilean moons through my own telescopes and have watched Io race around Jupiter, observing the change in its position during one night. Any modern telescope is capable of providing a good view of these moons, so don't neglect them if you have a telescope of your own!

Medicean planets was the name Galileo applied to the moons of Jupiter, in honor of the Medici family of Florence. At the time Galileo was looking for a change, he had his eye on a position in the court of Cosimo Medici. There is little doubt regarding Galileo's motives in naming the moons.

Galileo arrived in Florence in September of 1610. Shortly thereafter, he began his most important observations of Venus, which established that the planet orbited the Sun, not the Earth. These observations and others convinced Galileo that the Copernican heliocentric model of the solar system was correct, not the old geocentric (Earth-centered) model handed down from Aristotle and Ptolemy, the famous astronomer of Alexandria during the second century AD. The Catholic Church during the time was clinging to the old geocentric model and it was considered heresy to support a heliocentric model. The end result for Galileo was not as harsh as for some of his like-minded colleagues, but he did spend the latter years of his life under house arrest. New ideas do need time on occasion to gain acceptance, and such was the case for a heliocentric universe. Nevertheless, it is through this model that we can properly understand the apparent solar movements that relate to the sundial.

History of the Bergamo Sundial

If you can read Italian, this page has some interesting details regarding the history of the Bergamo sundial (in my case Dr. Ferri translated the page for me). The original sundial was designed by and constructed under the supervision of the abbot Giovanni Albrici (or Alberici or Albricci) in 1798. He selected the portico of the Palazzo della Ragione, which at the time had the west side enclosed by a wall, blocking some light, so that the pavement of the portico was well shaded. Placement of the sundial here provided the shading needed to see the image of the Sun projected by the gnomon. Additional shading was needed on the south side of the portico where the gnomon was located. This was due to the fact that the original gnomon was fairly small, about 20 x 30 cm, with a 15 mm hole for lensing the image of the sun. A shade made from a large metal sheet was installed in the central archway containing the gnomon (otherwise the Sun would shine through the archway onto the pavement and wash out the image of the sun produced by the gnomon).

The original design included a meridian line with the times of sunrise and sunset engraved at various positions along the line. At this point in history, local mean time was not the standard, an old system of keeping time was in force, which was calibrated by the real sun.

The sundial was attacked in 1799 because it was seen as a symbol of the new French progress which was despised. Stones were thrown at the gnomon and possibly the markings on the pavement were attacked as well. Fearing that the instrument had been damaged, in 1806 Albrici asked a young professor, Giuseppe Bravi, to check the accuracy of the instrument. After a thorough examination, Bravi determined that the sundial had retained its accuracy. It is thought that at this time Bravi added the additional lines that measure the times of 15 minutes prior and after local noon.

By 1857 the sundial was in poor condition and essentially useless when Francesco Valsecchi, a municipal engineer, undertook the task of a major renovation. He was assisted in the scientific aspects of the work by Cesare Noris and Carlo Ulietti and by the marble worker Costantino Brassola of the shop of Giuseppe Fossati. No change was made to the gnomon, but the marble was replaced with slabs of greater length and thickness. The lines marking 15 minutes prior and after local noon were set in marble (the previous lines were not in marble, just engraved in the stone pavement). Of key interest was the addition, for the first time, of a figure-8 analemma. With this addition we can conclude that Bergamo was at this time using the new method of keeping time by the mean local sun.

Another addition at this time was a square plate of marble containing a compass rose, indicating the true cardinal directions (north, north east, etc.). The center of this compass rose was aligned such that it was directly under the hole in the gnomon (that is, a plumb line centered on the compass rose would pass through the hole in the gnomon). This replaced another marking that was in place at the time the original sundial was constructed.

The placement of this compass rose brings an interesting question to my mind. Perhaps the answer is unknown at this point in the history of the sundial. Was the compass rose used as the corner of a triangle, utilizing trigonometry, to calculate the distance from the compass rose to points on the engraved meridian line representing the various days of the year? In other words, did Cesare Noris and Carlo Ulietti have in their possession astronomical tables or data that could be used to determine the altitude of the local sun on the meridian for each day of the year? If so, they could have used those altitude angles, and by knowing the distance from the gnomon to the compass rose (currently 7.64 meters), to calculate the distance along the engraved meridian line for each day of the year. I wonder if that was their method? And was that the method used by Albrici? If the pavement is not level, then the angle of of the engraved meridian line with respect to level must be accounted for as well in the calculations.

rose

The compass rose

 

With this restoration the hours and minutes of sunrise and sunset were again engraved at various positions along the engraved meridian line. As before, the times of sunrise and sunset were referenced to local noon. This brings up another interesting question. Why were these times of sunset and sunrise referenced to local noon and not mean local noon? Was it to preserve a historical detail? Or was the old practice of keeping time still in use simultaneously with the new method of timekeeping?

During renovations of the city center during the 1920s, the metal shade covering the central arch is believed to have been removed. The shade was removed because it was felt that it was blocking the attractive views of the surrounding area. With the shade removal, it became more difficult to view the image of the sun produced by the gnomon. That problem was rectified during the 1982 renovation, when a new gnomon was constructed.

The restoration completed in 1982 was undertaken by the architect Gianfranco Alessandretti. The old gnomon was replaced with a new, larger bronze disk, which cast a deeper shadow. This improvement negated the need to restore the shade in the central archway. The new gnomon created a condition whereby the solar image could be easily seen, even at the winter solstice. Apparently there was also some marble work done. Instead of the hours of sunrise and sunset, the days of the year were engraved into the marble of the meridian line. In addition, the positions of the zodiac symbols were adjusted to match geographic coordinates according to modern references.

The last reference to the zodiac above may hold interest to those interested in astrology, a subject where my knowledge is admittedly limited. But it does also bring up the subject of precession, which is the change of orientation of the Earth's axis with respect to the stars over a long time period. In fact, the Earth spins much like a top, with its axis marking out a circle in the sky over a period of about 26,000 years. I believe this presents something of a crisis to those practicing astrology due to the fact that the vernal equinox, also known as the first point of Aires, no longer occurs in the constellation of Aires, but now in the constellation of Pisces! In other words, the point where the celestial equator and the ecliptic intersect, that marks the the start of spring in the northern hemisphere, is constantly moving, and makes one circuit of the full zodiac in about 26,000 years! Thus, if we are to keep track of the geographical coordinates related to the zodiac over a long time period, it is necessary to periodically adjust the coordinate system to keep pace with the changes due to precession. The beauty of the Universe is in its incredibly intricate details!