# Astronomy

Astronomy was one of the oldest, most developed, and most esteemed exact
sciences of antiquity. Many of the mathematical sciences were originally
developed to facilitate astronomical research. Initial interest in astronomy
had its roots in astrology and the fascination with the powers and mysteries
of the heavens. Practical considerations, such as finding one's
direction during night travel or understanding the correlation between the
seasons of the year and the positions of the planets, provided additional
incentives for the study of astronomy. The Babylonians, Greeks, and Indians
had devised elaborate systems for the study of astronomy that went beyond
simple empirical observation and were characterized by various degrees of
mathematical rigor and sophistication. Before Islam, however, the Arabs had
no scientific astronomy. Their knowledge was empirical, and it was limited
to the division of the year into precise periods on the basis of the rising
and setting of certain stars. This area of astronomical knowledge was known
as *anwa*; it continued to attract attention under later Arab
astronomers after the rise of Islam, and its study gained much from the
mathematical methods employed by these astronomers.

From its beginnings in the ninth century through its maturity in the
sixteenth century, astronomical activity was widespread and intensive. This
activity is reflected in the large number of scientists working in practical
and theoretical astronomy, the number of books written, the active
observatories, and the new observations. Astronomy, it should be noted, was
unambiguously differentiated from astrology. Astrology continued to be
practiced and to draw on and encourage astronomical knowledge. In fact, a
good portion of the funding for astronomical research
was motivated by the desire to make astrological predictions. Nevertheless,
a clear line was drawn between the two disciplines. The vast majority of the
thousands of written works are on astronomy, whereas only a handful deal
with astrology. Many astronomers served as court astrologers, but many more
condemned astrology and distanced themselves from it. Distinct terms were
also used to refer to either field: *ilm ahkam al-nujum* or simply
*tanjim* referred to astrology, whereas *ilm al-falak, ilm
al-haya,* or *ilm al-azyaj* referred to the science of the
celestial orb, the science of the configuration of the heavens, and to major
astronomical treatises containing tables for the motion of the stars and
instructions on using these tables.

The first astronomical texts that were translated into Arabic in the eighth
century were of Indian and Persian origin. The earliest extant Arabic
astronomical texts date to the second half of the eighth century. Two
astronomers, Muhammad ibn Ibrahim al-Fazari (d. a. 777) and Yaqub ibn Tariq
(eighth century), translated an eighth-century Indian astronomical work
known as *Zij al-Sindhind* (a *zij* being an astronomical handbook
with tables). Sources indicate that they produced this translation after
770, under the supervision of an Indian astronomer visiting the court of the
Abbasid caliph al-Mansur (r. 754–75). Extant fragments of the
works of these two astronomers also reveal a somewhat eclectic mixing of
Indian parameters with elements of Persian origin as well as some from the
Hellenistic pre-Ptolemaic period. These fragments also reflect the use of
Indian calculation methods and the use of the Indian sine function in
trigonometry, in place of the cumbersome chords of arc used in Greek
astronomy. Late Arabic sources also contain references to *Zij
al-Shah*, a collection of astronomical tables based on Indian parameters,
which was compiled in Sasanid Persia over a period of two centuries.

Arab astronomers were first exposed to Persian and Indian astronomy, and they
continued to use some of the parameters and methods of these two traditions,
yet the greatest formative influence on Arabic astronomy was undoubtedly
Greek. In the early ninth century astronomers realized that the Greek
astronomical tradition was far superior to that of Persia or India, in both
its comprehensiveness and its use of effective geometrical representations.
One particular second-century Greek author, Ptolemy, and more specifically
one work by this author, the *Almagest,* exerted a disproportionate
influence on all of medieval astronomy through the Arabic period and until
the eventual demise of the geocentric astronomical system. That this text
exerted so much influence is neither accidental nor surprising, for it is
the highest achievement in Hellenistic mathematical astronomy and one of the
greatest achievements of all of Hellenistic science. Other works by Ptolemy,
commentaries on his works, and several treatises by other authors were also
used in conjunction with the *Almagest* and as introductions to it.
These include eleven short treatises in Greek, by different authors,
called the “Small Astronomy
Collection,” which were all translated into Arabic during the
ninth century.

In the *Almagest*, Ptolemy synthesized the earlier knowledge of
Hellenistic astronomy in light of his own new observations. The
book's main purpose was to establish the geometric models that
would accurately account for observational phenomena. A large part of the
work is dedicated to the methods for constructing various models and for
calculating their parameters. Ptolemy also provided tables for planetary
motions to be used in conjunction with these models. Of all the books of
antiquity, the *Almagest* represents the most successful work of
mathematical astronomy: its geometric representations of the universe
provided the most accurate and best predictive accounts for the celestial
phenomena. The Greek tradition of physical astronomy is reflected in the
*Almagest* and in Ptolemy's other influential work,
*Planetary Hypothesis*. According to this predominantly
Aristotelian tradition, the universe is organized into a set of concentric
spheres, each carrying a star and rotating around the stationary earth at
the center of the universe. Ptolemy adopted, at least in theory, these two
basic Aristotelian principles: that the earth is stationary at the center of
the universe and that the motion of heavenly bodies ought to be represented
by a set of perfectly uniform circular motions. In practice, however,
mathematical considerations often forced Ptolemy to disregard these
principles.

Arabic sources report at least four Arabic translations of the
*Almagest*, of which two are extant. The first is a translation by
al-Hajjaj ibn Matar in the first half of the ninth century. The second is a
translation by Ishaq, the son of the famous translator Hunayn; this second
translation was revised by Thabit ibn Qurra toward the end of the ninth
century. Separated by more than fifty years, the second translation
reflected the maturity of Arabic technical terminology; whereas certain
parts of the first translation lacked full clarity, the second translation
provided a coherent text that eliminated any need for further reference to
the Greek original.

The first extant original work of Arabic astronomy is
al-Khwarizmi's (fl. 830) *Zij al-Sindhind* (which is
unrelated to the translation of the Indian text mentioned earlier with same
name). This work contains tables for the movements of the sun, the moon, and
five planets, with explanatory remarks on how to use these tables. Most of
the parameters used by al-Khwarizmi are of Indian origin, but some are
derived from Ptolemy's *Handy Tables*, and no attempt is
made to harmonize the two sources. This work is significant not only for its
content but also because it was written simultaneously with the earliest
translations of the *Almagest*. The first introduction of Ptolemaic
astronomy into Arabic science thus occurred in the context of two
significant trends. First, research in Arabic astronomy went hand in hand
with translation; despite its manifest superiority, Ptolemaic astronomy
did not exclusively set the agenda for future research
in Arabic astronomy. The second trend was the selective use of parameters,
sources, and methods of calculation from different scientific traditions. As
a result, the Ptolemaic tradition was rendered receptive from the beginning
to the possibility of observational refinement and mathematical
restructuring. These revisionist tendencies characterize the first period of
Arabic astronomy.

A significant part of the intensive ninth-century astronomical research was
dedicated to the dissemination of Ptolemy's astronomy, not just
by translating parts or all of his work into Arabic, but also by composing
summaries and commentaries on it. Ptolemy's work was thus made
available and accessible to a large audience among the educated classes. In
the first half of the ninth century, al-Farghani (d. ca. 850), for example,
wrote *Kitab fi Jawami Ilm al-Nujum* (A compendium of the science of
the stars). This book was widely circulated in the Arabic version and also
in later Latin translations. This work provided a brief and simplified
descriptive overview of Ptolemaic cosmography, without mathematical
computations. Unlike the *Almagest*, however, it started with a
discussion of calendar computations and conversions between different eras.
Although its primary purpose was to introduce Ptolemaic astronomy in a
simplified way, it also corrected Ptolemy based on findings of earlier Arab
astronomers. Al-Farghani gave revised values for the obliquity of the
ecliptic, the precessional movement of the apogees of the sun and the moon,
and the circumference of the earth. This critical approach, thus far
restricted to the correction of constants and parameters, had already been
set by earlier astronomers at the beginning of the ninth century.

Under the Abbasid caliph al-Mamun, a program of astronomical observations was
organized in Baghdad and Damascus. Like any organized research project, this
program endowed astronomical activity in the Islamic world with formal
prestige. It also set a precedent for future support of scientific activity
by other rulers and established patronage as one of the modes of supporting
such activities. The professed purpose of this program was to verify the
Ptolemaic observations by comparing the results derived by calculation,
based on Ptolemaic models, with actual observations conducted in Baghdad and
Damascus some seven hundred years after Ptolemy. The results were compiled
in *al-Zij al-Mumtahan (*The verified tables), which is no longer
extant in its entirety but is widely quoted by later astronomers. The most
important correction introduced was to show that the apogee of the solar orb
moves with the precession of the fixed stars. On a more general note, this
program stressed the need for continuing verification of astronomical
observations and for the use of more precise instruments. The program also
represented the first recorded instance in history of a collective
scientific undertaking.

From its beginnings, Arabic astronomy set out to rectify and complement
Ptolemaic astronomy. Having noted several discrepancies between new
observations and Ptolemaic calculations, Arab astronomers then proceeded to
reexamine the theoretical basis of Ptolemy's results. This
critical reexamination took several forms. One example of the critical works
of the ninth century is *Fi Sanat al-Shams* (The book on the solar
year), which was wrongly attributed to the mathematician Thabit ibn Qurrah,
but was produced around his time. This work corrected some of
Ptolemy's constants, and although it retained
Ptolemy's geometrical representations, it questioned his
observations and calculations. Other astronomers devised enhanced methods of
calculation. New mathematical tools were introduced to modernize the
computational procedures. For example, in his *al-Zij al-Dimashqi* (The
Damascene zij) written around the middle of the ninth century, the
mathematician Habash al-Hasib (d. between 864 and 874) introduced the
trigonometric functions of sine, cosine, and tangent, which were at that
time unknown to the Greeks. Habash also worked on a problem that was not
treated in the Greek sources: he examined the visibility of the crescent
moon and produced the first detailed discussion of this complicated
astronomical problem. Habash is an example of an astronomer who undertook
his study to verify the results of the *Almagest*, but in the process
he expanded these results and applied them to new problems. Although the
general astronomical research of this period was largely conducted within
the framework of Ptolemaic astronomy, this research reworked and critically
examined the observations and the computational methods of Ptolemaic
astronomy and in a limited way was able to explore problems outside its
framework.

One of the main ninth-century scientists from whom several extant
astronomical manuscripts exist today is Thabit ibn Qurra (ca.
836–901). Thabit was a pagan from Harran (in southeast Turkey);
his native language was Syriac, but he was fluent in Greek and his working
language was Arabic. Thabit joined the Banu Musa circle in Baghdad, and
produced numerous works on several scientific disciplines. Of about forty
treatises on astronomy, only eight are extant. All the treatises reflect
Thabit's full command of Ptolemaic astronomy and illustrate the
level to which this astronomy was thoroughly absorbed by Arab astronomers. A
few of these are of particular interest. In one treatise, for example,
Thabit analyzed the motion of a heavenly body on an eccentric, and the model
he used was Ptolemaic. In contrast to Ptolemy's description,
which was stated without proof, Thabit provided a rigorous and systematic
mathematical proof with the aid of the theorems of Euclid's
*Elements*. In the course of this proof, Thabit introduced the
first known mathematical analysis of motion. For the first time in history,
he also referred to the speed of a moving body at a particular point. In
another work, Thabit provided general and exhaustive proofs
for problems that Ptolemy examined only for special
cases or for boundary conditions. Another work is exclusively devoted to
lunar visibility. Thabit's solution, which was far more complex
than that of Habash, exhibited the same mathematical rigor apparent
everywhere in his work: he proved the general law that applies to the
visibility of any heavenly body, then he applied this law to the special
case of the crescent moon. Thabit's work is significant because
it illustrates the high creativity of Arabic astronomy in its earliest
periods. The roots for this creativity lie in the application of diverse
mathematical disciplines to each other. This application had the immediate
effect of expanding the frontiers of various disciplines and introducing new
scientific concepts and ideas. The use of systematic mathematization
transformed the methods of reasoning and enabled further creative
developments in the diverse branches of science.

Another famous astronomer of this early period is Abu Abd Allah Muhammad ibn
Jabir al-Battani (ca. 858–929), who originally came from Harran
but lived in Raqqa in northern Syria. At Raqqa, al-Battani conducted
observations for more than thirty years. The results of his research were
recorded in *al-Zij al-Sabi* (The Sabian tables), which was translated
into Latin in the twelfth century and into Spanish in the thirteenth.
Although al-Battani did not contribute significantly to theoretical
astronomy, his meticulous observations enabled him to make some important
discoveries. For example, he noted the variations in the apparent diameters
of the sun and the moon and deduced, for the first time in the history of
astronomy, the possibility of an annular eclipse of the sun.

In the ninth century, then, Arabic astronomy had already struck deep roots.
It integrated all the knowledge there was to integrate from earlier
traditions and was justly positioned to surpass this knowledge. The
achievements of the ninth century laid the foundation for the high-quality
work in the following two centuries. The tenth and eleventh centuries
witnessed important developments in trigonometry, with dramatic effects on
the accuracy and facility of astronomical calculations. In this period steps
were taken toward the formal establishment of large-scale observatories.
Although the information from these two centuries is spotty and fragmented,
several extant sources provide evidence for significant attempts to
reevaluate Ptolemaic astronomy. In the tenth and eleventh centuries the
earlier examinations of Ptolemaic astronomy led to systematic projects that
rather than addressing the field in its totality, focused on specific
aspects of astronomy. The work of Abd al-Rahman al-Sufi (who was born in
Rayy and worked in the Iranian centers of Shiraz and Isfahan,
903–86) illustrates this tendency. In his famous book, *Kitab
Suwar al-Kawakib al-Thabita* (Book on the constellations), al-Sufi
reworked the star catalog of the *Almagest* on the basis of a corrected
value of 1°/66 years for the precessional movement (in the place
of Ptolemy's 1°/100 years), as well as
several
other new observations and verifications. Al-Sufi produced an accurate
representation of the constellations and their coordinates and magnitudes.
His work was translated into Latin and is the source of many Latin star
names of Arabic origin. Another example of the tendency to synthesize is Abu
al-Hasan Ali Ibn Yunus’ (Cairo, d. 1009) *al-Zij al-Hakimi
al-Kabir* (The Hakimi zij), a monumental work in eighty-one chapters,
of which only about one-half is preserved. The book is a complete treatise
on astronomy, which contains tables for the movement of
the heavenly bodies, their various parameters, and instructions on the use
of these tables. Here, too, the objective of the work was to provide an
exhaustive documentation of previous observations, subsequent verifications
or corrections of these, and new observations recorded by the author.

Some of the astronomers of this period were known as instrument builders and for their association with observatories. The astronomer Abu Mahmud Hamid al-Khujandi (d. a. 1000), for example, wrote several works on scientific instruments and built a large sextant at Rayy. The astronomer Abu al-Wafa al-Buzjani (940–98) worked in a large observatory built by the Buyid ruler Sharaf al-Dawla in the gardens of the royal palace in Baghdad. Like Abu Nasr Mansur ibn Iraq (d. a. 1036) of Ghazna, al-Buzjani was a mathematician-astronomer who made great contributions in the field of trigonometry. Although much of the trigonometric works of these early scientists is lost, ample information exists from the extensive discussion on these works by the illustrious scientist al-Biruni.

Al-Biruni was born in 973 in Khwarizm (modern-day Khorezm) and died in 1048
in Ghazna (in eastern Afghanistan). Among other places, he worked in Rayy,
where he collaborated with al-Khujandi. He also studied with Abu Nasr Mansur
ibn Iraq, who was a student of al-Buzjani. Al-Biruni considered these two
scholars as his teachers, and with them he shared a focused interest in
trigonometry and its application to astronomy. Al-Biruni's
native language was Persian, but he composed the vast majority of his works
in Arabic. He also knew Sanskrit, and as a result he had full command of
Indian astronomy in addition to the well-established Greek and Arabic
traditions. Al-Biruni wrote more than 150 works on most of the known
sciences of his time, including astronomy, mathematics, mathematical
geography, mineralogy, metallurgy, pharmacology, history, and philosophy.
Although only a third of his works are extant, these contain a wealth of
scientific and historical information. His *al-Oanun al-Masudi* (Canon
Macudicus) is a veritable treasure, which, as a great synthesis of the
Greek, Indian, and Arabic astronomical traditions, has been compared to the
synthesis produced in the *Almagest* by Ptolemy. The book is also a
history of Arabic astronomy through the early eleventh century, and it
provides the only extant source of information on many of the contributions
of earlier astronomers. The value of this and other historical works by
al-Biruni is further enhanced by his keen historical consciousness and
cultural sensitivity.

Advances in trigonometry resulting from the full integration of the Indian achievements in the field, as well as from new discoveries in the tenth and eleventh centuries, played a central role in the development of Arabic astronomy. This tendency is itself part of a larger phenomenon whereby the systematic mathematization of disciplines contributed to the expansion of their frontiers. Equipped with new and more rigorous mathematical tools, al-Biruni, like many of his predecessors and contemporaries, provided exhaustive studies of specialized topics within astronomy. His “exhaustive” treatises cover such topics as shadows; the theory, construction, and use of astrolabes; the coordinates of geographical locations; and many more. In most of these monographs, al-Biruni starts with a thorough critical overview of older theories and mathematical methods for solving the particular problems in question; he then proceeds either to choose one of these theories or to propose his own alternative theory. Al-Biruni's work as a whole represents a critical assessment of the state of mathematical astronomy through the early eleventh century. Such comprehensive surveys of earlier knowledge exhausted the possibilities of expanding the astronomical disciplines from within; to achieve further progress, scientists needed to move in new directions, devise new strategies, and explore new research programs.

Another characteristic of this period is the seemingly random use of old as
well as new mathematical methods in the solution of astronomical problems.
Thus the same author may have used an archaic method in one place and an
advanced method in another. Al-Biruni, for example, used both the old,
cumbersome Menelaus theorem as well as the new, elegant sine rule in several
solutions to the problem of determining the *qibla*, the direction that
Muslims have to face in prayers. This simultaneous use of different
mathematical procedures cannot be attributed to the slow dissemination of
scientific knowledge or to the limited circulation of this knowledge. There
is ample evidence for a high level of mobility and of efficient and speedy
communication among scientists working in various regions of the Muslim
world. Al-Biruni himself did not travel to Baghdad, but he apparently
corresponded with scientists there and was fully aware of scientific
developments there and elsewhere. The use of different methods is likely a
result of the increasing diffusion of scientific knowledge among large
segments of the educated elites. Within the broad ranks of these elites,
“full-time” scientists were expected to keep up with
the latest research in their fields, while scholars with partial interest in
science would be familiar only with older theories and methods. The use of a
variety of mathematical methods is thus an indication of the degree to which
scientific culture had filtered into society, and the extent to which it
became available to average members of the educated class.