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 Baghdad, the ruler of the time built the ‘House of Wisdom’, one of the great libraries and learning institutions of the time.  From about 800 A.D. – 1200 A.D. Arabic becomes the language of science in the western world. Arabic astronomy was influenced by a number of different sources including India, and the Greek astronomy of Aristotle and Ptolemy.

 

In this time, there were two main branches of astronomers

 

  1. Islamic  - this dealt with the issues of times and dates for religious purposes
  2. Arabic – this was the mathematical tradition based mostly on Ptolemy’s almagest that looked at planetary motion and star catalogues.

 

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 midday. For this reason mathematical calculations were necessary to standardize when prayers should be said according to the shadows cast. This would need to be adjusted depending on latitude. To do the astronomical observations and mathematics required for time keeping the position of muwaqqit was developed.

3-     The third important tradition was geographical. The tradition is that mosques must be oriented towards Mecca.  The Kaaba is actually oriented on the bright star Canopus on one axis and the minor axis is oriented on the summer solstice sunrise.  This involved some more sophisticated geometrical calculations, and models were later developed to this purposed.

 

 

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 Toledo Spain. 

 

The Arabs were active in two main areas - compiling tables of planetary motion, know as zij, and in producing stellar catalogues. Main of our modern stellar names are actually Arabic in origin from this time period.

 

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 Toledo.

 

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 India, so they could improve Ptolemy’s work.  One of their main goals was to remove the equant.

 

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.

 

 

Europe in the Middle Ages and Copernicus

              

Chapter 4 Cambridge

 

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 Europe. Knowledge wasn’t entirely lost, as the Church still had to be able to calculate the date for Easter. Some knowledge of constellations was stilled maintained, and some rudimentary astrological knowledge.

 

However in the first couple of centuries of the second millennium, stable powers began to emerge in Europe and with stable countries the quest for knowledge and the existence of universities and libraries emerge.

 

When the Arabs were pushed out of the Iberian peninsula, they left behind the written texts at their centres of learning, particularly in Toledo, Spain. Gerard of Cremona, in particular did a great deal of work in translating texts from the Arabic into Latin or European languages. This gives the Europeans access to works of Ptolemy, Aristotle, Plato etc.

 

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 (Cambridge page 91) does several things correctly.

 

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.

 

  1. Lack of parallax of stars  -  Copernicus answer  - well maybe the heavens are bigger than we think, so it is just too small to measure.
  2. Phases of Venus  -  Copernicus’ model implies we should see Venus go through phases -  this had not yet been observed.