Humboldt State University ® Department of Chemistry

Richard A. Paselk

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?

  1. 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?
  2. 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.
  3. Celestial Theory: How do we explain the movement of the stars?
  4. 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

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.


  1. Evans, James. The History & Practice of Ancient Astronomy. Oxford University Press, Oxford (1998).
  2. 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).
  3. McClusky, Stephen C. Astronomies and Cultures in Early Medieval Europe. Cambridge University Press, Cambridge (1998).

Workshops Medieval Science & Scientific Instruments


© R. Paselk
Last modified 6 August 1999