Babylonian astronomy

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Babylonian tablet recording Halley's comet in 164 BC.

According to Asger Aaboe, the origins of Western astronomy can be found in Mesopotamia, and all Western efforts in the exact sciences are descendants in direct line from the work of the late Babylonian astronomers.[1] Modern knowledge of Sumerian astronomy is indirect, via the earliest Babylonian star catalogues dating from about 1200 BC. The fact that many star names appear in Sumerian suggests a continuity reaching into the Early Bronze Age.

The history of astronomy in Mesopotamia, and the world, begins with 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. Astrolatry, 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 great and very small numbers. The modern practice of dividing a circle into 360 degrees, of 60 minutes each hour, began with the Sumerians.

During the 8th and 7th centuries BC, 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.[2] 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.

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.[3] 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."[4]

Old Babylonian astronomy[edit]

Old Babylonian astronomy refers to the astronomy that was practiced during and after the First Babylonian Dynasty (ca. 1830 BC) and before the Neo-Babylonian Empire (ca. 626 BC).

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.[5][6][7] There are dozens of cuneiform Mesopotamian texts with real observations of eclipses, mainly from Babylonia.

Planetary theory[edit]

The Babylonians were the first civilization known to possess a functional theory of the planets. 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.[7] The Babylonian astrologers also laid the foundations of what would eventually become Western astrology.[8] The Enuma anu enlil, written during the Neo-Assyrian period in the 7th century BC,[9] comprises a list of omens and their relationships with various celestial phenomena including the motions of the planets.[10]


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.[11] This is largely due to the current fragmentary state of Babylonian planetary theory,[3] and also due to Babylonian astronomy being independent from cosmology at the time.[12] 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 circularly with the heavens and the earth being equal and joined as a whole.[13] 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, linked possibly chronologically to the creation by seven generations of Gods.[14]

Neo-Babylonian astronomy[edit]

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). The systematic records of ominous phenomena in Babylonian astronomical diaries that began at this time allowed for the discovery of a repeating 18-year Saros cycle of lunar eclipses, for example.[15] The Greco-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.

The last stages in the development of Babylonian astronomy took place during the time of the Seleucid Empire (323–60 BC). In the 3rd 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.

Arithmetical and geometrical methods[edit]

Though there is a lack of surviving material on Babylonian planetary theory,[3] it appears most of the Chaldean astronomers were concerned mainly with ephemerides and not with theory. It had been thought that 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,[16] though the Babylonian astronomers were concerned with the philosophy dealing with the ideal nature of the early universe.[2] Babylonian procedure texts describe, and ephemerides employ, arithmetical procedures to compute the time and place of significant astronomical events.[17] More recent analysis of previously unpublished cuneiform tablets in the British Museum, dated between 350 and 50 BC, demonstrates that Babylonian astronomers sometimes used geometrical methods, prefiguring the methods of the Oxford Calculators, to describe the motion of Jupiter over time in an abstract mathematical space.[18][19]

In contrast to Greek astronomy which was dependent upon cosmology, Babylonian astronomy was independent from cosmology.[12] 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.[20] There is no evidence that the celestial bodies moved in uniform circular motion, or along celestial spheres, in Babylonian astronomy.[21]

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 swifter when it is nearer to the Sun at perihelion and moving slower when it is farther away at aphelion.[22]

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[edit]

Main article: Seleucus of Seleucia

The only surviving planetary model from among the Chaldean astronomers is that of Seleucus of Seleucia (b. 190 BC), who supported Aristarchus of Samos' heliocentric model.[23][24][25] 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.[26] Seleucus, however, was unique among them in that he was the only one known to have supported the heliocentric theory of planetary motion proposed by Aristarchus,[27][28][29] 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.[30]

According to Lucio Russo, his arguments were probably related to the phenomenon of tides.[31] 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.[26]

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.[32]

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).[33]

Babylonian influence on Hellenistic astronomy[edit]

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[edit]

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 4th 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[edit]

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 2nd-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.[34]

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 tough 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[edit]

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), 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.

See also[edit]


  1. ^ Aaboe, Asger. "The culture of Babylonia: Babylonian mathematics, astrology, and astronomy." The Assyrian and Babylonian Empires and other States of the Near East, from the Eighth to the Sixth Centuries B.C. Eds. John Boardman, I. E. S. Edwards, N. G. L. Hammond, E. Sollberger and C. B. F. Walker. Cambridge University Press, (1991)
  2. ^ a b D. Brown (2000), Mesopotamian Planetary Astronomy-Astrology, Styx Publications, ISBN 90-5693-036-2.
  3. ^ a b c Asger Aaboe (1958). "On Babylonian Planetary Theories". Centaurus. 5 (3–4): 209–277. doi:10.1111/j.1600-0498.1958.tb00499.x. 
  4. ^ A. Aaboe (May 2, 1974). "Scientific Astronomy in Antiquity". Philosophical Transactions of the Royal Society. 276 (1257): 21–42. Bibcode:1974RSPTA.276...21A. doi:10.1098/rsta.1974.0007. JSTOR 74272. 
  5. ^ Pingree, David (1998), "Legacies in Astronomy and Celestial Omens", in Dalley, Stephanie, The Legacy of Mesopotamia, Oxford University Press, pp. 125–137, ISBN 0-19-814946-8 
  6. ^ Rochberg, Francesca (2004), The Heavenly Writing: Divination, Horoscopy, and Astronomy in Mesopotamian Culture, Cambridge University Press 
  7. ^ a b Evans, James (1998). The History and Practice of Ancient Astronomy. Oxford University Press. pp. 296–7. ISBN 978-0-19-509539-5. Retrieved 2008-02-04. 
  8. ^ Holden, James Herschel (1996). A History of Horoscopic Astrology. AFA. p. 1. ISBN 978-0-86690-463-6. 
  9. ^ Hermann Hunger, ed. (1992). Astrological reports to Assyrian kings. State Archives of Assyria. 8. Helsinki University Press. ISBN 951-570-130-9. 
  10. ^ Lambert, W. G.; Reiner, Erica (1987). "Babylonian Planetary Omens. Part One. Enuma Anu Enlil, Tablet 63: The Venus Tablet of Ammisaduqa". Journal of the American Oriental Society. 107 (1): 93. doi:10.2307/602955. JSTOR 602955. 
  11. ^ F. Rochberg-Halton (January–March 1988). "Elements of the Babylonian Contribution to Hellenistic Astrology". Journal of the American Oriental Society. American Oriental Society. 108 (1): 51–62 [52]. doi:10.2307/603245. JSTOR 603245. 
  12. ^ a b Francesca Rochberg (December 2002). "A consideration of Babylonian astronomy within the historiography of science". Studies in History and Philosophy of Science. 33 (4): 661–684. doi:10.1016/S0039-3681(02)00022-5. 
  13. ^ Norriss S. Hetherington (1993). Cosmology: historical, literary, philosophical, religious, and scientific perspectives. Taylor & Francis. p. 46. ISBN 0-8153-0934-1. 
  14. ^ Norriss S. Hetherington (1993). Cosmology: historical, literary, philosophical, religious, and scientific perspectives. Taylor & Francis. p. 44. ISBN 0-8153-0934-1. 
  15. ^ A. Aaboe; J. P. Britton; J. A. Henderson; Otto Neugebauer; A. J. Sachs (1991). "Saros Cycle Dates and Related Babylonian Astronomical Texts". Transactions of the American Philosophical Society. American Philosophical Society. 81 (6): 1–75. doi:10.2307/1006543. JSTOR 1006543. One comprises what we have called "Saros Cycle Texts," which give the months of eclipse possibilities arranged in consistent cycles of 223 months (or 18 years). 
  16. ^ Sarton, George (1955). "Chaldaean Astronomy of the Last Three Centuries B. C.E". Journal of the American Oriental Society. 75 (3): 166–173 [169–170]. doi:10.2307/595168. 
  17. ^ Aaboe, Asger (2001), Episodes from the Early History of Astronomy, New York: Springer, pp. 40–62, ISBN 0-387-95136-9 
  18. ^ Ossendrijver, Mathieu (2015). "Ancient Babylonian astronomers calculated Jupiter's position from the area under a time-velocity graph". Science. 351 (6272): 482–484. Bibcode:2016Sci...351..482O. doi:10.1126/science.aad8085. the Babylonian trapezoid procedures are geometrical in a different sense than the methods of … Greek astronomers, since the geometrical figures describe configurations not in physical space but in an abstract mathematical space defined by time and velocity (daily displacement). 
  19. ^ "Babylonian astronomers computed position of Jupiter with geometric methods". Retrieved 2016-01-29. 
  20. ^ David Pingree (December 1992). "Hellenophilia versus the History of Science". Isis. University of Chicago Press. 83 (4): 554–563. Bibcode:1992Isis...83..554P. doi:10.1086/356288. JSTOR 234257. 
  21. ^ Ulla Koch-Westenholz & Ulla Susanne Koch (1995). Mesopotamian astrology: an introduction to Babylonian and Assyrian celestial divination. Museum Tusculanum Press. pp. 20–1. ISBN 87-7289-287-0. 
  22. ^ David Leverington (2003). Babylon to Voyager and beyond: a history of planetary astronomy. Cambridge University Press. pp. 6–7. ISBN 0-521-80840-5. 
  23. ^ Neugebauer, Otto E. (1945). "The History of Ancient Astronomy Problems and Methods". Journal of Near Eastern Studies. 4 (1): 1–38. doi:10.1086/370729. 
  24. ^ Sarton, George (1955). "Chaldaean Astronomy of the Last Three Centuries B. C.E". Journal of the American Oriental Society. 75 (3): 166–173 [169]. doi:10.2307/595168. 
  25. ^ William P. D. Wightman (1951, 1953), The Growth of Scientific Ideas, Yale University Press p.38.
  26. ^ a b van der Waerden, Bartel Leendert (1987). "The Heliocentric System in Greek, Persian and Hindu Astronomy". Annals of the New York Academy of Sciences. 500 (1): 525–545 [527]. Bibcode:1987NYASA.500..525V. doi:10.1111/j.1749-6632.1987.tb37224.x. 
  27. ^ Index of Ancient Greek Philosophers-Scientists
  28. ^ Seleucus of Seleucia (c. 190 BC-?), The SAO/NASA Astrophysics Data System (ADS)
  29. ^ Seleucus of Seleucia (ca. 190-unknown BC), ScienceWorld
  30. ^ van der Waerden, Bartel Leendert (1987). "The Heliocentric System in Greek, Persian and Hindu Astronomy". Annals of the New York Academy of Sciences. 500 (1): 525–545 [528]. Bibcode:1987NYASA.500..525V. doi:10.1111/j.1749-6632.1987.tb37224.x. 
  31. ^ Lucio Russo, Flussi e riflussi, Feltrinelli, Milano, 2003, ISBN 88-07-10349-4.
  32. ^ van der Waerden, Bartel Leendert (1987). "The Heliocentric System in Greek, Persian and Hindu Astronomy". Annals of the New York Academy of Sciences. 500 (1): 525–545 [527–529]. Bibcode:1987NYASA.500..525V. doi:10.1111/j.1749-6632.1987.tb37224.x. 
  33. ^ Shlomo Pines (1986). Studies in Arabic versions of Greek texts and in mediaeval science. 2. Brill Publishers. pp. viii & 201–17. ISBN 965-223-626-8. 
  34. ^ Asger Aaboe, Episodes from the Early History of Astronomy, New York: Springer, 2001), pp. 62-5; Alexander Jones, "The Adaptation of Babylonian Methods in Greek Numerical Astronomy," in The Scientific Enterprise in Antiquity and the Middle Ages, p. 99


  • 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.
  • Watson, Rita; Horowitz, Wayne (2011). Writing Science Before the Greeks: A Naturalistic Analysis of the Babylonian Astronomical Treatise MUL.APIN. Leiden: Brill Academic Pub. ISBN 90-04-20230-7.