Practical Medieval Astronomy
(Fall 2004)
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 antarctic 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).
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- © R. Paselk
- Last modified 18 October 2004
Medieval Science & Scientific
Instruments