Ch. 3 Islamic Astronomy

1. Ch. 3 Islamic Astronomy CC

2. Formerly “Arabian astronomy” – too limiting geographically • Used to be slighted coverage – “caretakers” for Greek works, esp. Almagest • Nowcalled“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

3. Islamic Astronomy

4. Chronology of Islamic Astronomy KEY AD • Arabia, Iraq, Syria • Persia (Iran) • Egypt • Uzbekistan • Spain • Turkey Hijrah – flight from Mecca to Medina = Year 1 of Islamic Calendar Baghdad founded House of Wisdom, Baghdad: translation of Greek works Almagest translated al-Khwarizmi (HW): zij; algebra ThabitibnQrra (HW): trepidation al-Battani: zij, sines etc. al-Sufi (HW): Book on Fixed Stars IbnYunus: Hakemite Tables, obs’ns al-Haytham: Optics; On Configuration of World al-Zarqala: Toledo Tables Isfahan Obs. Omar Khayyam: zij Cairo Obs. Maragha Obs. Sack of Baghdad al-Tusi: Tusi couple, Alfonsine Tables Ilkhanic Tables, Ibn al-Shatir, Rectification of Principles Samarkand Obs. Sultanic Tables Ulugh Beg Taqi al-Din Istanbul Obs.

5. 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

6. 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

7. Astronomy in Religious Practice • Calendar – month, year • Prayer (salator salah) – times, direction Astronomy in Religion

8. 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 Astronomy in Religion

9. 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 Astronomy in Religion

10. 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 Astronomy in Religion

11. Pray at certain times of day (schematic): (King) Astronomy in Religion

12. Crude estimate of times based on shadow lengths: (King) Astronomy in Religion

13. Laterdeveloped formula usingspherical trigonometry • Functionary at mosque to calculate times-- Muwaqqit • Also calculate direction to Kaaba, shrine in Mecca = qiblah; again spherical trigonometry Astronomy in Religion (Hoskin)

14. Table with times for candles to be extinguished at Cairo mosque for each day of year Astronomy in Religion

15. Tables with times all over world calculated using computer; chapter on history Astronomy in Religion

16. Kaaba, shrine in Mecca (hajj – pilgrimage required of faithful)

17. 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) Astronomy in Religion

18. House of Wisdom (Bayt al-Hikmah) Islamic Astrology

19. 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

20. 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

21. 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

22. ThabitibnQurra = 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

23. 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

24. Trepidation Red circle highlights location of equinox Islamic Astrology

25. 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

26. Solar Orbit To account for variable motion along ecliptic and unequal length of seasons, used eccentric: apogee (farthest point from Earth) Direction of advance =eastwards longitude of apogee Islamic Astrology (Hoskin)

27. Referenced extensively (almost two dozen times) by Copernicus later Islamic Astrology

28. 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

29. 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 Islamic Astrology (Hoskin, Cambridge Illustrated History)

30. 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) Islamic Astrology (Hoskin, Cambridge Illustrated History)

31. Abd al-RahmanibnYunus • 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

32. 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

33. 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

34. Invented two new instruments: sapheaarzachelis (latitude-independent or universal astrolabe), equatorium (maybe Greeks earlier) Islamic Astrology

35. 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 (Wikipedia)

36. 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 reform In other words, a polymath! (but not mentioned in Hoskin!) Islamic Astrology

37. 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.

38. 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

39. 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

40. 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 Jehudaben Moses Cohen • Completed 1272 • Became “gold standard” for planetary tables in Europe for next three centuries Islamic Astrology

41. Nasir al-Din al-Tusi • Religious scholar and mathematician at al-Alamut fortress until its fall to Mongols under Hulaguil 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

42. 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

43. 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.

44. Result of work at Maragha was Ilkhanic Tables (1272; named for Hulagu) • Eliminate equant by adding secondary epicycle • 3-d Tusi coupleto model motion in latitude • Almost exactly contemporaneous with Alfonsine Tables but not nearly as well known in Europe Islamic Astrology

45. Ibn al-Shatir • Followed al-Tusi by about a century • Served as muwaqqitat 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

46. 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 Angular diameter related to distance – spatial orbit, not just motion in longitude Islamic Astrology (Wikipedia)

47. Shortcomings of the Ptolemaic System According to Ancients • Moon’s distance varied by factor of 2 in model; angular size varies only ~10%. line of syzygy (new, full) (rotated 90° for easier comparison) (Pannekoek) Islamic Astrology

48. 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 longitude director Angular diameter observations  relative distance; spatial orbit! (Saliba) (not accurate)

49. Ibn al-Shatir’s Model for Mercury • Modern: Mercury’s orbit largest eccentricityofplanets • Mercury’s angular diameter too small – can’t see disk • Multiple epicycles as before to eliminate equant,eccentric • Good fit to motion in longitude

50. 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 identical Still considered inconclusive! Islamic Astrology