Middle Ages - Arabic Astronomy
Chapter 3
(Cambridge)
http://www-gap.dcs.st-and.ac.uk/~history/HistTopics/Arabic_mathematics.html#72
After the fall of the Roman civilization and the burning of
the Alexandrian library, some scholars fled eastward. With the arrival of Islam
as a dominating force, the Arabs took up the science and astronomy. In
In this time, there were two main branches of astronomers
In the Islamic tradition, astronomy had 3 main purposes
1- Calendar keeping. Islam runs on a strictly lunar calendar. This means that their year is actually 11 days shorter than a solar year. For this reason, holidays like Ramadan mover slowly back through the solar calendar. It takes about 30 years to move completely through the solar calendar. The new month also starts with the sighting of the crescent moon just after sunset. Depending on where you are in the world, this may vary by 2-3 days. Also local land features, or weather can alter when the moon is first spotted again after the new moon.
2- In
Islam prayers are said 5 times a day – daybreak, sunset, nightfall, midmorning
and
3- The
third important tradition was geographical. The tradition is that mosques must
be oriented towards
Arab astronomers (who were not always necessarily Muslims) were also very mathematically oriented. One of their major references would have been Ptolemy’s Almagest. This work seems to have been translated into Arabic around 800- 900 A.D.
Many of the works of these Arabic astronomers would later
become available to the European scholars through
The Arabs were active in two main areas - compiling tables
of planetary motion, know as zij, and in producing
stellar catalogues.
One of the first astronomers around 900 A.D. to produce a set of tables that is probably one of the majors works in astronomy between Ptolemy and Copernicus was al-Battani. His work in particular would be influential on later astronomers such as Copernicus, Kepler and Tycho Brahe. His major work was the Kitab al- Zij, which would later be translated into latin as De Motu Stellarum (on the motion of stars)
In his work he includes a catalogue of 489 stars, refined the existing values for the length of the year, ( to a value of 365 days 5 hours 48 minutes 24 seconds), and of the seasons as well as values for the motion of constellation due to precession and the inclination of the ecliptic (Earth’s axial tilt)
One of the important advances he also makes is in the use of trigonometric functions for his calculations rather than geometric methods.
http://www-gap.dcs.st-and.ac.uk/~history/Mathematicians/Al-Battani.html
Many of his calculations and measurements seem to be more accurate than Ptolemy’s, and he improves on his numbers.
.
The work of other Arabic astronomer in producing zij will later on be the model for a set of tables called
the Alphonsine Tables, which are based on Ptolemy’s
Almagest and the calculations of the Arabic astronomers in
In the area of cataloguing 2 major catalogues were produced. These are what give us the Arabic names for the visible stars (like Betelgeuse, Mizar and Alcor). One was by Ulagh Beg – a noble who built his own observatory and compiled a catalogue of over 1000’s stars. The other was Al-Sufi whose
‘Book on the Constellations of Fixed Stars’ was an improvement on the catalogue found in Almagest.
The other work that was more mathematical in nature was the
work done on Almagest. The Arabs were
excellent mathematicians. They had gotten updates in trigonometry in the form
of sines, cosine, and tangents from
Two individuals in particular contributed to the removal of the equant and the eccentric (since these were deviations from true circular motion). These two concepts could not be reconciled with the physical reality of Aristotle model of heavenly spheres, so they tried to remove them
(Nasir) Al –Tusi in the 13th century and Al Shatir in the 14th century both developed systems that needed deferents and epicycles only. Although we do not know for sure, it seems as though Copernicus may have been familiar with the work of Al- Tusi in particular as he uses techniques that are very similar (something called the Tusi – couple). Al – Tusi also was the driving force behind the construction of Maragheh - the major Arabic observatory of this period. Built in 1262, it became a centre of Arabic science. Copernicus did know about Al-Battani’s work, as he quotes him directly in Revolutions, so he may have also used the techniques of other Arab astronomers.
The Arabs did not develop any new cosmology of their own, but seemed content to accept the Greek geocentric models of Aristotle and Ptolemy. Their major contribution is to improve on these works and preserve for the later renaissance scientist, as well as developing better mathematics for the European astronomers to use.
Chapter 4
During the
middle ages the ability to read Greek was lost in Europe and only a few
scattered texts about science and astronomy were kept in monasteries in
However in
the first couple of centuries of the second millennium, stable powers began to
emerge in
When the
Arabs were pushed out of the Iberian peninsula, they
left behind the written texts at their centres of learning, particularly in
In this
time frame astronomy and astrology are grouped in as a branch of
mathematics. Because Aristotle gave us
the ‘macrocosm’ (universe) is reflected in the ‘microcosm’ (human body),
physicians were also trained in astrology as part of the diagnosis of what was
wrong with a patient, depending on what happened in the skies.
Thomas
Aquinas (a catholic saint), who was and Italian Dominican friar is responsible
for the transposing of the world view of Aristotle and other Greek philosophers
into the Christian viewpoint, and in this way Aristotlian
physics and the geocentric model of the universe become part of the Christian
view of the world. The spheres of the Aristotle’s model fit nicely fit the
Christian interpretations of the Bible and with the Book of Genesis. The
outermost sphere becomes the firmament, the crystalline heavens book the
‘waters above the firmament’ and the outer most part the container of the
Universe is the ‘Empyreum’, the domain of God and the
Angels (page 77)
At this
time the Alphonsine Tables, are translated from an
Arabic text based on the Almagest, and become the major source on planetary
motion. In the more mathematical sense, Ptolemy’s model dominates the way in
which planetary motions are calculated.
Earlier Toledo Tables of motion are replaced by the Alphonsine
tables (named after Alphonse X who was the patron) .
These tables are based on the calculations from the Almagest.
In the
early 1400’s there is an influx of Greek scholars into Italy and that part of
Europe as they are fleeing the Muslim/Arabic conquest of the middle east, and
the fall of Constantinople in 1453, bringing with them Greek versions of the
works of Aristotle, Ptolemy and others.
Nicholas
Copernicus (1473-1543) was a well educated church canon. This was not a
religious position with the church, but a secular, or administrative one. He
was a physician, and at that time physicians were trained in astrology as it
was thought that the skies (the macrocosm) were reflected in the behaviour of
the human body (the microcosm) so that to accurately diagnose a persons illness you needed to understand the motions of the
heavens. He was also trained in mathematics, and many aspects of astronomy were
taught at that point as a branch of mathematics.
Copernicus
worked out a heliocentric model of the solar system. He correctly placed the
sun at the centre and the Earth as simply one of the planets, with the moon
orbiting Earth. His model had the visible planets in the correct order, and at the correct
relative distances from the sun. However he made one major mistake in his
model. He retained circles for the orbits of planets, and therefore still
required a few epicycles to explain some aspects of planetary motion. His model is no more accurate than Ptolemy’s, nor are the
calculations any easier to do. This
model however, can explain certain observations, like the phases of Venus,
which cannot be explained by Ptolemy’s model, which among other things gained
it acceptance.
Also since it was a system where the model was the same for all planets, rather
than a separate one for each planet, it did have a certain mathematical
appeal.
Copernicus’
model (
It puts the
planets in their correct order, with the correct orbital periods. He also gets
the relative distances from the sun to each of the planets correct (orbital
radii)
Copernicus model has several major features.
1.
The sun is at the centre and all the planets orbit the
sun, while the moon orbits Earth. This changes the nature of objects in the
solar system, as now the sun is a different object from the other heavenly
bodies, while the Earth is just one of the planets. This also is in
contradiction to the Greek view that there can only be one centre of
revolution, as now there are two – planets going around the sun and the moon
orbiting Earth
2.
Retrograde is explained as simply the optical illusion
that occurs as Earth passes another planet
3.
The discrepancy of the behaviour of mercury and venus vs. mars, Jupiter and
Saturn, is explained as the difference between inner planets and outer planets.
4.
the planets
are in their correct order, and Copernicus figures out reasonably accurate
relative distances.
But, since
he is still stuck on the notion of circular orbits, he still needs to use some
epicycles to account for some planetary motion,
however, retrograde motion is now correctly identified as the optical illusion
of Earth passing other planets.
Copernicus’
work ‘ON the Revolution of Heavenly Spheres’ was finally published in 1543,
only shortly before his death. This work
is mostly a mathematical treatise, but the first few chapters do try to present
logical arguments for the physical reality of a heliocentric system. He argues for Earth being in motion and for
the sun as the centre.
Publication
of Revolutions is by some considered the beginning of the scientific
revolution. It is a scientist developing
his own model rather that using the ancient greek knowledge and simply trying to refine it. This brings revolutions into conflict with
both the religious and philosophical views of the day who both accept
Aristotle’s view of the cosmos.
In the publication of ‘revolutions’, one of
the editors a Lutheran by the name of Osiander, adds an
introduction where he implies that the author thinks this work is simply a
mathematical tool, not a real physical model.
This is not Copernicus’ intent, but is does cause problems later on.
Revolutions however was eventually put on the list of banned books by the
Church for discussing the heliocentric system, though it was definitely read by
later figures such as Galileo and Kepler.
Eramus Rheinhold a contemporary of Copernicus uses revolutions to
produce another set of planetary tables known as the “Prutenic
Tables.’ The Catholic Church also used the work of Copernicus to help in
their calculations in setting up the Gregorian calendar.
The
Copernican model is supported by certain observations like some of the motions
and size of the
planets observed that are not dealt with well by Ptolemy, but there are
a couple of things it implies that are not observed.