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date: 08 May 2021

# The Moon and Planets in Ancient Mesopotamia

• Mathieu OssendrijverMathieu OssendrijverFreie Universität Berlin

### Summary

In ancient Mesopotamia, all five planets visible to the naked eye were known and studied, along with the Moon, the Sun, the stars, and other celestial phenomena. In all Mesopotamian sources concerning the Moon and the planets, be they textual or iconographical, the astronomical, astrological, and religious aspects are intertwined. The term “astral science” covers all forms of Mesopotamian scholarly engagement with celestial entities, including celestial divination and astrology. Modern research on Mesopotamian astral science began in the 19th century. Much research remains to be done, because important sources remain unpublished and new questions have been posed to published sources.

From ca. 3000 bce onward, Mesopotamians used a calendar with months and years, which indicates that the Moon was studied at that early age. In cuneiform writing, the Sumerian and Akkadian names of the Moongod, Nanna/Sin, are attested since ca. 2500 bce. The most common Akkadian names of the five planets, Šiḫṭu (Mercury), Dilbat (Venus), Ṣalbatānu (Mars), White Star (Jupiter), and Kayyāmānu (Saturn), are attested first in 1800–1000 bce. The Moon, the Sun, and the planets were viewed as gods or manifestations of gods. From ca. 1800 bce onward, the phenomena of the Moon, the Sun, and the planets were studied as signs that were produced by the gods to communicate with humankind. Between ca. 600 bce and 100 ce, Babylonian scholars reported lunar and planetary phenomena in astronomical diaries and related texts. Their purpose was to enable predictions of the reported phenomena with period-based, so-called Goal-Year methods. After the end of the 5th century bce Babylonian astronomers introduced the zodiac and developed new methods for predicting lunar and planetary phenomena known as mathematical astronomy At about the same time they developed horoscopy and other forms of astrology that use the zodiac, the Moon, the Sun, and the planets to predict events on Earth.

### Introduction

The Moon and the planets are mentioned in a wide range of texts written over a period of about 3,200 years. A discussion of the role of the Moon and the planets, and they ways in which they were conceptualized, is incomplete without taking into account the Sun, which played a prominent role in Mesopotamian astral science and religion. (The term “astral science” covers all forms of Mesopotamian scholarly engagement with celestial entities, including celestial divination and astrology.) This article focuses on the most important concepts, theories, and practices in astral science (astronomy and astronomy), religion, and daily life that involve the Moon, the planets, and the Sun. It covers the history of research, calendars, cuneiform writing, religion, cult and mythology, celestial divination, astronomical diaries and related texts, mathematical astronomy, and zodiacal astrology.

### History of Research

Modern research on Mesopotamian astral science began in the 1870s, as large numbers of clay tablets from Nineveh, Babylon, and other sites in what is now Iraq began to arrive in Europe. In this early period of Assyriology, only a few decades after the cuneiform script was deciphered, interpretations of cuneiform texts were often speculative. After 1880, Joseph Epping, Johann Strassmaier, and Franz Xaver Kugler, German Jesuits trained in oriental languages and exact sciences, pioneered the reconstruction of Babylonian astronomy (de Jong, 2016). Near the beginning of the 20th century, a group of orientalists known as Pan-Babylonists claimed that the bible and Western culture are deeply dependent on ancient Mesopotamian astral cults (Lehmann, 1994; Marchand, 2009, pp. 237–244). Their controversial claims partly relied on speculative interpretations of cuneiform texts and were soon refuted, in no small part through the efforts of Kugler, who showed that Babylonian astronomy developed much later than claimed by them. As a result of the controversy, modern scholarship remains wary to propose astral interpretations of Mesopotamian literature (Cooley, 2013, pp. 1–13). Since 1955, the main corpora of Mesopotamian astral science (Hunger & Pingree, 1999) have appeared in scholarly editions by Otto Neugebauer (Jones, Proust, & Steele, 2016), Hermann Hunger, David Pingree, Erica Reiner, Francesca Rochberg, and others. Current research is characterized by a critical reflection on historiography and methodology (Rochberg, 2004) and by increasing efforts to explain the roles of astral science in Mesopotamian culture and society and to reconstruct its conceptual underpinnings (Rochberg, 2016, 2018).

### The Moon, the Sun, and the Planets in Cuneiform Writing

The earliest attestations of the names “Moon” and “Sun” date to the Early Dynastic period (ca. 2500 bce). Mesopotamian scribal culture was essentially bilingual at that time, with the Sumerian and Akkadian languages playing intertwined roles in the writing system and in all realms of knowledge (Rochberg, 2009). Deities, constellations, stars, and planets all had more or less distinct Sumerian and Akkadian names. Sumerian and Akkadian divine names may originally have designated distinct deities of the respective linguistic communities, but as early as 2500 bce they are usually indistinguishable. In cuneiform writing, gods, stars, and planets are distinct word categories marked by determinatives, which are logographic signs that were not pronounced. Divine names are nearly always preceded by the sign dingir, Sumerian for “god,” star names by the sign mul, Sumerian for “star,” and planetary names by the sign udu.idim, Sumerian for “planet” (literally: wild sheep). The names of the five planets are preceded by up to three of these determinatives. Planets were therefore formally in the same word categories as stars and gods, and in numerous texts they are referred to as stars or gods. By contrast, the names of the Moon and the Sun were, as far as is known, not preceded by the determinatives for stars or planets and they were only very rarely designated as such. Collectively, the seven were usually referred to as “the gods.” For instance, the Akkadian astral compendium Mulapin, “Plow Star,” attested from the 7th century bce onward, describes their motion among the fixed stars as follows: “The path that Sin (the Moon) travels Šamaš (the Sun) travels. The path that Sin travels Šulpaea (Jupiter) travels. (There follow four analogous statements about Venus, Mars, Mercury, and Saturn). Together six (expected: seven) gods, whose positions are one, who touch the stars of the sky, keep changing their positions” (Hunger & Steele, 2019, pp. 71–72). Two notable exceptions are the Great Star List, a compendium of associations between stars, planets, and deities, attested in copies from the 8th century bce onward (Koch, 1995, p. 201), and a ritual text from the temple of the skygod Anu in Uruk dating to ca. 200 bce (Linssen, 2004, pp. 40, 179). In these texts, the Moon, the Sun, and the five planets are collectively called the “seven planets.” In the Babylonian creation myth Enūma Eliš (“When Above”; Lambert, 2013) and other religious texts, the motion of stars and planets is compared with that of a herd of cattle, which might explain why the Sumerian and Akkadian words for “planet,” udu.idim/bibbu, denote a kind of sheep. The order of the planets in the mentioned passage from Mulapin—Sun, Jupiter, Venus, Mars, Mercury, Saturn—probably reflects a ranking of their astrological significance from benefic to malefic, as in celestial divination, but it also partly matches a ranking of their brightness. In other texts, slightly different astrologically motivated sequences are attested, nearly always with the most benefic planets Jupiter and Venus in first and second position (Hunger & Steele, 2019, p. 197; Rochberg-Halton, 1988b).

### The Moon, the Sun, and the Planets in Religion, Cult, and Mythology

The gods were, on the one hand, conceived of as anthropomorphic beings, as is evident from mythology, cult statues, and depictions on stelae and cylinder seals. Though similar to humans, they are crowned with horns to mark their divinity. As cult statues, the gods lived in earthly temples, where they ruled like kings while being venerated and cared for by priests through rituals and offerings. On the other hand, nearly all gods had at least one astral manifestation (Rochberg, 2009). The Moon was a male deity usually called Nanna (Sumerian) or Suen (Akkadian), which later became Sin, although in some Sumerian texts he is referred to as Dilimbabbar,1 “Lonely White Runner” (Stol, 1992). His main sanctuary was at Ur, where Enheduana, daughter of king Sargon, was his high priestess in the Old Akkadian period (2350–2200 bce). He is often depicted as a figure traveling the heavens in a crescent-shaped boat. Archaeological evidence from Ur suggests that his cult was very ancient, though his role may have increased under the Old Akkadian kings. The Sungod Utu/Šamaš was the god of justice. His main sanctuary was located in Sippar (Fig. 1). He is often depicted as a figure with rays emerging from his shoulders while rising from the eastern mountains (Black & Green, 1992). Venus, the brightest planet, was the astral manifestation of Inana/Ištar, goddess of love and war (Fig. 1). Nanna/Sin, Utu/Šamaš, and Inana/Ištar are more strongly identified with celestial bodies than other Mesopotamian gods. All three played prominent roles in Sumerian mythology. Utu and Inana are children of Nanna and his spouse Ningal, and Nanna is the son of Enlil, the Sumerian king of the gods, and his spouse Ninlil. According to another tradition, Inana/Ištar is the daughter of the skygod An/Anu. In glyptic art, deities were sometimes represented by emblems. Well-known examples are found on kudurrus, ovoid stone stelae inscribed with land grants that are attested ca. 1300–650 bce. The emblem of Nanna/Sin is a crescent (Stol, 1992), that of Utu/Šamaš is a disk with a four-pointed star and rays between the points of the star, and that of Inana/Ištar is an eight-pointed star (Fig. 1).

The association between celestial body and deity was expressed differently for the Moon and the Sun on the one hand and the planets on the other hand. For the Moon and the Sun no terminological distinction was made between celestial and divine entity. The five planets were also associated with major deities, but the names of these deities rarely functioned as planetary names. Instead, for each planet several different Sumerian or Akkadian names are attested, depending on period and context (Brown, 2000). Many of them can be understood as epithets of the planet or names of minor deities with a connection to the planet or the major deity. In mythological texts, narratives about the major deities are sometimes interwoven with references to astral phenomena that reflect their association with a planet. In Inana’s Descent, a Sumerian myth from the Old Babylonian period, Inana enters the netherworld as “Inana towards the place where Utu rises,” which may correspond to the disappearance of Venus as an evening star and its reappearance as a morning star (Heimpel, 1982; Rochberg, 2009, p. 56). Astral interpretations have also been proposed for Inana and Šukaletuda (Cooley, 2008; Cooper, 2001), another Sumerian myth from the Old Babylonian period (Volk, 1995), and Nergal and Ereškigal, an Akkadian myth attested from the 14th century bce onward (Ponchia & Luukko, 2013, p. xix, 55). The absence of distinct deities associated with Venus as a morning and Venus as an evening star suggests that they were known to be phenomena of the same planet from a very early date (Cooley, 2013, p. 35).

From ca. 1800 bce onward, the planets are increasingly mentioned in scholarly sources. Across this entire period the most common name of Venus was Dilibad (perhaps to be read Dilbat in Akkadian), which probably means “Radiant One” (Bruschweiler, 1987, p. 112). In the omen series, Enūma Anu Enlil, Venus was also called Ninsianna, Sumerian for “Radiant Lady of the Sky” or, in an apparent exception to the rule, Ištar (Reiner & Pingree, 1998, pp. 169–193). In some omens Ištar as an evening star is described as a male deity with a beard (Reiner, 1995, p. 6). In Sumerian hymns from the Old Babylonian period the former two names are attested as epithets of Inana (Bruschweiler, 1987). Mercury was called Gud/Šiḫṭu, which can mean “rising,” “attack,” or “jump,” and probably reflects the rapid motion of this planet. In the 1st millennium bce Mercury was usually identified with Nabû, the Babylonian god of writing and accounting, but the astral compendium Mulapin (“Plow Star”) associates Mercury with the warrior deity Ninurta. Jupiter’s association with Marduk, supreme god of the Babylonian pantheon, may go back to the Old Babylonian period. At least six names of this planet are attested: Mulbabbar/Kakkabu Peṣû, “White Star,” Sagmegar, a name of unknown meaning, Šulpaea, Sumerian for “Youth Appearing Brilliantly,” Nēberu, Akkadian for “Crossing,” Udaltar/Dāpinu, “Heroic One,” and “Star of Marduk” (Rochberg, 2009, p. 58–61). Šulpaea was a minor warrior deity mentioned in Sumerian texts as early as 2500 bce. In a Sumerian hymn from the Old Babylonian period he is said to “rise like the moonlight,” clearly a reference to an astral aspect (Falkenstein, 1963), but the use of Šulpaea as a name for the planet Jupiter becomes evident only by the end of the 2nd millennium bce. Mars was the astral manifestation of Nergal, the god of pestilence (Rochberg, 2009, p. 63; Ponchia & Luukko, 2013, p. lxxx). The usual name of this planet was Ṣalbatānu, of unclear meaning. Saturn was called Saguš/Kayyāmānu, “Steady One,” or Genna (Sumerian), with the same meaning. Saturn was sometimes identified with Ninurta, but was usually viewed as the malefic, nightly manifestation of the Sungod. In astrological contexts Saturn was sometimes called the Scales, which also denotes a constellation. Like its usual name, this alternative name reflects the planet’s connection to the divine judge Šamaš.

In addition to the emblems of the major deities associated with the Moon, the Sun, and the planets, only a few depictions of the planets themselves are attested. On an astrological tablet from Uruk dating to ca. 200 bce (Weidner, 1967), Jupiter, here called Sagmegar, and Mercury, here called Šiḫṭu, are depicted as eight-pointed stars next to the zodiacal constellations in which they attain their greatest astrological influence (Figs. 2 and 3).

There are numerous Akkadian hymns and prayers to Šamaš, Sin, and the planetary deities Ištar, Marduk, Nabû, Ninurta, and Nergal from the 1st millennium bce (Foster, 2005, pp. 583–767). Sin, Šamaš, and Ištar are most clearly addressed as astral deities in these compositions. With the exception of several hymns to Nergal (Foster, 2005, pp. 708–709; Ponchia & Luukko, 2013, p. lxvii), the other compositions largely avoid astral aspects. In his capacity of divine judge, Šamaš was responsible for writing verdicts in the entrails of animals in response to questions or issues that were posed to him in extispicy rituals. The art of extispicy—the interpretation of divine signs in the entrails of animals—was practiced by a specialist called a barû. Before opening the animal, the barû asked Šamaš, sometimes also a group of stars and Sagmegar (Jupiter), to “place truth in the lamb,” as is stated in the Old Babylonian Prayer to the Gods of the Night (Horowitz, 2000, pp. 196–198). In a similar prayer, Ninsianna (Venus) is invoked (Reiner, 1995, p. 68). During the 1st millennium bce, planets, rather than the major deities associated with them, were invoked in many other kinds of rituals (Krul, 2018 pp. 181–190) and official acts in order to enhance their effect. For instance, in antiwitchcraft rituals (Krul, 2018, pp. 184–185), purification rituals, rituals for bringing to life divine statues (Reiner, 1995, pp. 140–143), and Assyrian vassal treaties (Reiner, 1995, p. 18). In Seleucid Uruk (ca. 200 bce) the seven planets were addressed in rituals that were performed in the temple of the skygod Anu and on top of its ziqqurat (Krul, 2018).

### Celestial Divination

From the Old Babylonian period onward, celestial divination triggered increasing scholarly attention to phenomena in the sky. Underlying all Mesopotamian divination is the assumption that the gods produce signs to communicate with mankind. Signs could occur at any time and in all realms of experience, real or imaginary. Divination was not a fringe activity, but an integral part of Mesopotamian religion, daily life, and royal ideology. Compared to other forms of divination, celestial omens stand out in that their predictions exclusively concern king and state. By seeking divine approval of their decisions in celestial signs, kings construed their reign as being in line with the intentions of the gods and therefore legitimate. In the case of an unfavorable sign, such as an eclipse, rituals were available for appeasing the gods and annulling the prediction or diverting it away from the king or his country. Celestial signs were interpreted by specialized scribes on the basis of omen compendia and explanatory works. Mesopotamian omens are statements of the kind “if X then Y,” where X is a description of a concrete phenomenon and Y the corresponding prediction (Rochberg, 2010). Certain general principles connect some phenomena to favorable predictions and others to unfavorable ones. They can be inferred from the omens (Brown, 2000), but were rarely formulated in texts. Instead, Mesopotamian divination operated on a casuistic basis, as is true for medicine, law, and other realms of scholarship. The frequent use of metaphorical language, such as “if Sin is covered by a crown” or “if Šamaš is weeping” (Rochberg, 1996) makes identifying the astronomical phenomena underlying X difficult, at least for the modern reader. Some may derive from empirical observations, but quite a few are astronomically impossible and clearly constructed. For instance, Tablets 15–22 of the celestial omen series Enūma Anu Enlil (“When Anu and Enlil”) mention lunar eclipses on day 20 of the month (Rochberg, 1988a), which is impossible because Full Moon can only occur near day 14. The usual assumption is that such omens were added to achieve an enhanced form of completeness (Brown, 2000, pp. 136–137). However, they might be connected to observable phenomena by substituting certain words, a practice known from learned commentaries (Frahm, 2011) and astrological reports that were sent to the Neo Assyrian kings at Niniveh (Hunger, 1992).

The earliest known celestial omen tablets are written in Akkadian and date to the Old Babylonian period. They include lunar and solar eclipse omens quite similar to the later ones (Rochberg, 2006). However, the bulk of the evidence for celestial divination dates to the 1st millennium bce. Especially the Neo Assyrian kings at Niniveh (7th century bce), who consulted astrologers at an unprecedented scale. By that time, thousands of celestial omens were collected in the compendium Enūma Anu Enlil (“When Anu and Enlil”), thus named after its opening line. It was widely distributed and existed in at least four slightly different recensions, each comprising between 63 and 70 numbered tablets (Fincke, 2001; Koch, 2015) of typically 50–100 omens. A “scribe of Enūma Anu Enlil” was originally a specialist of celestial divination, but could later designate any scholar of the astral sciences.

Tablets 1–14 of Enūma Anu Enlil (in the Nineveh recension) form a subseries named “Appearances of Sin,” which deals with lunar phenomena in different months of the year or at different days of the month (Verderame, 2002). Tablet 14 is unusual because it consists of numerical tables, such as zigzag sequences for the length of daylight in each month of a schematic year and for the duration of visibility of the Moon on each day of a schematic month (al-Rawi & George, 1991). Their purpose is a matter of debate. While Brown (2000) asserts that the tables represent ideal lunar behavior that triggered favorable predictions, Rochberg (2004, 2016) proposes that they were also predictive tools. Tablets 15–22 (Fincke, 2016; Rochberg, 1988a) deal with lunar eclipses, which were considered particularly dangerous signs for king and state (Stol, 1992, pp. 258–259). Tablets 23–39 deal with the Sun, including solar eclipses (Fincke, 2013b; van Soldt, 1995), Tablets 40–49 with weather phenomena. Tablets 50–70 deal with stars and planets, but only a few are well enough preserved to allow a reconstruction. Tablet 56 mainly deals with unspecified “planets” that become visible or “approach” stars, constellations, or named planets (Fincke, 2015; Largement, 1957). Up to seven tablets deal with Venus (Fincke, 2001). Tablets 59 and 60 concern conjunctions of Venus with stars, constellations, and other planets (Fincke, 2013a; Reiner & Pingree, 1998). Tablet 63 (Reiner & Pingree, 1975) is unusual in several respects. It begins with a sequence of 10 cycles of first and last appearances of Venus, called Ninsianna, as a morning and an evening star, which appear to be actual observations reformulated as omens. They are followed by an isolated phrase and a second sequence of first and last appearances that was clearly not observed but constructed using a simple mathematical scheme. The phrase matches a year formula of the Old Babylonian king Ammiṣaduqa (ca. 1650 bce), which some scholars have taken to imply that the preceding sequence was observed during his reign. On that assumption the data can be compared with modern computations to derive an absolute chronology for the Old Babylonian period. The problems are formidable, because the oldest extant copy of Tablet 63 was written about a thousand years after the events (for the latest attempts see Mebert, 2010; Huber, 2011, and de Jong, 2012, 2013). Numerous fragments, probably belonging to Tablets 64–66, deal with phenomena of Jupiter, here called Sagmegar, such as conjunctions with planets, stars, and constellations, including astronomically impossible ones, and Jupiter’s color and brightness (Reiner & Pingree, 2005). Omens about Mercury, Mars, and Saturn are attested on several tablets with lunar or stellar omina, but no tablets dedicated to these planets have been identified.

Apart from the main series, Enūma Anu Enlil, omens and schematical statements about the Moon and the planets can be found in other tablet series and commentaries (for an overview see Koch, 2015, pp. 179–185). In this connection the compendium Mulapin (“Plough Star”) must be mentioned again. Tablet 2 includes schematic values of the duration of visibility and invisibility between first and last appearances, or vice versa, for each of the planets Venus, Jupiter, Mars, Saturn, and Mercury (Hunger & Steele, 2019). Enūma Anu Enlil, other divinatory series, their commentaries, and Mulapin amount to an impressive body of systematic knowledge about the Moon, the Sun, and the planets. Apart from the bulk of casuistic omens, this knowledge includes tabular and other schematic mathematical abstractions derived from empirical data, such as those found in Enūma Anu Enlil Tablets 14 and 63 and in Mulapin. It is unclear when most of these compositions were originally produced. Using astronomical methods, some of the stellar data in Mulapin have been dated to ca. 1200 bce (de Jong, 2007), but the composition may not have existed before about 750 bce (Hunger & Steele, 2019). With regard to Enūma Anu Enlil, any date ca. 1000–750 bce seems possible for the final redaction, although some parts, perhaps including the Venus Tablet of Ammiṣaduqa, were compiled from precursor tablets.

### Babylonian Astronomical Diaries and Related Texts

From the 7th century bce until the 1st century ce, Babylonian scholars reported lunar and planetary phenomena in astronomical diaries and related texts (Hunger, 2001, 2006, 2014; Sachs & Hunger, 1988, 1989, 1996). These activities were conducted primarily at Babylon, where more than 1,000 fragments of such texts were found; only a small number originate from Uruk and Nippur. As far as this could be established, the texts from Babylon were produced by scholarly priests connected to the main temple Esagila, sanctuary of Marduk. Diaries, the most common type of report, contain astronomical, meteorological, economic, and historical data for a period of usually six or seven months (Sachs & Hunger, 1988). Compared to the omen texts, the diaries employ an unambiguous, though highly abbreviated and technical, terminology without any explicit reference to the ominous significance of the reported phenomena. Diaries were compiled from short-term reports, some of which are also preserved (Mitsuma, 2015).

In each monthly section, positions of the Moon and the five planets are reported as distances to the nearest reference star, measured roughly along and perpendicular to the ecliptic (Graßhoff, 1999; Jones, 2004). About 32 stars that straddle the ecliptic, called Normal Stars by modern scholars, were used for this. The positions were reported at irregular intervals: for the Moon almost on a daily basis and for the planets less frequently, depending on their apparent speed. At the beginning, middle, and end of each month, six different time intervals between the rising or setting of the Moon and that of the Sun, called Lunar Six by modern scholars, were measured, perhaps with a water clock, in units of time degrees, where 1 time degree = 4 min. It suffices to mention three intervals here. On day 1 the scholars measured the interval from sunset until the first visible setting of the new crescent, which is abbreviated “NA” in the diaries. In modern scholarship it is called $NA1$ to distinguish it from an identically named one that was measured near Full Moon. The observation of the crescent is what triggered this day to be declared day 1 of the new month. Near Full Moon, in the middle of the month, the scholars reported the interval between the last moonset before sunrise and sunrise, which was called $ŠU2$. One day later the order of moonset and sunrise has reversed and the interval from sunrise until the first moonset after sunrise, called $NA$, was reported. Apart from the Lunar Six, lunar and solar eclipses were reported.

The planetary data include dates and positions of the synodic phenomena. They form periodically repeating sequences, which are distinct for Mercury and Venus on the one hand and for Mars, Jupiter, and Saturn on the other hand. For Mercury and Venus the cycle comprises the first appearance, station, and last appearance in the evening, and analogously in the morning. Between last and first appearances, the planet is invisible due its proximity to the Sun. Between morning station and evening station a planet moves in the normal, roughly eastward direction along the ecliptic, between evening station and morning station in the retrograde, roughly westward direction. For Mars, Jupiter, and Saturn the cycle comprises first appearance, first station, acronychal rising, second station, and last appearance. “Acronychal rising” is the modern term for the last visible rising of the planet after sunset, which happens at most a few days before its opposition with the Sun; this was called “rising to daylight” in Babylonian. Most of these phenomena were systematically reported, with the exception of the stations of Mercury and Venus, which were only very rarely reported (Hunger, 2001, pp. 356–357; Sachs & Hunger, 1988). In diaries written after ca. 400 bce, each monthly section also includes a list of the zodiacal signs of the planets and the dates when they moved from one zodiacal sign into the next.

Apart from 6-monthly diaries, various compilations of lunar and planetary data covering longer periods of time were produced (Hunger, 2001). They include tablets with positions and synodic phenomena of one planet for up to ca. 100 years, tablets with Lunar Six data for several years, and eclipse reports (Huber & De Meis, 2004). Some tablets with observations of Venus, Jupiter, or lunar eclipses are arranged in columns that reflect an approximate period for the reported phenomena. For Venus these columns cover 8 years (Hunger, 2001, No. 56; Fig. 4), for Jupiter 12 years (Hunger, 2001, No. 54), and for lunar eclipses 18 years (Hunger, 2001, Nos. 4, 9–10). The planetary compilations also include tablets with reports of conjunctions between planets or between the Moon and a planet (Hunger, 2001, Nos. 58–59).

The reasons these phenomena were systematically reported for many centuries in almost unchanged fashion are only partly understood. It has become increasingly clear that the main purpose of the diaries was to enable predictions of the reported phenomena. Probably already by the beginning of the diary project, Babylonian scholars had developed methods for predicting most of the lunar and planetary phenomena that are reported in the diaries. These Goal-Year methods, as they are known in modern scholarship, exploit that lunar and planetary phenomena repeat near the same celestial position and Babylonian calendar date after a characteristic period, which is 8 years for Venus, 47 or 79 years for Mars, 71 or 83 years for Jupiter, 59 years for Saturn, and 18 years for the Moon (Steele, 2011). It is important to note that these numbers of years are actually Babylonian shorthand for whole numbers of lunar months. For instance, the 8-year period for Venus actually denotes a period of 99 months, which does not always correspond to 8 calendar years. Due to intercalation, an interval of 99 months sometimes links two identical months separated by 8 years, sometimes two shifted months. Similarly, the 18-year period for the Moon actually denotes a period of 223 months, which is known in modern scholarship as the Saros. By copying reported phenomena from diaries that precede the Goal Year by these periods, reckoned in months, passages of the planets by the Normal Stars, positions and dates of synodic phenomena, and Lunar Six intervals could be predicted for a future year—the Goal Year. None of the planetary periods is fully exact, but the Babylonian scholars were aware of corrections, which they applied to the predicted calendar dates; these corrections, which typically amount to a few days, were different for each planet and listed on tablets (Britton, 2002).

The most interesting Goal-Year rules concern the Lunar Six intervals, which are more complex than those for the planets. For instance, the value of $NA1$ for month $i$ in the Goal Year is predicted as $NA1(i)=NA1(i−223)−[ŠU2(i−229)+NA(i−229)]/3$, that is, from the value of $NA1$ preceding month $i$ by 223 months one subtracts a third of the sum of two other Lunar Six intervals, $ŠU2$ and $NA$, that pertain to the Full Moon preceding month $i$ by 229 months (Brack-Bernsen & Hunger, 2002). The nontrivial astronomical arguments that explain why this procedure produces essentially correct results were presented by Lis Brack-Bernsen (1997) using a modern formalism, but it is unclear how the Babylonian scholars came up with this procedure and five analogous ones for the other Lunar Six intervals. This appears to have happened around 600 bce (Huber & Britton, 2007; Huber & Steele, 2007).

From the 3rd century onward, Goal-Year predictions for planets, Lunar Six intervals, and eclipses are attested on special tablets known as Goal-Year texts (Hunger, 2006). However, in diaries as early as the 6th century bce, phenomena that could not be observed, for instance due to bad weather, were replaced by predictions probably obtained with Goal-Year methods. Since each prediction requires a record of the same phenomenon from an earlier year, in the case of the Lunar Six of three intervals from two different years, the Goal-Year methods partly explain why diaries continued to be written for many centuries. However, important questions remain unanswered. Some of the astronomical phenomena that were routinely reported, in particular the frequent Normal Star passages of the Moon, are not known to have been predicted and there is no textual evidence for a Goal-Year method to predict them. In fact, due to the complexities of lunar motion, a reasonably accurate method for predicting lunar positions may be difficult to obtain with Goal-Year principles. Therefore, the alternative hypothesis, namely that Normal Star passages of the Moon were reported with the aim of developing, one day, a method for predicting them, cannot be fully discarded. Indeed, by ca. 330 bce a working method for computing lunar positions was developed within the framework of mathematical astronomy, but it is unclear whether this was achieved by analyzing Normal Star passages reported in diaries.

The question of why lunar and planetary phenomena were predicted can only be partially answered. Eclipses continued to be viewed as ominous signs of concern to rulers. By predicting the months during which an eclipse could happen—these months are referred to as “eclipse possibilities” in modern scholarship—priests could prepare the necessary rituals to annul their evil. Lunar eclipse possibilities were predicted by the 6th century bce, and solar eclipse possibilities by the 5th century bce (Steele, 2000, pp. 432–433). The interval $NA1$ is connected to the first appearance of the lunar crescent, which marks the beginning of the month. Babylonian scholars could predict future month lengths—29 or 30 days—by computing $NA1$ for two successive sunsets after New Moon at the end of days 29 and 30, and comparing them with a threshold value, which was typically 10 time degrees = 40 minutes, above which the new crescent was considered visible. As we have seen, the prediction of $NA1$ proceeded from records of three Lunar Six intervals, which explains why they were reported. A full explanation of why the other Lunar Six intervals were reported and predicted remains to be found.

The planetary phenomena had no relevance for the calendar and were most likely predicted for astrological purposes, but on this topic much research remains to be done. Possible applications in predicting weather and market prices are suggested by several astrological procedure texts in which weather phenomena and the price of grain are inferred from planetary positions, conjunctions, and synodic phenomena (Hunger, 1976a, 1976b, No. 94). However, no actual predictions of weather or prices that were made with these procedures have been discovered yet, which suggests that there were other applications of the synodic phenomena that remain to be identified (Ossendrijver, 2019). This is particularly true for the period before ca. 410 bce, when horoscopic astrology emerged as an additional application of the planetary predictions.

### Babylonian Mathematical Astronomy

After ca. 400 bce, Babylonian scholars developed mathematical techniques for predicting lunar and planetary phenomena. They are attested in ca. 450 tablets from Babylon and Uruk dating between 380 and 45 bce. Approximately 340 of the tablets are computed tables (Neugebauer, 1955), the remaining 110 or so are procedure texts with instructions related to the tables (Ossendrijver, 2012). All of these texts employ the zodiac, which was introduced near the end of the 5th century bce (Britton, 2010) by dividing the path of the Sun into 12 sections of 30 degrees and naming each one after a nearby constellation. In Babylonian mathematical astronomy, the zodiac functions as a coordinate system for computing positions. The coordinate along the ecliptic was called “position” (qaqqaru in Akkadian) and expressed as a zodiacal sign and a number of degrees within it between 0 and 30. The perpendicular coordinate, the distance above or below the ecliptic, was called “height” or “depth” and expressed as a positive number measured in degrees or other units.

All computations are done in sexagesimal place-value notation, which was used in Mesopotamia from the Ur III period (2100–2000 bce). It functions analogously to the modern decimal notation: a number is represented as a sequence of digits between 0 and 59, each of which is associated with a power of 60 that decreases by one in the rightward direction. Unlike modern decimal notation, the Babylonian sexagesimal notation is floating, because vanishing initial or final digits (0) were not always written and there was no equivalent of the decimal point. Consequently, the power of 60 corresponding to each digit must be inferred from the context. In the modern notation for sexagesimal numbers, their absolute values are represented by placing a semicolon between the digit pertaining to 1 and the digit pertaining to 1/60, and commas between all other digits.

In all known Babylonian astronomical sources, the motion of the Moon, the Sun, and the planets is described or computed in at most two dimensions, while ancient Greek astronomers often conceived their motion in three dimensions. There is no cuneiform evidence for Babylonian theories concerning the spatial arrangement of the Moon, the Sun, and the planets in relation to the Earth.

#### Planetary Algorithms

About half of the tables are concerned with the Moon, the other half with the planets Mercury, Venus, Mars, Jupiter, and Saturn, apart from a few tables with daily positions of the Sun. The traditional names of the planets are used, but some are written with heavily abbreviated logograms and the divine determinatives are usually omitted. For instance, the Moon is written with the logogram 30, to be read Sin, the Sun with 20, to be read Šamaš, and Mars with the sign AN, probably a phonetic abbreviation of Ṣalbatānu. Most of the tabular texts are synodic tables, in which consecutive rows correspond to successive instances of a synodic phenomenon. The synodic tables for the planets contain up to six pairs of columns, each containing successive times (called $T$ in modern scholarship) and zodiacal positions ($B$) of a different synodic phenomenon (Fig. 5). Some procedure texts contain algorithms for a planet’s distance to the ecliptic, but that quantity is not attested in the tables. Column $T$ mentions the date, expressed as a year number, month and “day” number between 0 and 30 within the month. The “days” actually correspond to an artificial unit of time corresponding to 1/30 of the mean synodic month called mean tithi by modern scholars, a term borrowed from Sanskrit astronomy. The reason for using mean tithis instead of real days is that this removes the need for computing the lengths of the future months, 29 or 30 days, in which the predicted planetary phenomena occur. As a consequence, the actual date may differ from the computed number of mean tithis by about 1.

The tables were computed from top to bottom and from left to right like a modern spreadsheet. After writing down the initial values in row 1, the rest of the table was filled by updating all quantities from one to the next instance of the same phenomenon (Fig. 5) or from day to day. These methods may have offered a significant practical advantage compared to the Goal-Year methods, because they yield almost arbitrarily long sequences of predictions setting out from a few initial values, whereas the Goal-Year methods require for every prediction a reported observation of the same phenomenon. However, the Goal-Year methods continued to be used after the emergence of mathematical astronomy.

In column $B$ the position of the planet is expressed as a zodiacal sign and a number of degrees measured from its beginning. Some tables also include columns for the line-by-line differences of $T$ and $B$, known as the synodic time $Δt$ and the synodic arc $Δλ$. The position and time of the synodic phenomenon are updated as $Bi=Bi−1+Δλ$ and $Ti=Ti−1+Δt$, where $i$ labels the rows of a synodic table. Two different types of algorithms for computing the synodic arc are attested. In system A, a zigzag algorithm is used, in system $B$ a step function algorithm. For most planets, several variants of both systems are available. Both types of algorithms are tuned to reflect the periodically varying motion of the planet at synodic phenomena. With the zigzag algorithm, the synodic arc varies periodically between a minimum and a maximum with a constant difference. For instance, a procedure for Jupiter’s system $B$ includes instructions for updating the synodic arc of Jupiter from one to the next instance of its first appearance as a zigzag sequence that goes up and down between a minimum value (m) 28;15,30 degrees and a maximum value ($M$) 38;2 degrees with a difference of 1;48 degrees (Ossendrijver, 2012, No. 37). The position of Jupiter’s first appearance is then updated as $Bi=Bi−1+Δλ$. Some properties of the algorithm accurately reflect empirical behavior. The mean synodic arc, , is close to the actual value of 33;7 degrees.

From a modern astronomical point of view, the periodic variations of $Δλ$ are a combined effect of the variable apparent velocities of the planet and the Sun along the ecliptic and, for first and last visibilities, changes in the visibility of the planet caused by the annually changing angle between the ecliptic and the horizon. It can be shown that the computed positions satisfy a period relation, such that Jupiter returns to the same position after $∏=391$ iterations (rows), corresponding to $Z=36$ full revolutions around the zodiac (Neugebauer, 1975, pp. 388–390; Ossendrijver, 2012, p. 60). The corresponding number of revolutions of the Sun, that is, the number of years, is $∏+Z$, which equals 427 years for this algorithm. This period relation, $∏$ repetitions of the synodic phenomenon = Z revolutions = Y years, belongs to the empirical core of the algorithm. The dates of Jupiter’s first appearance are obtained with a similar zigzag algorithm for the synodic time $Δt$.

In system A, so-called step functions are used for computing the synodic arc. The step-function algorithm is based on a division of the zodiac into a number of zones ranging from two (Jupiter system A) to six (Mars system A). In each zone, the synodic arc $Δλ$ assumes a constant value, at least initially, which yields a step-like graph if plotted agains the position in a modern fashion. The preliminary value of $Δλ$ to be used for updating the position is determined by the zone in which the planet is located. If the addition of this value to the position causes the planet to cross into the next zone the position is modified by an additional rule; for detailed explanations see Ossendrijver (2012, 2014)

#### Geometric Methods

Until recently, the impression prevailed that Babylonian astronomers only used purely arithmetic methods, as opposed to ancient Greek astronomers, who developed geometric methods to compute the orbits of the planets. Four Babylonian procedure texts (Ossendrijver, 2016, 2017) refute this characterization, which is firmly entrenched in the historiography of ancient astronomy. In these procedures, the distance traveled by Jupiter along the zodiac during a given number of days is computed as the area of a trapezoidal figure that represents the linearly changing value of its daily displacement against time (Fig. 6). The time that it takes Jupiter to reach half that distance is also computed by bisecting the trapezium into two smaller ones of equal area using an algorithm known from Old Babylonian mathematics (Ossendrijver, 2018). These geometric methods, which look familiar to any modern student of physics, have no known parallels in other ancient cultures and there is no evidence that they survived the end of cuneiform. It appears that they were forgotten until similar ones emerged in the 14th century ce, when the Parisian philosopher and mathematician Nicole Oresme (1320–1382) proved that the distance covered by a uniformly accelerating or decelerating body corresponds to the area of the trapezoidal graph that represents its “velocity” against time (Clagett, 1968, pp. 13–14, 33, 46–47; Pedersen, 1974, pp. 193–198).

#### Lunar Algorithms

Most of the lunar tables and procedure texts are concerned with New Moon, when Moon and Sun are in conjunction, and Full Moon, when they are in opposition. A typical table contains predictions for one calendar year, with the New Moon data written on the obverse and the Full Moon data on the reverse. Unlike the planetary tables, the purpose of the lunar tables goes beyond the prediction of times and positions of synodic phenomena. Many lunar tables include columns for eclipse magnitude, Lunar Six intervals and up to a dozen auxiliary columns that are needed for computing the mentioned “final” quantities. Like the planetary tables, the lunar tables were computed from top to bottom and from left to right. Nearly all of the extant lunar texts belong to systems A or B. As with the planets, the main difference between them concerns the synodic arc, which is computed with a step-function algorithm in system A and a zigzag algorithm in system B. However, even though most columns are computed with simple algorithms, the large number of columns and the dependencies between them result in a complexity far exceeding that of the planetary systems. Since it is impossible to fully describe them here, only some important features of the remarkably ingenious and elegant lunar system A are pointed out. For more details and for lunar system B see Neugebauer (1955, 1975) and Ossendrijver (2012).

In both systems, three periodic contributions are taken into account. In modern terms these are the solar variation, the lunar variation, and the nodal motion. The solar, also called zodiacal variation, concerns quantities that repeat when Full Moon or New Moon returns to the same position in the zodiac; the corresponding period is the solar year. The lunar variation concerns quantities that vary with the same characteristic period as the Moon’s apparent velocity. This period is the anomalistic month of about 27.56 days. Because the positions of smallest and largest lunar velocity are not fixed but drift with the nodal motion, quantities controlled by the lunar variation do not repeat when Full Moon or New Moon returns to the same position in the zodiac. The third contribution reflects the nodal motion, which concerns the retrograde rotation of the lunar nodes—the points where the path of the Moon intersects the ecliptic, which complete one revolution around the zodiac in 18.6 years. This motion is embedded in the algorithms for the Moon’s distance to the ecliptic and the eclipse magnitude.

Only some columns of a New Moon table computed with system A are briefly discussed here. The leftmost column is known as $Φ$ in modern scholarship. Its values form a simple zigzag sequence, which has a surprisingly complex astronomical interpretation. $Φ$ in row $i$, which pertains to New Moon $i$, is the amount, expressed in time degrees, by which the interval between that New Moon and New Moon $i+223$ exceeds 6,585 days. In practice though, $Φ$ merely serves to read off from an auxiliary table with fixed pairs of numbers $Φ$ and $G$, and using certain interpolation rules, the value to be written in column $G$, which models the duration of the synodic month. In other words, the duration of 1 month is computed from that of 223 months—a remarkable approach whose genesis remains to be convincingly explained; for two attempts see Brack-Bernsen (1997, 2002) and Britton (2007, 2009). The interpretation of $Φ$ is complicated further because $Φ$ turns out to reflect only the lunar contribution to the length of 223 months, while the actual, empirical length of that interval is dominated by the solar variation (Brack-Bernsen, 1997). The question of how Babylonian scholars succeeded in isolating the lunar contribution to 223 months has not been resolved. The period of $Φ$ carries over to $G$, which represents the lunar contribution to the synodic month.

The second column, $B$, contains the zodiacal position of the New Moon. Column $K$, computed as the sum of two periodic terms reflecting the lunar variation (column $G$) and the solar variation (column $J$), contains the monthly differences for the next column $M$, which contains the time of New Moon expressed in time degrees with respect to the following sunset. If the New Moon is sufficiently close to the ecliptic, a solar eclipse may occur. In order to predict eclipses, the Moon’s distance to the ecliptic is computed and written in column $E$. Eclipses were considered possible if $E$ is less than a threshold value. All columns that are computed from $Φ$ or $B$ inherit their respective periodic behavior. The nodal motion, which is embedded in $E$, is not represented by its own column in the synodic tables. Several of the columns up to $M$ serve as input for the so-called Lunar Six module, of which there is one version for the New Moon intervals (e.g., $NA1$) and another one for the Full Moon intervals (e.g., $SU2$ and $NA$). Its 13 complex subalgorithms are described in procedure texts (Ossendrijver, 2012). The module entails a rigorous analysis of the Lunar Six intervals in terms of the different astronomical and geometrical effects that control their variations.

#### Daily Motion Tables

Apart from synodic tables, ca. 30 daily motion tables are extant. In these tables, the position of the Moon, the Sun, or a planet is tabulated at intervals of 1 day. Those for the planets were computed from various assumptions about how the planet’s daily displacement along the ecliptic varies in the course of the synodic cycle and in relation to the planet’s position in the zodiac. In most tables, the planet moves at constant speed for a certain duration before abruptly switching to a different constant speed, for instance when the planet reverses its motion at a station. However, in some procedure texts or tables, the planet’s speed changes linearly or even quadratically with time (Huber, 1957). The various schemes for daily motion were probably constructed, roughly, by interpolating between the dates and positions of the synodic phenomena that are obtained with the synodic tables. That is, the synodic phenomena that are contained in the daily motion table of a planet are usually roughly consistent with a known algorithm for the synodic phenomena of that planet.

### The Moon and the Planets in Late Babylonian Zodiacal Astrology (ca. 410–50 bce)

Along with mathematical astronomy, new forms of astrology that employ the zodiac were developed in Babylonia from the end of the 5th century bce onward. In this area, much research remains to be done. A common feature of the new astrology is the important role played by the zodiac, the Moon, and the five planets. The best known example are ca. 30 Babylonian horoscopes, which report computed positions of the Moon, the Sun, and the five planets for the date of birth of a child (Rochberg, 1998). They reflect a “personal turn” in astrology, which could henceforth be invoked by private individuals, unlike earlier celestial divination, which was the privilege of kings. The daily motion tables of mathematical astronomy are almost certainly the sources of some of the horoscopes. Compendia with omen-like statements about the birth of a child in different astrological situations were probably used by the astrologers to infer the fate of the newborn from the horoscope. Zodiacal astrology was also linked with medical traditions, resulting in astro-medical doctrines that employ astrological criteria based on the zodiac, the Moon, the Sun, and the planets for determining treatments. The Babylonian understanding of how lunar, solar, and planetary phenomena are correlated with events on Earth appears to have changed with respect to traditional omen divination. Their status as signs produced by gods to announce future events on Earth is not always apparent in the sources. Instead, the predicted celestial phenomena are correlated with earthly events, such as rainfall, river levels (Hunger, 1976a; Schreiber, 2018), and market prices (Hunger, 1976b, No. 94; Ossendrijver, 2018), in almost mechanical fashion. Nevertheless, there is no evidence to suggest that the Babylonian scholars, most of whom were priests at the main temples, did not consider their gods to be responsible for these correlations.

### Transmission to Egypt and the Greco-Roman World

Numerous elements of Babylonian astral science were transmitted to Egypt, the Greco-Roman world, and beyond, especially after Alexander the Great’s conquest of Babylonia (Brown, 2018; Steele, 2016). In the Almagest, the influential ancient work on mathematical astronomy by Claudius Ptolemy (ca. 150 ce), a Greek version of sexagesimal place value notation is used and passages from Babylonian astronomical diaries are quoted. This Babylonian knowledge may have been introduced to Greek scholars during the 2nd century bce by the astronomer Hipparchus (Toomer, 1988). The Babylonian priest Berossos (ca. 330 bce) wrote a treatise called Babyloniaca, in which he explains his culture to a Greek audience. Several passages deal with astronomy, but their Babylonian origin has been questioned (de Breucker, 2011). According to Plutarch, the philosopher Seleucus of Seleucia, who defended the heliocentric hypothesis of Aristarchus of Samos, lived in Babylonia around 150 bce (Neugebauer, 1975, pp. 610–611, 697). No traces of his theories have been found in cuneiform sources. Substantial discoveries of Babylonian-style computations in Greek (Jones, 1999, 2001) and Demotic sources (van der Waerden, 1960, 1972; Ossendrijver & Winkler, 2018) have revealed that the Babylonian mathematical methods for predicting lunar and planetary phenomena were also transmitted to Greco-Roman Egypt. Around the same time, horoscopy and other forms of Greco-Roman astrology emerged in Egypt as a bilingual amalgam of native traditions and Babylonian practices (Quack, 2018).

### Conclusion

The Moon and the planets were observed, conceptualized, interpreted, and predicted by Mesopotamians across three millennia. The concepts, theories, and practices that emerged were different from region to region and changed over time. At least from the 2nd millennium onward they were conceived of as manifestations of gods. At the same time, the Moon and the planets were studied in the context of divination as carriers of signs produced by the gods. Apart from casuistic knowledge, the omen tablets also contain a body of schematic, theoretical knowledge about the motion of the Moon and the planets. During the 1st millennium bce, Babylon became the center of an intensive and long-lasting program of celestial observation attested in diaries and related texts. In its wake, two different methods for predicting lunar and planetary phenomena emerged: Goal-Year methods and mathematical astronomy. Elements of knowledge from the diaries and mathematical astronomy were transmitted to Egypt and the Greco-Roman world.

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### Notes

• 1. Dilimbabbar has now been proven to be the correct Sumerian reading of the Moongod’s name that was previously read as Ašimbabbar (Delnero, 2018, p. 308).