Transcript CC - UF Astronomy

CC
Ch. 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 o
but nothing fundamentally different; still appearances
Islamic Astronomy
Islamic Astronomy
Chronology of Islamic Astronomy
600 AD
Arabia, Iraq, Syria
Persia (Iran)
Egypt
Uzbekistan
Spain
Turkey
Hijrah – flight from Mecca to Medina = Year 1 of Islamic Calendar
700
800
Baghdad founded
House of Wisdom, Baghdad: translation of Greek works
Almagest translated
al-Khwarizmi (HW): zij; algebra
Thabit ibn Qrra (HW): trepidation
900
KEY
al-Battani: zij, sines etc.
al-Sufi (HW): Book on Fixed Stars
1000
al-Haytham: Optics; On Configuration of
World
1100
Ibn Yunus: Hakemite Tables, obs’ns
al-Zarqala: Toledo Tables
Omar Khayyam: zij
Isfahan Obs.
Cairo Obs.
1200
al-Tusi: Tusi couple, Sack of Baghdad
Ilkhanic Tables, Alfonsine Tables
Maragha Obs.
1300
Ibn al-Shatir, Rectification of Principles
1400
Ulugh Beg
Sultanic Tables
Samarkand Obs.
1500
1600
Taqi al-Din
Istanbul Obs.
• 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 alMan’sur’s palace library), expanded by alMa’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
Astronomy in Religion
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
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
• Pray at certain times of day (schematic):
(King)
Astronomy in Religion
• 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 year
Astronomy in Religion
Tables with times all over world calculated using
computer; chapter on history
Astronomy in Religion
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)
Astronomy in Religion
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
Trepidation
Red 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 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
(Hoskin)
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
Islamic Astrology
(Hoskin, Cambridge Illustrated History)
• 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)
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 alHakim
• 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 AristotleIslamic Astrology
Ibn al-Zarqali = Azarqueil/Arzachel
• Resided in Toledo, in Spain
• Toledo Tables – based on al-Khwarizmi and alBattani 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
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
(Wikipedia)
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 reform
In 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 Thou
Beside me singing in the Wilderness-Oh, Wilderness were Paradise enow!
***
The Moving Finger writes: and, having writ,
Moves on: nor all thy Piety nor Wit
Shall lure it back to cancel half a Line,
Nor all thy Tears wash out a Word of it.
• Connected with Isfahan Observatory 10741092
• 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 =
Islamic Astrology
more practical for agriculture etc.
• 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 alAlamut 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 --
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
Angular diameter related to
distance – spatial orbit, not
just motion in longitude
(Wikipedia)
Islamic Astrology
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
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)
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 alShatir’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
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:
 Isfahan (virtually unknown)
 Maragha (most famous)
 Samarkand (second most famous)
• Two major observatories were laid waste only a
few years after their inception:
 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 volumes
Islamic Observatories
• Large cylindrical observing tower
• Fairly large (radius 14 ft) mural quadrant
• Armillary sphere 5 ft radius
Islamic Observatories
• 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
Islamic Observatories
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
View in
meridian plane
Russian model of observatory
Mural quadrant 125-ft
radius (Tycho’s much
smaller)
Islamic Observatories
Mural quadrant
125-ft radius
ground level
Islamic Observatories
Samarkand mural quadrant
Islamic Observatories
• Effectively ended when Beg assassinated by son
in 1449
• Less influential than Maragha
Islamic Observatories
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, handheld quadrant, and sextant
Islamic Observatories
Which instruments do
you recognize?
Islamic Observatories
• 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.
Islamic Observatories
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
Islamic Observatories
• Ended after assassination of vizier and death of
Sultan, 1092; widow cut off support
Islamic Observatories
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).
Islamic Observatories
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 Observatories
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
Approximate date
Length (days)
(Thurston)
All estimates predate the invention of the telescope
around 1608.
Islamic Astronomy
Accuracy Comparison -- Obliquity
Obliquity
*
* Obliquity changes over time; error based on contemporary value.
Islamic Astronomy
End Ch. 3