early astronomy || arabic astronomy
TRANSCRIPT
CHAPTER 8
Arabic Astronomy
Greek astronomy came to an end in Europe with the collapse of Hellenistic civilization not long after Ptolemy's time. But it was carried on by the Arabs, or rather by the people of the middle-eastern Arabic-speaking Islamic civilization that arose as a result of Mohammed's conquest in the seventh century A.D. This civilization comprised not only Arabs but Persians and Turks, as well as Moors, Kurds, and others. Writers on architecture use the word "Saracenic" to describe this culture, but historians of seience seem to prefer "Arabic." Arabic astronomy is a substantial and specialized subject; here I can deal only with some of the more interesting highlights.
Serious Arabic astronomy started through contact with India. At any rate, the earliest surviving Arabic work that is anywhere near complete is the Zij at sind-hind of al-Khwarizmi (born shortly before A.D. 800). Zij is an Arabic word often used for astronomical tables and sind-hind is an arabicized version of the Sanskrit siddhiinta. The zij used Indian parameters [135].
Two consequences of the contact with India were important not just for astronomy but for mathematics in general. One was the introduction of the Hindu-Arabic numerals
/! f ~ 0'1 VA9
(still to be seen, for example, on automobile number plates in Cairo), which evolved into our familiar 1, 2, 3, 4, 5, 6, 7, 8, 9, O. Even sexagesimal calculation is much easier with these digits than with either Babylonian wedges or Greek letters, and Europe eventually changed to pure decimal calculations, as the Chinese had been doing all along, though those astronomers who quote angles in degrees, minutes, and seconds instead of decimals of a degree have not yet completed the change. The other important consequence was the replacement of tables of chords by tables of sines.
190
H. Thurston, Early Astronomy© Springer-Verlag New York, Inc. 1994
F
E
T
Na~i
r ai
-Din
's t
heor
y of
the
mot
ion
of
a pl
anet
.
T:
the
eart
h.
E:
Pto
lem
y's
equa
nt.
EF
is
of c
onst
ant
leng
th (
equa
l to
the
rad
ius
of P
tole
my'
s de
fere
nt)
and
rota
tes
arou
nd E
at
a co
nsta
nt s
peed
(in
the
lo
ngit
udin
al p
erio
d of
the
pla
net)
. FG
= G
C =
iTE
. FG
ro
tate
s ar
ound
F t
wic
e as
fas
t as
EF
aro
und
E b
ut
in t
he o
ppos
ite
dire
ctio
n, s
tart
ing
wit
h T
EF
G i
n a
stra
ight
lin
e.
GC
is
para
llel
to
TE.
Thi
s en
sure
s th
at t
he a
ngle
EF
G
is eq
ual
to t
he a
ngle
GC
F,
whi
ch e
nsur
es t
hat
C i
s on
th
e lin
e E
F.
C
is th
e ce
nter
of
the
epic
ycle
. It
mov
es u
nifo
rmly
rou
nd
G,
whi
ch m
oves
uni
form
ly r
ound
F,
whi
ch m
oves
uni
form
ly
roun
d E
.
The
mot
ion
of t
he p
lane
t ro
und
C is
the
sam
e as
in
Pto
lem
y's
theo
ry.
(a)
FIG
UR
E 8
.1.
E
D
T
Na~ir
ai-D
in a
nd P
tole
my
com
pare
d.
D:
cent
er o
f P
tole
my'
S d
efer
ent.
C
p:
cen
ter
of Ptol~my's
epic
ycle
. en
: ce
nter
of
al-D
in's
epi
cycl
e.
The
lin
e fr
om E
to
the
cent
er o
f th
e ep
icyc
le i
s th
e sa
me
in b
oth
theo
ries
. C
p is
the
poi
nt w
here
thi
s lin
e cr
osse
s th
e de
fere
nt.
(b)
;J>
.....
:>l
cr'
(i'
;J>
~
.....
0 =- 0 3 '<
......
\Q
.....
192 8. Arabic Astronomy
FIGURE 8.2.
The Arabs translated Ptolemy's Almagest and other works. Indeed, the very name Almagest is a version of the Arabic name al-majasti for the work which Ptolemy called the Syntaxis [136]. More important, most of the Hypotheseis ton Planomenon would have been irretrievably lost, were it not for the Arabic translation [137]. The Arabic theorists did not follow Ptolemy slavishly but disagreed on a number of points. For example, Ibn al-Haytham (A.D. 965-1040) wrote a treatise Al-shukiik 'ata Batlamyiis [Doubts about Ptolemy] objecting to motions that could not be produced by a combination of regular circular motions, particularly to the use of the equant [138].
Three centuries later, Na~ir ai-DIn (A.D. 1201-1294), also known as alTiisI, devised combinations of regular circular motions that reproduced closely the motion given by Ptolemy's theory (see Figure 8.1(a,b». The last part of his linkage is particularly interesting: the rotations of CG and CF (see Figure 8.1(a» make C move along EF, and so two regular circular motions combine to produce a straight-line motion. We will meet this again, as it was to be used by Copernicus (page 209) [139].
The theory was modified slightly by his pupil Qutb ai-DIn ai-ShIrazi (A.D. 1236-1311) and by Ibn al-Shatir (A.D. 1304-1376), who also devised a greatly improved theory for the moon [140].
Ptolemy's theory for the moon (page 148) gave an obviously incorrect ratio between the greatest and least distances of the moon from the earth.
Arabic Astronomy 193
FIGURE 8.3. Bust of Ulugh Beg. (Photograph by Ernest W. Piini.)
He had found it necessary to increase the apparent size of the epicycle at half moon, which he did by means of a crank that drew the epicycle nearer to the earth then. AI-Shatir instead increased the size of the epicycle: he had the moon moving round a small extra epicycle whose center moves round the epicycle just mentioned at such a speed that at half moon it is at A (see Figure 8.2) and so is effectively on an epicycle of radius CA, and at new moon and full moon it is at B, effectively on an epicycle of radius CB. This device was also used by Copernicus.
Arabic astronomers were also keen observers and measurers. Caliph al-Ma'mun had an observatory built in Baghdad in A.D. 829, Na~ir ai-Din established an observatory in Maragha in A.D. 1259, and Arabic astronomy culminated in the work of Ulugh Beg (A.D. 1394-1449) (Figure 8.3), whose enormous observatory at Samarkand was described on page
194 8. Arabic Astronomy
32. He produced tables based on an extremely accurate estimate of sin 1°, and he compiled a catalogue of stars with 1,018 entries.
Arabic astronomers were able to calculate parameters more accurately than the Greeks, partly because of the longer time-spans available, and partly because of their larger instruments. For example, al-Battanl (active at Raqqa between A.D. 878 and 918) found the obliquity of the ecliptic to be 23°35' [141]; Ulugh Beg found it to be 23°31'17" [142]. Here, reduced to decimals for ease of comparison, is a summary.
Approximate date Error
Eratosthenes 200 B.C. 23.86° 0.12° Ptolemy A.D. 140 23.86° 0.170
AI-Battan! A.D. 900 23.58° 0.01° Guo Shoujing A.D. 1280 23.56° 0.03° Ulugh Beg A.D. 1400 23.52° 0.00° Copernicus A.D. 1500 23.47° -0.04° Brahe A.D. 1600 23.525° 0.025°
AI-Battanl also estimated the length of the year by comparing the time of the autumn equinox in A.D. 880 with the one recorded by Ptolemy in A.D.
139. His result is 2! minutes too small (compared with modern estimates of the average length of the year at that date) [143]. Most of the error is due to Ptolemy, who put his equinox a day too late; had he put it on the right day al-Battani's estimate would have been only half a minute too small. Later, Ulugh Beg estimated the year to be 365 days, 5 hours, 49 minutes, 15 seconds; this is 25 seconds too large [144]. Here is a summary.
Error
Hipparchus 150 B.C. 365.24667 0.00433 AI-BattanI A.D. 900 365.24056 -0.00273 AI-Zarqali A.D. 1270 365.24225 0.00028 Guo Shoujing A.D. 1280 365.2425 0.00023 Ulugh Beg A.D. 1400 365.24253 0.00027 Copernicus A.D. 1500 365.24256 0.00030 Brahe A.D. 1600 365.24219 -0.00001
Improved parameters made improved astronomical tables possible, especially the Great Hakemite tables (about A.D. 1000) by Ibn Yunus, the Toledan tables, slightly later, of al-Zarqali, and the widely used Alphonsine tables, introduced in A.D. 1272 and so called because they were devised for King Alfonso X of Spain.
Arabic Astronomy 195
Arabic astronomy played a substantial role within Arabic culture, for example, in accurately determining the direction of Mecca from localities in the wide-ranging Islamic domain; but its main importance for the general history of astronomy lies in:
(i) the preservation of Ptolemy's work; (ii) the improved theory of the moon; and (iii) accurate determination of parameters.