Practical Medieval Astronomy (Summer 1999)

Practical Medieval Astronomy

(Summer 1999)

Astronomy in the high Middle Ages (12th -15th centuries) was a true science - based on sophisticated theory (as conveyed by Ptolemy in the Almagest) and by measurement. Ptolemy and other authorities were not taken strictly at their word, rather a continuous tradition of measurement obtained.

Why did people care about astronomy? Curiosity of course was important to some. But an overriding concern was the proper determination of when to celebrate Holy days, when to plant crops, etc. Of particularly great concern was the determination of Easter, a non trivial task. According to the Testament the Last Supper took place on a Thursday (the Passover meal), the Crucifixion on Friday, and the Resurrection the following Sunday. (Keep in mind - the Resurrection symbolized the rebirth of the World, it was of absolutely paramount importance to get it right.) The difficulty of determining Easter is due to the fact that it is based on the Hebrew calendar, a mixed Lunar and Solar calendar. The result is that Easter must be celebrated on the Sunday following the first full Moon of spring. Unfortunately, the Solar and Lunar theories of Ptolemy and thus of the Medieval period were not sufficient to predict the date of Easter for long time intervals - astronomical observation was required to bring theory into congruence with reality.

What are the main theories/observations current in the Middle Ages?

Solar Theory: The Sun is the most obvious and important celestial object. How do we explain and therefore predict seasons, etc. For example, how do we determine the length of a year accurately and precisely?
Lunar Theory: The Moon is the second most obvious and important celestial object (tides, biological cycles etc.). How do we explain and predict its phases, etc.
Celestial Theory: How do we explain the movement of the stars?
Planetary Theory: We will not discuss today - too complex (retrograde motion etc.).

Observations, Tools, and Models. The simplest models for explaining the various celestial motions are based on spherical motion. Spherical models are not only relatively simple mathematically, they also have a certain aesthetic and philosophical appeal. Aristotelian philosophy considered the sphere to be the perfect shape - thus it stands to reason that God in His/Her perfection would choose the sphere as the basis for the motion of the most perfect of objects, those in the celestial sphere. As it turns out, spherical models also do a good job of predicting the behavior of the Universe at the resolution possible with the unaided eye over short time periods. For example a spherical model of stellar movement is good for decades without corrections.

Example Models/Tools

Celestial Sphere: This is a globe with the stars and constellations represented on it. From the Greek's through the Medieval period the assumption was that in fact the stars existed as fixed objects on a "crystalline sphere" enclosing the spheres of the planets etc. Thus the celestial sphere at this period of history is a true model of the the natural world, not just the 3-D universe mapped onto the 2-D surface of a globe. The normal perspective is a "God's eye view," that is, looking at the sphere from the outside.
Armillary Sphere: In the armillary sphere only the major circles charecterizing the celestial sphere are represented as rings: the equator, the ecliptic, the tropics, the meridians, and the earth in its center. (The arctic and natarctic circles may also be represented.)
Planispheric Astrolabe: In this instrument the celestial sphere from the tropic of capricorn to the north celestial pole are projected onto a plane. It is thus a more compact model still capable of demonstrating/calculating teh phenomena modelled by the celestial sphere. In addition an alidade (sighting rule) on the back allows measurments of celestial objects to be taken.
Torquetum: Here the main circles of the armillary sphere are represented by flat disks: the base represents the horizon, the equatorial table represents the equator, the ecliptic table represents the Suns path in the sky, and the head represents the meridian. The torquetum is set up for measurements of celestial phenomena in all three coordinate systems. It may also be used for demonstrating the relationships between the various coordinate systems and make interconversions beteween them.

Solar anomaly: A spherical model of the Universe is reasonably successful, however, one may quickly find that the Sun does not move with uniform circular motion across the sky - it takes longer for the sun to go from the vernal equinox to the autumnal equinox than it does from the autumnal equinox to the vernal equinox (the sun moves across the sky slightly faster in winter than in summer, that is summer is longer than winter). How can this be explained? Today we say the sun and the earth are at the foci of an ellipse. But in ancient times circular orbits were preferred both for philosophy/religion and because the mathematics is easier.

So the challenge is to try to explain the solar anomaly using circular orbits. It turns out this is readily accomplished by assuming the Sun's orbit is offset, that is, the Earth is not at the center, but is slightly offset. With a proper offset the Sun's motion is readily modeled to an accuracy exceeding that of unaided vision. The Greek (and thus Medieval) solar model of Hipparchus/Ptolemy is good to one minute of arc. This is better than could be measured (it was not until about 1600 that measurements of one second were accomplished). Thus there is no reason to assume anything but circular motion!

Still, it would be nice if the Earth could be at the center of the Universe instead of offset to the side. It turns out that putting the Sun on an epicycle, a small circle riding on the larger orbital circle, where the Sun goes around the epicycle once for each revolution around its orbit give an identical path to the offset circle. That is the two solutions; circle plus epicycle and offset circle, are mathematically identical. The Greeks knew of both solutions and their equivalence. Ptolemy chose to believe in the epicycle solution as physical reality. It placed the Earth in the center and was more philosophically satisfying. (Note that there is nothing wrong with using philosophy, aesthetics, etc. to choose between two equivalent scientific theories. No one is being cheated or mislead.)

(Note that many European astrolabes have an offset calendrical circle on the back. This offset is intended to account for the solar anomaly, giving the proper number of days in each season etc. In fact not all examples are accurate, giving only apparent corrections. Many astrolabe makers probably did not understand the various projections involved in astrolabe construction and merely copied other instruments.)

Coordinate Systems

In making celestial observations, an important practical consideration is the coordinate system used. There are three important celestial coordinate systems: horizon, celestial equatorial, and ecliptic.

Horizon coordinates: This is the simplest system, measuring elevation above the horizon (altitude) and "compass" direction (azimuth). Altitude varies from 0° (in the plane of the horizon) to 90° (perpendicular to the plane of the horizon). Azimuth ranges from 0° (pointing to true north), increasing eastward around a circle to 360°. Horizon coordinates are easy to measure since the reference points are in the reference frame of the observer (the Earth's surface) and it is easy to make devices for making such measurements (such as self leveling astrolabes etc.). However, the disadvantage is the measurements made are dependent on locality - different numbers will be recorded for the same observation made in different places and at different times.
Celestial Equatorial Coordinates: In this case the reference is the sky itself - one may think of celestial equatorial coordinates being like a grid of meridians and parallels "painted on the sky." The advantage of these coordinates is that they rotate with the celestial sphere and are thus the same for all earthly observers. For equatorial coordinates the elevation is referred to as the Declination, and is measured as the angular distance above (north of, +) or below (-) the equatorial plane in degrees. The second coordinate or direction is then measured as the angle eastward along the equatorial plane. But now a reference point must be defined, since a circle has no beginning or end! The vernal equinox is defined as zero. This angle, the Right Ascension, is measured in units of time, eastward from 0 - 24 hours (1 hr = 15°). (Note that the fractional units are minutes and seconds for both time and angle measurements, but the minutes and seconds are not the same size!)
Ecliptic Coordinates: Again the reference points will be in the sky, but in this case the plane of the ecliptic will be used instead of the equatorial plane. The elevation, known as the celestial latitude, is now measured as the angular distance above (north of, +) or below (-) the plane of the ecliptic (the path of the Sun on the celestial sphere). The second direction is now measured along the ecliptic, again eastward from the vernal equinox, but now in degrees. Traditionally ecliptic coordinates were measured in signs. For 12 zodiac signs have 360°/12 = 30° each. The vernal equinox is the first point of Aries (the Ram). Thus 5° = Aries 5°, 37° = Taurus 7° etc. Similarly, a difference of 90° along the ecliptic would be reported as three signs apart.

References:

Evans, James. The History & Practice of Ancient Astronomy. Oxford University Press, Oxford (1998).
Lindberg, David C. The Beginnings of Western Science: The European Scientific Traditions in Philosophical, Religious, and Institutional Context, 600 B.C. to A.D. 1450. University of Chicago Press. Chicago (1992).
McClusky, Stephen C. Astronomies and Cultures in Early Medieval Europe. Cambridge University Press, Cambridge (1998).