Ch. 3 Islamic Astronomy

CCCh. 3 Islamic Astronomy

• Formerly “Arabian astronomy” – too limiting geographically

• Used to be slighted coverage – “caretakers” for Greek works, esp. Almagest

• Now called “Islamic astronomy” – lands where Islam was dominant

• Not all were Muslims – some Christians, Jews, and others

Significant improvements of Ptolemy’s work, spatial orbits – but nothing fundamentally different; still appearances

Islamic Astronomy

Islamic Astronomy

Chronology of Islamic Astronomy600

700

800

900

1000

1100

1200

1300

1400

1500

1600

Hijrah – flight from Mecca to Medina = Year 1 of Islamic Calendar

Baghdad foundedHouse of Wisdom, Baghdad: translation of Greek works Almagest translated al-Khwarizmi (HW): zij; algebraThabit ibn Qrra (HW): trepidation

al-Battani: zij, sines etc.al-Sufi (HW): Book on Fixed Stars

Ibn Yunus: Hakemite Tables, obs’nsal-Haytham: Optics; On Configuration of World

al-Zarqala: Toledo Tables

Cairo Obs.

al-Tusi: Tusi couple, Maragha Obs.

Taqi al-Din Istanbul Obs.

Alfonsine TablesIlkhanic Tables,

Ulugh Beg Samarkand Obs.Sultanic Tables

Omar Khayyam: zij Isfahan Obs.

KEYArabia, Iraq, SyriaPersia (Iran)EgyptUzbekistanSpainTurkey

AD

Ibn al-Shatir, Rectification of Principles

Sack of Baghdad

• Islamic world common language = Arabic

• Mecca spiritual center of Islamic world

• “Islamic astronomy” basically started in Baghdad, founded 762 by Caliph al-Man’sur

• Man from India who could predict eclipses (773) founding of House of Wisdom in Baghdad by Caliph Harun al-Rashid (building upon al-Man’sur’s palace library), expanded by al-Ma’mun

Islamic Astronomy

• Islamic world had two main uses for astronomy:

in religious practice

as basis of astrology

• Astrology unacceptable to strict Muslims -- BUT…

• Astrology used by: rulers to guide decision-making

physicians in medical practice

Islamic Astronomy

Astronomy in Religious Practice• Calendar – month, year

• Prayer (salat or salah) – times, direction

Astronomy in Religion

• Calendar originally lunar – synodic months

• Later lunisolar, with empirical intercalation

• Muhammad decreed return to pure lunar calendar: 12 synodic months or 354 days

• Ramadan “floats” in Western calendar

• Month starts with hilal – first time Moon visible


HILAL • Very thin crescent immediately following new Moon

• Not easy to spot even in clear skies of Middle East

• Difficult to catch where skies cloudier – need formula tied to Sun-Moon distance


HILAL • Very thin crescent immediately following new Moon

• Not easy to spot even in clear skies of Middle East

• Difficult to catch where skies cloudier – need formula tied to Sun-Moon distance


• Pray at certain times of day (schematic):

(King)


• Crude estimate of times based on shadow lengths:

(King)Astronomy in Religion

• Later developed formula using spherical trigonometry

• Functionary at mosque to calculate times -- Muwaqqit

• Also calculate direction to Kaaba, shrine in Mecca = qiblah; again spherical trigonometry

(Hoskin)Astronomy in Religion

Table with times for candles to be extinguished

at Cairo mosque for each day of yearAstronomy in Religion

Tables with times all over world calculated using computer; chapter on history


Kaaba, shrine in Mecca

(hajj – pilgrimage required of faithful)

Alignment of Kaaba• Sides directly face four wind directions

• Main axis towards rising point of Canopus, a bright star in southern sky

• Shorter axis roughly aligned with summer solstice sunrise = winter solstice sunset

(King)


House of Wisdom (Bayt al-Hikmah)

Islamic Astrology

House of Wisdom (Bayt al-Hikmah)

• Originally translation from Greek, Syriac, and other languages into Arabic

• Later a center for scholarship and research = Institute for Advanced Studies

• Translation of Almagest in 827

• Under al-Ma’mun measurement of length degree of latitude Earth’s circumference = 26, 560 mi (7% too high)

Islamic Astrology

Zij: Planetary Tables and Other Matter• Modeled along lines of Ptolemy’s Handy Tables for practical use

• Later ones more elaborate, additional material:• mathematical tables

• star catalogues (usually Ptolemy’s corrected for precession)• collections of observational data on eclipses, conjunctions, etc.

More than 200 known, probably many more!Islamic Astrology

al-Khwarizmi

• Associated with House of Wisdom

• Zij al-Sindhind earliest surviving – based on Hindu, pre-Ptolemy Greek, and Persian elements

• Also wrote early book on algebra (Arabic name al-Jabr); first to solve equations using general methods

• His name basis of term algorithm in mathematics, computer science Islamic Astrology

Thabit ibn Qurra = Tobit

• Associated with House of Wisdom

• Contributed to mathematics and physics (statics)

• Criticized Ptolemy for inconsistencies between Almagest and Planetary Hypotheses

• Identified with concept of trepidation – variation in rate of precession and obliquity

Islamic Astrology

Trepidation• Suggested by two errors of Ptolemy:

underestimation of rate of precession as 1°/100 yr instead of 1°/72 yr overestimation of obliquity as 23° 51’ instead of 23° 34’

• Persisted through Copernicus’s time

Islamic Astrology

TrepidationRed circle highlights location of equinox

Islamic Astrology

Muhammad al-Battani = Albategnius • Not associated with House of Wisdom (Raqqa, in Syria)

• Az-Zij as-Sabi included advance of Sun’s apogee, accurate eccentric for orbit

• Length of year 365.2406; 365.2412 but for error of one day in Ptolemy (actual 365.2422); obliquity 23° 35’ (actual 23° 27’)

• Introduced half-chords, now known as sines, in tables; rigorous formula for spherical triangle

Islamic Astrology

Solar OrbitTo account for variable motion along ecliptic and unequal length of seasons, used eccentric:

(Hoskin)

apogee (farthest point from Earth)

longitude of apogee

Direction of advance =eastwards

Islamic Astrology

• Referenced extensively (almost two dozen times) by Copernicus later

Islamic Astrology

Abd al-Rahman al-Sufi = Azophi • Worked at court of Isfahan in Persia (Iran)

• Book on Fixed Stars – star catalogue with positions, magnitudes, and colors as well as pictures of constellations

• Mix of Ptolemaic and old Arabian constellations

• Positions based on Ptolemy, not new; magnitudes new

• Many star names are from Arabs, not necessarily original with al-Sufi

Islamic Astrology

• Fish are from old Arabian constellation

• Standing figure is Andromeda, a princess in Greek mythology

• Stippled area in front of the larger fish’s nose is M 31, the Andromeda Galaxy – visible to naked eye; few others noted(Hoskin, Cambridge Illustrated History)

Islamic Astrology

• Perseus, hero from Greek mythology, slaying Medusa, a Gorgon, to rescue Andromeda

• Star Algol (al-Ghul) in Medusa’s head (now known to be variable – close binary system)

(Hoskin, Cambridge Illustrated History)Islamic Astrology

Abd al-Rahman ibn Yunus • Astrologer of newly-founded city of Cairo

• Hakemite Tables (Zij al-Hakim al-Kabir) named for Caliph who sponsored his work (one of several)

• Tables unusual – contained extensive compilation of observations, his and earlier – conjunctions, eclipses

• Observed with somewhat large instruments Islamic Astrology

Ibn al-Haytham = Alhazen • Also associated with Cairo and Caliph al-Hakim

• Book on Optics important, influenced Roger Bacon and Kepler later; based on experiments

• Doubts on Ptolemy – criticized equant, eccentric; Ptolemaic system mathematical, not physical

• On the Configuration of the World – geocentric, homocentric similar to Aristotle

Islamic Astrology

Ibn al-Zarqali = Azarqueil/Arzachel • Resided in Toledo, in Spain

• Toledo Tables – based on al-Khwarizmi and al-Battani as well as Ptolemy

• Toledo Tables included descriptions of instruments and their use

• Translated into Latin by Gerard of Cremona, became popular in Europe

Islamic Astrology

• Invented two new instruments: saphea arzachelis (latitude-independent or universal astrolabe), equatorium (maybe Greeks earlier)

Islamic Astrology

(Wikipedia)

Equatorium

• Used to obtain positions of Sun, Moon, and planets • Based on Ptolemaic models• Worked like analog computer, replacing hand calculations using tables• Particular example shown is for Saturn

Islamic Astrology

Omar Khayyam • Persian; famous for poem The Rubaiyat of Omar Khayyam

• Noteworthy for mathematics, including work on parallel lines anticipating non-Euclidean geometry

• Also worked in philosophy and astronomy, the latter in connection with calendar reformIn other words, a polymath!

(but not mentioned in Hoskin!)

Islamic Astrology

The Rubaiyat of Omar Khayyam(FitzGerald translation – best known)

A Book of Verses underneath the Bough,A Jug of Wine, a Loaf of Bread--and ThouBeside me singing in the Wilderness--Oh, Wilderness were Paradise enow!

The Moving Finger writes: and, having writ,Moves on: nor all thy Piety nor WitShall lure it back to cancel half a Line,Nor all thy Tears wash out a Word of it.

***

• Connected with Isfahan Observatory 1074-1092

• Work led to Zij al-Malikshahi (named for Sultan Malik Shah I) and Jalali calendar (collaboration of eight including Khayyam)

• Jalali calendar based on Sun’s passage through 12 divisions of ecliptic, some elements from India

• Alternative to Islamic lunar calendar; solar = more practical for agriculture etc.Islamic Astrology

• Months of lengths ranging from 29 to 32 days; vary year to year

• Average length of year in Jalali calendar 365.24219858156 days vs. actual 365.2422464

• Calendar continued in use for centuries; with slight modification up to present in Iran

Islamic Astrology

Alfonsine Tables • Sponsored by King Alfonso X (“Wise”) of Leon and Castile; Christian but studied under Muslim and Jewish scholars

• Developed by team led by Isaac ben Said and Jehuda ben Moses Cohen

• Completed 1272

• Became “gold standard” for planetary tables in Europe for next three centuries

Islamic Astrology

Nasir al-Din al-Tusi • Religious scholar and mathematician at al-Alamut fortress until its fall to Mongols under Hulagu il Khan (grandson of Genghis Khan)

• Became astrologer to Hulagu; persuaded him to fund Maragha Observatory near Tabriz (Iran)

• Devised Tusi couple in 2-d and 3-d versions to eliminate eccentric, describe motion in latitude

• Established Maragha School of planetary theory

Islamic Astrology

Tusi couple

• Converts rotary motion to oscillation along a line – linear motion in superlunary region!

• Can be employed in variety of ways

• one element in Maragha School models

Islamic Astrology

Tusi couple and eccentric

• Dashed circle is path followed by point on small circle.• It is offset by diameter of small circle.• Earth could be at center of solid circle and displaced from center of dashed one.HOWEVER –Angular rate seen at C is constant.

• Result of work at Maragha was Ilkhanic Tables (1272; named for Hulagu)

• Eliminate equant by adding secondary epicycle

• 3-d Tusi couple to model motion in latitude

• Almost exactly contemporaneous with Alfonsine Tables but not nearly as well known in Europe Islamic Astrology

Ibn al-Shatir • Followed al-Tusi by about a century • Served as muwaqqit at large mosque in Damascus

• Worked in Maragha tradition; published improved models in Rectification of Principles

• Eliminated equants by adding epicycles, also added epicycle to correct problem with Ptolemy’s lunar model (2× distance variation)

• Tested models against observations -- empirical

Islamic Astrology

Ibn al-Shatir’s Lunar Model

• Uses secondary epicycle instead of Tusi couple

• Achieves good fit to Moon’s motion in longitude without Ptolemy’s 2× variation in distance

(Wikipedia)

Angular diameter related to distance – spatial orbit, not just motion in longitude

Islamic Astrology

Shortcomings of the Ptolemaic SystemAccording to Ancients

• Moon’s distance varied by factor of 2 in model; angular size varies only ~10%.

line of syzygy (new, full)

(Pannekoek)

(rotated 90° for easiercomparison)

Islamic Astrology

Ibn al-Shatir’s Solar Model

• Uses secondary epicycle (“director”), not Tusi couple• Center of deferent uniform around O• Director uniform retro around A AB || OCT• True Sun 2× around B• Matches Ptolemy’s motion in longitudeAngular diameter observations relative distance; spatial orbit!

director

(Saliba) (not accurate)

Ibn al-Shatir’s Model for Mercury• Modern: Mercury’s orbit largest eccentricity of planets

• Mercury’s angular diameter too small – can’t see disk

• Multiple epicycles as before to eliminate equant, eccentric

• Good fit to motion in longitude

• Some features of al-Shatir’s models showed up in Copernicus’s work later • Question of whether Copernicus knew al-Shatir’s models – transmission from Maragha through Constantinople?

• Byzantine Greek documents (scholar at Maragha) containing the Tusi couple in Italy by 15th century

• Lunar models nearly identicalStill considered inconclusive!

Islamic Astrology

Ulugh Beg • Grandson of Tamerlane (Timur), Turko-Mongol conqueror • Governor of Samarkand (Uzbekistan), succeeded father as Sultan after death

• Built up Samarkand as intellectual center –started madrasah (university or institute)

• Interested and knowledgeable about astronomy as well as mathematics

Islamic Astrology

• Inspired by Maragha, established Samarkand Observatory which produced Zij i-Sultani = Sultanic Tables (1437)

•Tables had improved parameters for planetary orbits, obliquity, length of year • Included sine and tangent tables

• Uniquely, included star catalogue with (mostly) newly measured positions (992, combined with few from al-Sufi), not just rehash of Ptolemy’s Islamic Astrology

Observatories in the Islamic Period

• Few major observatories, some small ones (e.g. Baghdad)• Only three major observatories lasted a couple of decades:

• Two major observatories were laid waste only a few years after their inception:

Isfahan (virtually unknown) Maragha (most famous) Samarkand (second most famous)

Cairo Istanbul

Islamic Observatories

Maragha Observatory

• Established by Nasir al-Din al-Tusi in 1259, right after Sack of Baghdad (and not too long before Gaocheng)

• Sponsored by Hulagu il Khan, Mongol ruler

• Large staff drawn from many lands: Persia (Iran), Syria, Anatolia (Turkey), and China -- not just Muslims; al-Urdi, al-Shirazi also important

• Extensive library of 40,000 volumesIslamic Observatories

• Large cylindrical observing tower • Fairly large (radius 14 ft) mural quadrant• Armillary sphere 5 ft radius


• After al-Tusi’s death in 1274 was succeeded by son

• Declined thereafter, abandoned by ca. 1350

• Ruins visited by Ulugh Beg, inspired him to establish Samarkand


Samarkand Observatory

• Established by Ulugh Beg in 1429

• Somewhat modeled after Maragha, influenced by Maragha School

• Directed by al-Kashi, Beg’s protegé and a mathematician (law of cosines)

• Instruments of large size – continued trend in Islamic astronomy to increase precision

Not always the case! Islamic Observatories

Armillary Sphere

• Human figures indicate size

• Armillary made of bronze (?), support frame made of wood

• Larger radius = longer baseline higher precision

BUT –

Instrument bends under own weight distorts scale loss of accuracy!

(Hoskin, Cambridge Illustrated History) Islamic Observatories

Mural quadrant 125-ft radius (Tycho’s much smaller)

View in meridian plane

Russian model of observatory


Mural quadrant 125-ft radius

ground level


Samarkand mural quadrantIslamic Observatories

• Effectively ended when Beg assassinated by son in 1449

• Less influential than Maragha


Istanbul Observatory

• Established by Taqi al-Din in 1577; almost exactly contemporaneous with Uraniborg, Tycho Brahe’s first observatory

• Sponsor was Ottoman Sultan Murad III; expected high-quality astrological advice

• Equipped with large armillary sphere, mural quadrant, triquetrum, astrolabe, saphea, hand-held quadrant, and sextant


Which instruments do you recognize?


• Comet appeared shortly after completion; Sultan requested advice.

• Taqi al-Din’s astrological prediction of Sultan’s glorious victory over the Persians failed badly, followed by plague and deaths of some important people.

• Clerical opponents of astrology prevailed, and observatory was destroyed in 1580.


Isfahan Observatory

• Isfahan capital of Seljuk Turk Empire in 11th century (S of Tehran)

• Observatory established 1074 by Sultan Malik Shah I and vizier; Omar Khayyam invited to be director

• First major observatory?

• Not much seems known about instruments


• Ended after assassination of vizier and death of Sultan, 1092; widow cut off support


Cairo Observatory

• Vizier of Caliph started construction of large observatory in 1120.

• Work continued after his death, but new vizier was executed in 1125 by Caliph for “communicating with Saturn.”

• Observatory was demolished and staff had to “flee for their lives” (Hoskin).


Torquetrum

• Devised to convert between three coordinate systems: altazimuth, equatorial, ecliptic

• Analog computer

• Invented by Abu Muhammad Jabir ibn Aflah = Geber around middle of 12th century in al-Andalus (Spain)


Islamic Astronomy -- Summary

• Observations – improved accuracy over Greeks, partly by using larger-sized instruments

• Theory – more sophisticated than Ptolemy, eliminated perceived problems with his models

• Advances in theory and analysis of observations connected with advances in mathematics; somewhat linked – astrologers and mathematicians

• Disconnect between mathematical models and physical reality – reluctant to pursue physics of orbits

• (Of course, neither did Europeans before Kepler!)

• See beginnings of what would become two significant institutions in the West:

Universities – foreshadowed by madrasahs such as the one at Samarkand (Greeks had academies)

Research observatories – large scale, with major instruments, staff, library as at Maragha

Islamic Astronomy

Accuracy Comparison – Tropical Year

All estimates predate the invention of the telescope around 1608.

Approximate date Length (days)

(Thurston)

Islamic Astronomy

Accuracy Comparison -- Obliquity

*

* Obliquity changes over time; error based on contemporary value.

Obliquity

Islamic Astronomy

End Ch. 3

Documents

Ch. 3 Islamic Astronomy