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Astronomy for Amateurs
Chapter 6
Medieval Astronomy
Now that we have taken a break to familiarize ourselves with the sky, let’s see what astronomers did for a living between Ptolemy and Copernicus.
Ptolemeic to Arabic astronomy
As we follow the path of Ptolemaic astronomy around the Mediterranean, we find ourselves in the Holy Land, North Africa, and Spain. The pre- and post-Islamic Arabs adopted and refined Ptolemy’s model and tools. The Crusaders and Spanish Christians found that the Arabs had a mature method of predicting astronomical events, which was adopted by late medieval astronomers. Professional astronomy appears to have not otherwise made it to Western Europe until it was received from Arab astronomers early in the second century.
Astronomy was not unknown in early Medieval Europe, as certain astronomical events were essential to that culture. Churches tended to be aligned such that congregations faced the rising sun. Some archeologists claim that many of the thousands of churches were accurately aligned with the sunrise on the feast day of that church’s patron saint.
Many churches had windows placed such that sunlight shining through the window fell on a painting or statue of the church’s patron saint at noon on that saint’s feast day.
The job of the medieval astronomer
Early medieval astronomers tended to be professional clerics with astronomy as a sideline. Whether amateur, part-time, or full-time professional, there were certain tasks required of them. Here are some of those jobs.
Determining the Length of the year
Recall that the Earth takes about 23 hours, 56 minutes, and four seconds to rotate a full 360 degrees, marking one sidereal day. In that time, the Earth has revolved about one degree counterclockwise in its orbit around the Sun (as viewed from the north). Therefore, from our perspective, the Sun has appeared to move east by about one degree. Thus, it takes about another three minutes and 56 seconds for the Earth to rotate another degree to face the Sun again as it had the previous day. This makes the solar or synodic day average 24 hours (varying by a few minutes throughout the year due to the varying speed of the Earth in its elliptical orbit).
In 365 sidereal days, the Earth makes a bit less than one revolution around the Sun. It takes about another five hours and 49 minutes for the Earth to complete the circuit. Therefore, the year is approximately 365.25 days.
By 2000 BC, the ancient Egyptians had already calculated the length of the year at 365¼ days. They originally had a year of 365 days (12 months of 30 days each plus five extra “epagomenal days” [Greek for induced days]). This was refined to 365¼ days after carefully measuring the drift of the heliacal rising of Sirius by about one day per four years. Around that time, Hipparchus determined the tropical year (the time between two solar crossings of the vernal equinox) to be 365.2467 days (modern measurements put it at 365.2422, only about six minutes shorter). He determined this by averaging many observations (his own and from Babylonian records) of how many days elapsed between equinox crossings.
Maintaining the calendar
In 46 BC, Julius Caesar commissioned the Julian Calendar, which set the year at exactly 365 days, with each fourth year having 366 days (adding a 29th day to February), thus incorporating an error of about 11 minutes per year. This caused the official day of the Vernal Equinox (March 21) to drift ahead of the astronomical equinox by about one day every 130 years.
Over the centuries, the small error in the Julian Calendar added up significantly. For example, the Christian holiday, Candlemas (which Protestants would eventually celebrate as Badger Day, and in America, Groundhog Day), occurred halfway between the Winter Solstice and the Vernal Equinox. This was not only an important holy day but also the time for farmers to begin assessing the conditions to prepare for spring planting. This was not to mention that accurately determining the day of the Vernal Equinox was essential to calculating the day of Easter (the first Sunday after the first full Moon after the Vernal Equinox), the accurate celebration of which was critical to one’s salvation. By the 1500s, March 21 was occurring 10 days before the astronomical Vernal Equinox. Had this drift been allowed to continue, by the year 2000, March 21 would occur 13 days ahead of the astronomical Vernal Equinox.
In 1582, Pope Gregory XIII commissioned a corrected calendar that eliminates most leap years that fall at the beginning of centuries and removed 10 days from the year 1582 to realign March 21 with the astronomical Vernal Equinox. This also religned Candlemas, and thus Groundhog Day, back to their proper places, 6½ weeks before the official first day of spring.
Determining the day of the Vernal Equinox
As mentioned above, the early Catholic Church relied on the Julian Calendar to determine the day of the Vernal Equinox (always March 21). Some clerics/astronomers attempted to realign the observed Day of the Vernal Equinox with the astronomical Equinox. However, their efforts were not met with widespread acceptance before Pope Gregory XIII commissioned the Gregorian Calendar.
In the later medieval period, some churches had a hole in the wall or ceiling (an ocular) aligned such that sunlight shining through the hole fell on a scale marking the day of the Vernal Equinox. Some had even more elaborate markings, making a full calendar using the sun as an indicator.
Perhaps the most famous is the Basilica of Saint Mary of the Angels and the Martyrs, near the Vatican. Around 1700, Pope Clement XI commissioned Francesco Bianchini to embed a bronze meridian line in the floor to become the official Rome meridian at 12° 30’ E longitude (finished in 1702).
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An oculus with a diameter of about two centimeters was added to the south wall 20 meters above the meridian line. The Basilica acts like a pinhole camera, with the oculus casting a low-resolution image of the Sun on the floor, having a diameter between 20 and 25 centimeters (depending on the time of year and thus how far the image is from the ocular).
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The meridian line is marked to indicate the date by the location of the solar image. Information is embedded with the meridian line to tell how to correct for the equation of time (deviation between local time and solar time due to the varying speed of the Earth in its elliptical orbit around the Sun). The system was designed to check the accuracy of the Gregorian calendar and to indicate the date of the Vernal Equinox.
Timekeeping
Monastic prayer times were tightly regulated, so methods were needed to tell time. This was done in the daytime by observing the shadows of important structures. Sundials appeared around the 5th century, many of which showed the canonical prayer times in addition to, or instead of, the time of day.
Ancient astronomers had a dilemma. Civilization generally reckoned time by the sun, but the stars made a better master clock. The Earth rotates once every 23 hours, 56 minutes, and 4.1 seconds. However, due to the Earth revolving around the sun, it takes, on average, about 3 minutes and 56 seconds longer for the sun to go from one noon to the next.
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Furthermore, that time varies from season to season. In the summer, it takes about an extra 30 seconds for the Sun to go from one noon to the next. In the winter, it takes about 30 seconds less. A clock based on the Sun takes 24 hours (86,400 seconds) to mark one day. The fact that the Sun gets ahead of and behind this timing over the year is corrected as needed. Therefore, to indicate correct civil time, sundials needed a correction factor.
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However, precision was apparently not important to early timekeepers, since they did not appear to correct for the then-known annual drift of solar time. As the Earth orbits around the Sun, it speeds up and slows down due to being in an elliptical orbit (faster when closer to the Sun and slower when farther away). This causes a sundial to get ahead of the average 24-hour day in January when the Earth is closer to the sun and thus traveling faster than in July, when the opposite is true.
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If you look at some modern globes, you will see a figure-eight symbol in the Pacific Ocean. This symbol is marked with the months and days of the year and has a scale parallel to the equator labeled “Scale of Time,” or “Equation of Time.” This figure-eight symbol is called the Analemma.
The Analemma can be used to correct for the aforementioned errors for any day of the year. Some modern sundials have the Analemma built into the gnomon such that the shadow indicates the corrected local time.
If you take a picture that includes the Sun at the same local time every day for a year, the Sun will trace the shape of the Analemma in the picture. The following picture was taken with a rigidly mounted camera left in place for one year. The images of the sun were taken about two weeks apart through a dark filter, allowing only a small portion of the Sun’s light to reach the photo sensor or film. This created the multiple-exposure image with the Sun tracing the shape of the Analemma. A final image was taken without the filter, using normal exposure techniques, without the sun in the frame. This resulted in a final image with a normal picture and the Sun-traced analemma in one photographic field.
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At night, time could be determined by the positions of stars. One of the aforementioned part-time astronomers was Pacificus of Verona, a 9th-century religious leader in Northern Italy. Pacificus introduced a horologium (a fancy name for a clock) that determined the time at night from the angle of Polaris around a faint star (probably HD112028 in Camelopardalis [the Giraffe]) that was very near the celestial north pole at the time. This would give the sidereal time, which is based on the actual time of one rotation of the Earth compared to the stars. Pacificus undoubtedly had a table to correct sidereal time to mean solar time, which is based on the average time it takes the Sun to reach high noon.
In the 7th century, mechanical clocks began to appear in monasteries. These clocks eventually replaced sundials and star clocks, although the mechanical clocks had to be periodically calibrated to the sun or stars.
Astrology (it’s a living)
Astrology was virtually the same discipline as astronomy in the Middle Ages. The Catholic Church had disavowed divination via astrology throughout the ages. Nevertheless, the Church used astrological symbology in connection with the movement of the Sun and Moon. Apparently, some progressive priests incorporated horoscopic astrology into their teachings. The Church’s rejection of astrology did not prevent some, if not many, rank-and-file Catholics from adhering to astrology. It was, of course, the job of the astronomer/astrologer to calculate horoscopes and make other astrological divinations. Recent archeological findings indicate that early medieval astrologers had the astronomical tools to compute which zodiacal signs were rising or the positions of planets at any particular date and time.
Tools of the medieval astronomer
The armillary sphere
The armillary sphere is said to be an astronomical instrument used to measure the positions of stars and planets along with the celestial equator, tropics, the ecliptic, etc. However, all the drawings and pictures of armillary spheres I have seen lack mechanisms, such as independently movable rings and pointers, that would enable the measurement of unknown quantities or enhance the precision of known quantities. Although some apparently had sighting tubes to aid with alignment against the sky. Therefore, I believe that armillary spheres were essentially framework versions of celestial globes. They modeled the sky and were useful as teaching tools and pointers to celestial objects. Some appear to have mechanisms to align with the sky at different latitudes and sidereal times; the rings representing the sky could be aligned with the celestial poles and rotated to align with the stars at a particular date and time. However, these armillary spheres still appear to have lacked mechanisms to measure unknown angles, etc.
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The armillary sphere in Figure 99 has a mechanism to align it with the celestial pole at any northern latitude. It also has a mechanism to rotate the sphere to align it with the sky at any particular date and time. It has five parallel rings, representing the celestial equator, tropics, and Arctic and Antarctic circles. It also has a ring canted to these by 23.5 degrees, representing the ecliptic.
The astrolabe
The astrolabe was an instrument developed by the Arabs for measuring the positions of astronomical objects. It resembles a modern planesphere but was typically a precision instrument made from brass. It featured movable pointers to measure angles, particularly the altitude of an object above the horizon.
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Although made for astronomical use, they were also used by surveyors and others. It seems that no two astrolabes were quite alike, and many astronomers designed and made their own.
Sextants, quadrants, octants, and triquetrums
Sextants, quadrants, octants, and triquetrums are all instruments for measuring angles in parts of a circle. A quadrant could measure angles up to a quarter of a circle or 90 degrees. An octant could measure up to one-eighth of a circle or 45 degrees, and a sextant could measure up to one-sixth of a circle or 60 degrees. Smaller instruments were used for navigation or triangulation on land. Some were made very large to increase accuracy.
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Modern mirror sextants or mirror octants were developed in the 1700s. These use movable mirrors so that the user can bring the object being sighted, the Sun or a star, and the horizon next to each other. A second advantage of such instruments is that the object and horizon remain together even on a moving boat or ship.
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A triquetrum is similar to the above instruments except that it uses a straight scale instead of a curved one and was designed specifically for astronomical use. It purportedly overcame the difficulty of graduating (marking for making measurements) a curved surface. Not being schooled in instrument making, I cannot explain that difficulty. I also cannot find an adequate description of how a triquetrum was used. Nevertheless, the triquetrum was the primary instrument for measuring the altitude of celestial objects before the invention of the telescope.
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Metrological precision
You may wonder how medieval astronomers made their remarkably precise measurements with such primitive instruments. First of all, they used the largest versions of their instruments as was practical. An astrolabe with a diameter of 30 cm is about one-third as accurate as a triquetrum with an arm length of a meter. Some of these instruments, as shown in images in the previous chapter, were enormous. They also used geometry to obtain indirect measurements when necessary and averaged multiple measurements to enhance accuracy.
For example, let’s look at one way they measured the Sun's position relative to the background stars. They certainly couldn’t observe the Sun against the stars, so they had to use an indirect method. By the Middle Ages, astronomers could accurately predict the moon's position against the stars. To measure the Sun's position, they would measure it relative to the Moon when both were high in the sky (to avoid atmospheric refraction). Even though they couldn’t see the stars behind the Moon either, they could calculate its position. This yielded the Sun's position relative to the Stars. Of course, by the Middle Ages, astronomers could already accurately predict the Sun's position as well. However, this ability had been obtained by averaging such measurements over nearly two millennia.
Measuring the positions of other objects was also performed by measuring the position of one object relative to another. To determine the position of the celestial equator, one only needed to precisely know one’s latitude. The position of the celestial equator is determined by subtracting one’s latitude from one’s zenith (your zenith is straight up; the opposite is your nadir, which is straight down). Sighting along an imaginary disk fixed at this angle to the southern horizon would delineate the celestial equator. Other celestial coordinates were determined using a similar geometric approach
Terms learned in this chapter
Analemma
Armillary sphere
Astrolabe
Epagomenal days
Equation of time
Graduating
Occulus
Octant
Quadrant
Sextant
Triquetrum
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