Astronomy, Calenders, and Time in the Middle Ages (Summer 1998)

Astronomy, Calenders, and Time in the Middle Ages

(Summer 1998)

Romans lost interest and ability to do technical stuff towards end of empire (5th cent?)

How dark were the Dark Ages? When I was young I thought the entire period of the Middle ages was pretty dismal, especially for the life of the mind. Now the High Middle ages are thought quite respectable, in the opinions of many producing, as examples, some of the greatest architecture (Gothic Cathedrals) and one of the greatest technical inventions (the clock). The High Middle Ages was both a period of renewal and of creativity. It was a renaissance before the more famous Renaissance.

Two of the preeminent symbols of the Medieval period, the tower clock and the European Astrolabe indicate the importance of time to the Medieval mind. These are both products of the High Middle Ages. What are their precursors? Did they arise out of a vacuum? In today's view most of the products of the High Middle Ages and of the Renaissance were built on a background of centuries of prior work - they achieved much because the stood on the shoulders of giants. In this workshop we want to explore this background and discover just how broad these shoulders were.

Consider how a thirteenth-century scientist/scholar might view his position. Very loosely, I will take that perspective for our discussion:

Here in the thirteenth century of our Lord Jesus' reign we have made much progress in understanding God's work. I would dare to say, after centuries of ignorance brought on by pagan invaders and their unenlightened understanding, we now possess greater knowledge of the world than any in the past. We have not only regained the knowledge of the Greeks, including that of the Master (Aristotle), we now are adding to that knowledge and going beyond it. Today I wish to demonstrate this premise to you with a review of our knowledge of the calender, time, and astronomy.

All calenders and time are based on the movement of the Heavens. In particular the movements of three 'bodies' have been used to determine time and season: the Sun, the Moon, and the Firmament, that is the sphere of the fixed stars, itself. Four different astronomies have been important to determine time and date: the division of the year by observing the position of the Sun, the computation of the date of the Easter Full Moon, the determination of time for prayer by observation of the stars, and the geometrical astronomy of the ancients, particularly Ptolemy.

To understand these astronomies we will look at the sphere of the fixed stars, and then at a model of the Earth-centered Universe known as an armillary sphere.

The sphere of the fixed stars can be represented on a celestial globe. Here we see a map of the sky with the major visible stars fixed on a spherical surface. With this model we are viewing the sphere from the outside - taking a "God's-eye-view," if you will. The celestial globe is held in a ring, representing the meridian. The meridian is a circle passing through the north and south poles of the sky. It is also the highest apparent point reached by a celestial body during its orbit. Because the celestial sphere rotates as a rigid shell, some stars will reach higher points in the sky, but in each case the peak will be on the meridian.

The apparent rotation of the sky is also dependent on our relative position on the Earth, that is our latitude. The latitude will determine the horizon we see. In our model the meridian ring fits into a horizon ring (in the case of the model use, the horizon was formed by the hole in the box in which the celestial sphere and meridian reside). We can now adjust the celestial sphere to correspond to our latitude by rotating the meridian ring within the horizon ring or plate. To adjust the celestial sphere we take our latitude (the angle of our location above the equator which is at 0°, while the north pole is at 90°), and subtract it from 90°. The meridian ring is then turned until the difference is aligned with the horizon. For example, for the workshop we can assume a latitude of approximately 40°. Thus the 60° mark on the meridian ring is set to the horizon.

The planets, which in ancient times included the Sun and Moon, move in the sky as opposed to the fixed stars (planet is derived from the Greek meaning wanderer). This does not imply that they wander all over the sky - all of the planets as well as the Sun and Moon have paths within the band of the ecliptic. We can use the armillary sphere to demonstrate the remaining aspects of the Earth centered Universe.

The main sphere in the armillary is defined by three perpendicularly arranged rings. (Note that these rings are set in the sphere of the fixed stars, so the armillary and celestial spheres are readily related to one another.) In the discussion below the numbers correespond to the numbers on the linked image:

The solsticial colure (2): this ring passes through the north and south poles as well as the summer and winter solstices (the points of highest and lowest meridional positions of the Sun during the year).
The equinoctial colure (1): this ring passes through the north and south poles as well as the the spring and autumnal equinoxes (the points of the Sun's passage when the length of day and night are equal - equal night).
The equator (3): the ring which divides the sphere into equal northern and southern hemispheres.

A fourth ring, the ecliptic band (4) is set at an angle of 23.5° to the equator on an axis through the two equinoxes. The ecliptic defines the annual path of the Sun through the year. It is marked with the signs of the Zodiac graduated in degrees so one may find the position of the Sun in the constellations of the fixed stars on any particular day. As mentioned above the paths of the Moon and planets also fall within the area defined by the ecliptic. Four additional rings, parallel to but above or below the equator, complete the sphere. Beginning nearest the north pole we see:

The Arctic circle (5): this defines the latitude above which the Sun no longer rises and sets on a daily basis.
The tropic of Cancer (6): this circle defines the northernmost latitude reached by the Sun in its annual cycle, it is the northern turning point of the Sun's annual journey (thus tropic meaning turning).
The tropic of Capricorn (7): this circle defines the southernmost latitude reached by the Sun in its annual cycle, it is the southern turning point of the Sun's annual journey.
The Antarctic circle (8): this defines the latitude below which the Sun no longer rises and sets on a daily basis.

An axis (9) passes though the sphere via the poles. A ball centered on this axis represents the Earth. Small armillary spheres with the axis terminating in a handle below the south pole demonstrating the basic arrangement of the Earth-centered Universe, were frequently used in lectures, and are often represented in art works.

The armillary sphere, like the celestial sphere may also be held in a meridian ring (10) by the shaft of the axis above. The sphere is then generally set in a stand with a horizon ring so it can be set to the local latitude as described above for the celestial sphere. The horizon ring is commonly marked with the four compass points, a degree scale, a calender scale, and a zodiac scale. The calendar and zodiac scales enable the user to correlate the day of the year with the Sun's position on the sky. (Note that the sky and the calendar drift relative to one-another on an approximately 23,000 year cycle - thus a conversion table is needed for the years of the instrument's intended use. Gradually the scales will drift out of sync and new conversion tables will be required. The basic armillary sphere however will be accurate for many millions of years.)

We can now set our armillary sphere to the local latitude as was done with the celestial sphere above, and follow the path of the Sun for any given day of the year. We may determine times of sunrise and sunset, meridian height of the Sun, etc. With this model of the Universe in hand, we can continue our discussion of the calendar and time.

The use of the Sun to monitor the seasons is both fundamental and ancient. The seasons after all determine times of planting, harvest etc. Of course pagans monitored the Sun's position from time immemorial, celebrating solstices and equinoxes, planting and harvesting festivals, etc. As the Church established its position during the early Middle ages, it took over these celebrations with Saint's Days to help the people overcome their pagan past.

Another mode of astronomy practiced in the Medieval period is the use of the stars to tell time.* This was long a tradition in Monasteries for determining the time for prayers. Of course one can only use stars to tell time at night. Telling time by the stars requires only the determination of a particular stars altitude, and knowing what its altitude should be at different hours. The pre-eminent instrument for telling time by the stars was the planispheric astrolabe.** (CR pp 66-9)

Let's now look at the lunar astronomy used to compute Easter. First, to bring perspective, Easter is the most important Holy day of the Christian calendar. It is the date for "reestablishing the time of Creation, the time of salvation in which humankind is renewed, to be once again at that time, in illo tempore. (SM, p 80, top) Remember that Jesus arose on the sunday following the Paschal meal. But the time of the Paschal meal is determined using the Hebrew lunar calendar. Christians wanted to express Easter in terms of the civil, not the Hebrew calendar.

In order to accomplish this we need to consider the determination of the dates of the spring equinox and the full Moon. (For a modern version of these calculations see CR pp 26-7.) This may seem simple. However, there are 365 1/4 days in one Julian year, while there are 12 lunar months of 29 1/2 days, giving a lunar year of 354 days. So our first task is to determine how frequently these two cycles will come into agreement. A little calculation will show that the full moon will fall on the same date approximately every 19 years (see Table 2, SM, p 83). *** Unfortunately we're not finished, Easter must also fall on a sunday, so we have another cycle to bring day of the week and day of the month into agreement, which occurs every 28 years. Combining these two cycles give a fully recurring system with a period of 532 years. Now the computus, or computation of the date of Easter using these cycles is fairly simple, requiring only arithmetic, but a table encompassing 532 years is a bit much. It is not only a lot to compute, it is a lot to copy! So, many early tables only covered a sequence of 5 x 19 years = 95 years (other cycles were also used***). The 95 year cycle almost gives an Easter cycle. Now you might say, wait a minute, its not that difficult to note when the full moon is, and figure out when Easter will be on the Sunday following. But keep in mind how important this Holy day is, and then recall that one also needed to know when to begin the Lenten Fast (40 days before Easter) as well as Ash Wednesday which is also linked. In fact, to get out the word etc. the date of Easter had to be known almost by Christmas! Finally, it was also felt important that all of Christendom should celebrate Easter on the same date! Thus the long time-line tables, and passionate theological disputes. (SM p84)

* The stars may also be used to monitor the seasons. One can look for the appearance and disappearance of stars near the southern horizon. This is really an indirect measure of solar altitude. That is the stars positions are fixed, but you can't see them in the daylight, so as the Sun goes down earlier in the winter, additional stars become visible. Noting the heliacal rising and setting of these southern stars can therefore provide another measure of time of year. This can be an important consideration in areas where clouds and overcast obscure viewing and one must use every available signal to accurately determine the solstices and equinoxes.

** This was made slightly more complex in Medieval times because of the use of unequal hours in time keeping, while the fixed stars keep equal time. Prior to the invention of the mechanical clock most cultures used systems of unequal hours, where the day is broken up into the same number of divisions summer or winter. Thus at European latitudes summer hours are about 1 1/4 hr long and winter hours would be about 3/4 hr long. Only at the equinoxes are unequal hours of the same length as equal hours. (CR pp 22-3)

***A very thorough discussion of the Lunar computus and the various cycles and bringing them into congruence is given in chapter 5 of McClusky (SM).

References : Much of this workshop is derived from McClusky. If you want to further pursue the concepts of astronomy and the calendar in the Middle Ages read McClusky. The astronomy books by Lippincott and by Ronan are written for beginners, but have much to offer even those familiar with observing the night sky. Both use historical examples, are profusely illustrated, and demonstrate historical instruments and modes of observing. Ronan is particularly interesting for the many home-made instruments he describes.

KL = Lippincott, Kristen. Eyewitness Science Astronomy. DK Publishing, New York (1994);
SM = McClusky, Stephen C. Astronomies and Cultures in Early Medieval Europe. Cambridge University Press, Cambridge (1998).
CR = Ronan, Colin A. The Practical Astronomer. Macmillan publishing Co. Inc., New York (1981).