History of astronomy

The history of astronomy is the study of astronomical observances that date back to antiquity, with its origins in the religious, mythological, cosmological, calendrical, and astrological beliefs and practices of prehistory: vestiges of these are still found in astrology, a discipline long interwoven with public and governmental astronomy, and not completely disentangled from it until a few centuries ago in the Western World (see astrology and astronomy). In some cultures, astronomical data was used for astrological prognostication. Ancient astronomers were able to differentiate between stars and planets, as stars remain relatively fixed over the centuries while planets will move an appreciable amount during a comparatively short time.

Archaeoastronomy

Archaeoastronomy is the study of how people in the past "have understood the phenomena in the sky, how they used these phenomena and what role the sky played in their cultures". Early cultures identified celestial objects with gods and spirits. They related these objects (and their movements) to phenomena such as rain, drought, seasons, and tides. It is generally believed that the first astronomers were priests, and that they understood celestial objects and events to be manifestations of the divine, hence early astronomy's connection to what is now called astrology. Ancient structures with possibly astronomical alignments (such as Stonehenge) probably fulfilled astronomical, religious, and social functions. Calendars of the world have often been set by observations of the Sun and Moon (marking the day, month and year), and were important to agricultural societies, in which the harvest depended on planting at the correct time of year, and for which the nearly full moon was the only lighting for night-time travel into city markets. The common modern calendar is based on the Roman calendar. Although originally a lunar calendar, it broke the traditional link of the month to the phases of the moon and divided the year into twelve almost-equal months, that mostly alternated between thirty and thirty-one days. Julius Caesar instigated calendar reform in 46 BCE and introduced what is now called the Julian calendar, based upon the 365  1⁄4 day year length originally proposed by the 4th century CE Greek astronomer Callippus.

Early observations

Since 1990 our understanding of prehistoric Europeans has been radically changed by discoveries of ancient astronomical artifacts throughout Europe. The artifacts demonstrate that Neolithic and Bronze Age Europeans had a sophisticated knowledge of mathematics and astronomy. Among the discoveries are:

• Ancient bone sticks from Africa and Europe are marked in ways that track the moon's phases.
• The Warren Field lunar calendar is an ancient monument believed to correlate with phases of the Moon. It is considered to be the oldest lunar calendar to date.
• The Goseck circle in Goseck, Saxony-Anhalt, Germany, is considered by some to be the oldest solar observatory in the world.
• The Nebra sky disc reconfirms that astronomical knowledge and abilities of the people of the European Bronze Age included close observation of the yearly course of the Sun, and the angle between its rising and setting points at summer and winter solstice.
• The Kokino site is a Bronze Age observatory in the Republic of Macedonia that consists of two platforms having a combined area of about 5000 square meters. It uses stone markers to track the movement of the Sun and Moon on the eastern horizon. The observatory used the method of stationary observation, marking positions of the Sun at the winter and summer solstice, as well as the equinox.
• The Golden hats, rare artifacts from Bronze Age Europe, have symbols that likely represent a lunisolar calendar. The object would have permitted the determination of dates or periods in both lunar and solar calendars. The functions discovered so far would permit the counting of temporal units of up to 57 months. A simple multiplication of such values would also permit the calculation of longer periods, e.g. metonic cycles.

Mesopotamian astronomy

Astronomy can trace a large part of its roots to Mesopotamia from the observance of stars recorded as early as the Babylonian star catalogues. Although there are traces of Prehistoric astronomical observances, Babylonian astronomy owes its lot to Sumerian astronomy that was observed in the Fertile Crescent. Modern knowledge of Sumerian astronomy is indirect, only via the earliest Babylonian star catalogues that date from about 1200 BC. The fact that many star names appear in Sumerian suggests a continuity reaching into the Early Bronze Age. Babylonian astronomy strongly influenced Hellenistic astronomy, even up to medieval Islamic astronomy.

Sumerian astronomy

Early Mesopotamian astronomy is lent to the Sumerians who developed the earliest writing system, known as cuneiform, around 3500-3200 BC. The Sumerians developed a form of astronomy that had an important influence on the sophisticated astronomy of the Babylonians. Astral theology, which gave planetary gods an important role in Mesopotamian mythology and religion, began with the Sumerians. They also used a sexagesimal (base 60) place-value number system, which simplified the task of recording very large and very small numbers. The modern practice of dividing a circle into 360 degrees, of 60 minutes each, began with the Sumerians. The Sumerian constellations were inherited by Babylonian astronomy. There are various Babylonian star catalogues or lists of stars, notably the MUL.APIN, a text dating to the Late Bronze Age, ca. 14th to 12th century BC.

Babylonian astronomy

Babylonian astronomy refers to the astronomical methods and theories that were developed in Mesopotamia (modern-day Iraq), particularly in Babylonia but inheriting earlier concepts developed in Sumer. Babylonian astronomy was the basis for much of the astronomical traditions that later developed in Greek and Hellenistic astronomy, in Egyptian astronomy, in Sassanid Persian astronomy, in Syrian and Byzantine astronomy, in medieval Islamic astronomy, and in Western European astronomy.

The origins of Western astronomy can be found in Mesopotamia. In the course of the last few decades it has become increasingly clear that all Western efforts in the exact sciences are descendants in direct line from the work of the late Babylonian astronomers. Our knowledge of Sumerian astronomy is indirect, via the earliest Babylonian star catalogues dating from about 1200 BCE. The fact that many star names appear in Sumerian suggests a continuity reaching into the early Bronze Age.

Only fragments of Babylonian astronomy have survived, consisting largely of contemporary clay tablets with ephemerides and procedure texts, hence current knowledge of Babylonian planetary theory is in a fragmentary state. Nevertheless, the surviving fragments show that, according to the historian A. Aaboe, Babylonian astronomy was "the first and highly successful attempt at giving a refined mathematical description of astronomical phenomena" and that "all subsequent varieties of scientific astronomy, in the Hellenistic world, in India, in Islam, and in the West - if not indeed all subsequent endeavour in the exact sciences - depend upon Babylonian astronomy in decisive and fundamental ways."

Old Babylonian astronomy

See also: Babylonian star catalogues

Old Babylonian astronomy refers to the astronomy that was practiced during and after the First Babylonian Dynasty and before the Neo-Babylonian Empire.

The Babylonians were the first to recognize that astronomical phenomena are periodic and apply mathematics to their predictions. Tablets dating back to the Old Babylonian period document the application of mathematics to the variation in the length of daylight over a solar year. Centuries of Babylonian observations of celestial phenomena are recorded in the series of cuneiform tablets known as the Enûma Anu Enlil — the oldest significant astronomical text that we possess is Tablet 63 of the Enûma Anu Enlil , the Venus tablet of Ammisaduqa, which lists the first and last visible risings of Venus over a period of about 21 years. It is the earliest evidence that planetary phenomena were recognized as periodic.

The MUL.APIN contains catalogues of stars and constellations as well as schemes for predicting heliacal risings and settings of the planets, and lengths of daylight as measured by a water clock, gnomon, shadows, and intercalations. The Babylonian GU text arranges stars in 'strings' that lie along declination circles and thus measure right-ascensions or time intervals, and also employs the stars of the zenith, which are also separated by given right-ascensional differences. There are dozens of cuneiform Mesopotamian texts with real observations of eclipses, mainly from Babylonia.

Planetary theory

The first civilisation known to possess a functional theory of the planets were the Babylonians. The oldest surviving planetary astronomical text is the Babylonian Venus tablet of Ammisaduqa, a 7th-century BC copy of a list of observations of the motions of the planet Venus that probably dates as early as the second millennium BC. The Babylonian astrologers also laid the foundations of what would eventually become Western astrology. The Enuma anu enlil, written during the Neo-Assyrian period in the 7th century BC, comprises a list of omens and their relationships with various celestial phenomena including the motions of the planets.

The Sumerians, predecessors of the Babylonians who are considered to be the first civilization and are credited with the invention of writing, had identified at least Venus by 1500 BC. Shortly afterwards, the other inner planet Mercury and the outer planets Mars, Jupiter and Saturn were all identified by Babylonian astronomers. These would remain the only known planets until the invention of the telescope in early modern times.

Cosmology

In contrast to the world view presented in Mesopotamian and Assyro-Babylonian literature, particularly in Mesopotamian and Babylonian mythology, very little is known about the cosmology and world view of the ancient Babylonian astrologers and astronomers. This is largely due to the current fragmentary state of Babylonian planetary theory, and also due to Babylonian astronomy being independent from cosmology at the time. Nevertheless, traces of cosmology can be found in Babylonian literature and mythology.

In Babylonian cosmology, the Earth and the heavens were depicted as a "spatial whole, even one of round shape," with references to "the circumference of heaven and earth" and "the totality of heaven and earth." Their worldview was not exactly geocentric either. The idea of geocentrism, where the center of the Earth is the exact center of the universe, did not yet exist in Babylonian cosmology, but was established later by the Greek philosopher Aristotle's On the Heavens. In contrast, Babylonian cosmology suggested that the cosmos revolved around the "cult-place of the deity," who held ultimate authority as ruler of the cosmic polity. The Babylonians and their predecessors, the Sumerians, also believed in a plurality of heavens and earths. This idea dates back to Sumerian incantations of the 2nd millennium BC, which refers to there being seven heavens and seven earths.

Neo-Babylonian astronomy

Neo-Babylonian astronomy refers to the astronomy developed by Chaldean astronomers during the Neo-Babylonian, Achaemenid, Seleucid and Parthian periods of Mesopotamian history. A significant increase in the quality and frequency of Babylonian observations appeared during the reign of Nabonassar (747-734 BC), who founded the Neo-Babylonian Empire. The systematic records of ominous phenomena in astronomical diaries that began at this time allowed for the discovery of a repeating 18-year Saros cycle of lunar eclipses, for example. The Egyptian astronomer Ptolemy later used Nabonassar's reign to fix the beginning of an era, since he felt that the earliest usable observations began at this time.

During the 8th and 7th centuries BCE, Babylonian astronomers developed a new empirical approach to astronomy. They began studying philosophy dealing with the ideal nature of the universe and began employing an internal logic within their predictive planetary systems. This was an important contribution to astronomy and the philosophy of science, and some scholars have thus referred to this new approach as the first scientific revolution. This new approach to astronomy was adopted and further developed in Greek and Hellenistic astronomy. Classical Greek and Latin sources frequently use the term Chaldeans for the astronomers of Mesopotamia, who were, in reality, priest-scribes specializing in astrology and other forms of divination.

The last stages in the development of Babylonian astronomy took place during the time of the Seleucid Empire (323-60 BC). In the third century BC, astronomers began to use "goal-year texts" to predict the motions of the planets. These texts compiled records of past observations to find repeating occurrences of ominous phenomena for each planet. About the same time, or shortly afterwards, astronomers created mathematical models that allowed them to predict these phenomena directly, without consulting past records.

Empirical astronomy

Though there is a lack of surviving material on Babylonian planetary theory, it appears most of the Chaldean astronomers were concerned mainly with ephemerides and not with theory. Most of the predictive Babylonian planetary models that have survived were usually strictly empirical and arithmetical, and usually did not involve geometry, cosmology or speculative philosophy like that of the later Hellenistic models, though the Babylonian astronomers were concerned with the philosophy dealing with the ideal nature of the early universe.

In contrast to Greek astronomy which was dependent upon cosmology, Babylonian astronomy was independent from cosmology. Whereas Greek astronomers expressed "prejudice in favor of circles or spheres rotating with uniform motion," such a preference did not exist for Babylonian astronomers, for whom uniform circular motion was never a requirement for planetary orbits. There is no evidence that the celestial bodies moved in uniform circular motion, or along celestial spheres, in Babylonian astronomy.

Contributions made by the Chaldean astronomers during this period include the discovery of eclipse cycles and saros cycles, and many accurate astronomical observations. For example, they observed that the Sun's motion along the ecliptic was not uniform, though they were unaware of why this was; it is today known that this is due to the Earth moving in an elliptic orbit around the Sun, with the Earth moving faster when it is nearer to the Sun at perihelion and moving slower when it is farther away at aphelion.

Chaldean astronomers known to have followed this model include Naburimannu (fl. 6th–3rd century BC), Kidinnu (d. 330 BC), Berossus (3rd century BCE), and Sudines (fl. 240 BCE). They are known to have had a significant influence on the Greek astronomer Hipparchus and the Egyptian astronomer Ptolemy, as well as other Hellenistic astronomers.

Heliocentric astronomy

The only surviving planetary model from among the Chaldean astronomers is that of Seleucus of Seleucia (also known as Seleucus of Babylon) (b. 190 BC), who proposed a heliocentric model similar to that attributed to Aristarchus of Samos. Seleucus is known from the writings of Plutarch, Aetius, Strabo and Muhammad ibn Zakariya al-Razi. Strabo lists Seleucus as one of the four most influential Chaldean/Babylonian astronomers, alongside Kidenas (Kidinnu), Naburianos (Naburimannu) and Sudines. Their works were originally written in the Akkadian language and later translated into Greek. Seleucus, however, was unique among them in that he was the only one known to have proposed a heliocentric theory of planetary motion, where the Earth rotated around its own axis which in turn revolved around the Sun. According to Plutarch, Seleucus even proved the heliocentric system through reasoning, though it is not known what arguments he used. Plutarch stated:

Was [Timaeus] giving the earth motion ..., and should the earth ... be understood to have been designed not as confined and fixed but as turning and revolving about, in the way expounded later by Aristarchus and Seleucus, the former assuming this as a hypothesis and the latter proving it?

According to Strabo, Seleucus was also the first to assume the universe to be infinite. Seleucus is also known for being the greatest authority on tidal theory in antiquity.

According to Lucio Russo, his arguments were probably related to the phenomenon of tides. Seleucus correctly theorized that tides were caused by the Moon, although he believed that the interaction was mediated by the Earth's atmosphere. He noted that the tides varied in time and strength in different parts of the world. According to Strabo (1.1.9), Seleucus was the first to state that the tides are due to the attraction of the Moon, and that the height of the tides depends on the Moon's position relative to the Sun.

According to Bartel Leendert van der Waerden, Seleucus may have proved the heliocentric theory by determining the constants of a geometric model for the heliocentric theory and by developing methods to compute planetary positions using this model. He may have used trigonometric methods that were available in his time, as he was a contemporary of Hipparchus.

None of his original writings or Greek translations have survived, though a fragment of his work has survived only in Arabic translation, which was later referred to by the Persian philosopher Muhammad ibn Zakariya al-Razi (865-925).

Babylonian influence on Hellenistic astronomy

See also: Egyptian astronomy

Many of the works of ancient Greek and Hellenistic writers (including mathematicians, astronomers, and geographers) have been preserved up to the present time, or some aspects of their work and thought are still known through later references. However, achievements in these fields by earlier ancient Near Eastern civilizations, notably those in Babylonia, were forgotten for a long time. Since the discovery of key archaeological sites in the 19th century, many cuneiform writings on clay tablets have been found, some of them related to astronomy. Most known astronomical tablets have been described by Abraham Sachs and later published by Otto Neugebauer in the Astronomical Cuneiform Texts (ACT).

Since the rediscovery of the Babylonian civilization, it has become apparent that Hellenistic astronomy was strongly influenced by the Chaldeans. The best documented borrowings are those of Hipparchus (2nd century BCE) and Claudius Ptolemy (2nd century CE).

Early influence on Greek astronomy

Greek astronomy was built on Mesopotamian foundations. They defined the Zodiac and at least another 18 constellations adapted by the Greeks:

The earliest direct evidence for the constellations comes from inscribed stones and clay writing tablets dug up in Mesopotamia (within modern Iraq)... It appears that the bulk of the Mesopotamian constellations were created within a relatively short interval from around 1300 to 1000 B.C [...]

The Mesopotamian groupings turn up in many of the classical Greek constellations. The stars of the Greek Capricorn and Gemini, for example, were known to the Assyrians by similar names - the Goat-Fish and the Great Twins. A total of 20 constellations are straight copies. Another 10 have the same stars but different names. The Assyrian Hired Man and the Swallow, for instance, were renamed Aries and Pisces.

Many scholars agree that the Metonic cycle is likely to have been learned by the Greeks from Babylonian scribes. Meton of Athens, a Greek astronomer of the 5th century BCE, developed a lunisolar calendar based on the fact that 19 solar years is about equal to 235 lunar months, a period relation already known to the Babylonians.

In the fourth century, Eudoxus of Cnidus wrote a book on the fixed stars. His descriptions of many constellations, especially the twelve signs of the zodiac, are suspiciously similar to Babylonian originals. The following century Aristarchus of Samos used an eclipse cycle of Babylonian origin called the Saros cycle to determine the year length. However, all these examples of early influence must be inferred and the chain of transmission is not known.

Influence on Hipparchus and Ptolemy

In 1900, Franz Xaver Kugler demonstrated that Ptolemy had stated in his Almagest IV.2 that Hipparchus improved the values for the Moon's periods known to him from "even more ancient astronomers" by comparing eclipse observations made earlier by "the Chaldeans", and by himself. However Kugler found that the periods that Ptolemy attributes to Hipparchus had already been used in Babylonian ephemerides, specifically the collection of texts nowadays called "System B" (sometimes attributed to Kidinnu). Apparently Hipparchus only confirmed the validity of the periods he learned from the Chaldeans by his newer observations. Later Greek knowledge of this specific Babylonian theory is confirmed by second-century papyrus, which contains 32 lines of a single column of calculations for the Moon using this same "System B", but written in Greek on papyrus rather than in cuneiform on clay tablets.

It is clear that Hipparchus (and Ptolemy after him) had an essentially complete list of eclipse observations covering many centuries. Most likely these had been compiled from the "diary" tablets: these are clay tablets recording all relevant observations that the Chaldeans routinely made. Preserved examples date from 652 BC to AD 130, but probably the records went back as far as the reign of the Babylonian king Nabonassar: Ptolemy starts his chronology with the first day in the Egyptian calendar of the first year of Nabonassar, i.e., 26 February, 747 BC.

This raw material by itself must have been hard to use, and no doubt the Chaldeans themselves compiled extracts of e.g., all observed eclipses (some tablets with a list of all eclipses in a period of time covering a saros have been found). This allowed them to recognise periodic recurrences of events. Among others they used in System B (cf. Almagest IV.2):

• 223 (synodic) months = 239 returns in anomaly (anomalistic month) = 242 returns in latitude (draconic month). This is now known as the saros period which is very useful for predicting eclipses.
• 251 (synodic) months = 269 returns in anomaly
• 5458 (synodic) months = 5923 returns in latitude
• 1 synodic month = 29;31:50:08:20 days (sexagesimal; 29.53059413... days in decimals = 29 days 12 hours 44 min 3⅓ s)

The Babylonians expressed all periods in synodic months, probably because they used a lunisolar calendar. Various relations with yearly phenomena led to different values for the length of the year.

Similarly various relations between the periods of the planets were known. The relations that Ptolemy attributes to Hipparchus in Almagest IX.3 had all already been used in predictions found on Babylonian clay tablets.

Other traces of Babylonian practice in Hipparchus' work are:

• first Greek known to divide the circle in 360 degrees of 60 arc minutes.
• first consistent use of the sexagesimal number system.
• the use of the unit pechus ("cubit") of about 2° or 2½°.
• use of a short period of 248 days = 9 anomalistic months.

Means of transmission

All this knowledge was transferred to the Greeks probably shortly after the conquest by Alexander the Great (331 BC). According to the late classical philosopher Simplicius (early 6th century AD), Alexander ordered the translation of the historical astronomical records under supervision of his chronicler Callisthenes of Olynthus, who sent it to his uncle Aristotle. It is worth mentioning here that although Simplicius is a very late source, his account may be reliable. He spent some time in exile at the Sassanid (Persian) court, and may have accessed sources otherwise lost in the West. It is striking that he mentions the title tèresis (Greek: guard) which is an odd name for a historical work, but is in fact an adequate translation of the Babylonian title massartu meaning "guarding" but also "observing". Anyway, Aristotle's pupil Callippus of Cyzicus introduced his 76-year cycle, which improved upon the 19-year Metonic cycle, about that time. He had the first year of his first cycle start at the summer solstice of 28 June 330 BC (Julian proleptic date), but later he seems to have counted lunar months from the first month after Alexander's decisive battle at Gaugamela in fall 331 BC. So Callippus may have obtained his data from Babylonian sources and his calendar may have been anticipated by Kidinnu. Also it is known that the Babylonian priest known as Berossus wrote around 281 BC a book in Greek on the (rather mythological) history of Babylonia, the Babyloniaca, for the new ruler Antiochus I; it is said that later he founded a school of astrology on the Greek island of Kos. Another candidate for teaching the Greeks about Babylonian astronomy/astrology was Sudines who was at the court of Attalus I Soter late in the 3rd century BC.

In any case, the translation of the astronomical records required profound knowledge of the cuneiform script, the language, and the procedures, so it seems likely that it was done by some unidentified Chaldeans. Now, the Babylonians dated their observations in their lunisolar calendar, in which months and years have varying lengths (29 or 30 days; 12 or 13 months respectively). At the time they did not use a regular calendar (such as based on the Metonic cycle like they did later), but started a new month based on observations of the New Moon. This made it very tedious to compute the time interval between events.

What Hipparchus may have done is transform these records to the Egyptian calendar, which uses a fixed year of always 365 days (consisting of 12 months of 30 days and 5 extra days): this makes computing time intervals much easier. Ptolemy dated all observations in this calendar. He also writes that "All that he (=Hipparchus) did was to make a compilation of the planetary observations arranged in a more useful way" (Almagest IX.2). Pliny states (Naturalis Historia II.IX(53)) on eclipse predictions: "After their time (=Thales) the courses of both stars (=Sun and Moon) for 600 years were prophesied by Hipparchus, ...". This seems to imply that Hipparchus predicted eclipses for a period of 600 years, but considering the enormous amount of computation required, this is very unlikely. Rather, Hipparchus would have made a list of all eclipses from Nabonasser's time to his own.

Sassanid astronomy

See also: Zij and Science and technology in Iran

The capital of the Sassanid Persian Empire, the city of Ctesiphon, was founded in Mesopotamia. Astronomy was studied by Persians and Babylonians in Ctesiphon and in the Academy of Gundishapur in Persia. Most of the astronomical texts during the Sassanid period were written in the Middle Persian language. The Zij al-Shah, a collection of astronomical tables compiled in Persia and Mesopotamia over two centuries, was the most famous astronomical text from the Sassanid period, and was later translated into Arabic.

Islamic astronomy

Main: Islamic astronomy

Islamic astronomy comprises the astronomical developments made in the Islamic world, particularly during the Islamic Golden Age (9th–13th centuries), and mostly written in the Arabic language. These developments mostly took place in the Middle East, Central Asia, Al-Andalus, and North Africa, and later in the Far East and India. It closely parallels the genesis of other Islamic sciences in its assimilation of foreign material and the amalgamation of the disparate elements of that material to create a science with Islamic characteristics. These included Greek, Sassanid, and Indian works in particular, which were translated and built upon.

After the Islamic conquest of Persia, the province of Mesopotamia came to be known as Iraq in the Arabic language. During the Abbasid period of the region's history, Baghdad was the capital of the Arab Empire, and for centuries, remained the centre of astronomical activity throughout the Islamic world. Astronomy was also studied in Basra and other Iraqi cities. During the Islamic period, Arabic was adopted as the language of scholarship, and Iraq continued to make numerous contributions to the field of astronomy, up until the 1258 sack of Baghdad, when many libraries were destroyed and scientific activity in Iraq came to a halt. Despite this, the work that did survive had an impact on the subsequent development of astronomy, through the medieval Arabic-Latin translation movement in Europe and Maragheh observatory in Persia.

Islamic astronomy played a significant role in the revival of Byzantine and European astronomy following the loss of knowledge during the early medieval period, notably with the production of Latin translations of Arabic works during the 12th century. Islamic astronomy also had an influence on Chinese astronomy and Malian astronomy. A significant number of stars in the sky, such as Aldebaran, Altair and Deneb, and astronomical terms such as alidade, azimuth, and nadir, are still referred to by their Arabic names. A large corpus of literature from Islamic astronomy remains today, numbering approximately 10,000 manuscripts scattered throughout the world, many of which have not been read or catalogued. Even so, a reasonably accurate picture of Islamic activity in the field of astronomy can be reconstructed.

See also

• Babylonian star catalogues
• Babylonian calendar
• Babylonian mathematics
• Egyptian astronomy
• Hebrew astronomy
• Islamic astronomy
• Islamic science and technology

Resources

• Aaboe, Asger. Episodes from the Early History of Astronomy. New York: Springer, 2001. ISBN 0-387-95136-9
• Jones, Alexander. "The Adaptation of Babylonian Methods in Greek Numerical Astronomy." Isis, 82(1991): 441-453; reprinted in Michael Shank, ed. The Scientific Enterprise in Antiquity and the Middle Ages. Chicago: Univ. of Chicago Pr., 2000. ISBN 0-226-74951-7
• Kugler, F. X. Die Babylonische Mondrechnung ("The Babylonian lunar computation.") Freiburg im Breisgau, 1900.
• Neugebauer, Otto. Astronomical Cuneiform Texts. 3 volumes. London:1956; 2nd edition, New York: Springer, 1983. (Commonly abbreviated as ACT).
• Toomer, G. J. "Hipparchus and Babylonian Astronomy." In A Scientific Humanist: Studies in Memory of Abraham Sachs, ed. Erle Leichty, Maria deJ. Ellis, and Pamela Gerardi, pp. 353–362. Philadelphia: Occasional Publications of the Samuel Noah Kramer Fund 9, 1988.

External links

• The Arab Union for Astronomy and Space Sciences (AUASS)
• King Abdul Aziz Observatory
• History of Islamic Astrolabes