Celestial Measurement in Babylonian Astronomy

Summary

Late Babylonian astronomical texts contain frequent measurements of the positions of the Moon and planets. These measurements include distances of the Moon or a planet from a reference star and measurements of the position of celestial bodies within a sign of the zodiac. In this paper, I investigate the relationship between these two measurement systems and propose a new understanding of the concepts of celestial longitude and latitude in Babylonian astronomy. I argue that the Babylonians did not define latitude using the ecliptic but instead considered the Moon and each planet to move up or down within its own band as it travelled around the zodiac.

Acknowledgements

I wish to thank J. P. Britton, A. Jones, F. Rochberg, and N. M. Swerdlow for many fruitful discussions during the course of this work; the Trustees of the British Museum for permission to study and publish cuneiform tablets in their collection; and the Royal Society for supporting my research through the award of a University Research Fellowship.

Notes

¹F. Rochberg-Halton, Aspects of Babylonian Celestial Divination: The Lunar Eclipse Tables of Enūma Anu Enlil (Horn, Austria, 1988), 19–22.

²BM 17175 + 17284; see H. Hunger and D. Pingree, MUL.APIN: An Astronomical Compendium in Cuneiform (Horn, Austria, 1989), 163–64 and D. Brown, J. Fermor and C.B.F. Walker ‘The Water Clock in Mesopotamia’, Archiv für Orientforschung, 46–47 (1999–2000), 132–48.

³F.N.H. al-Rawi and A.R. George, ‘Enūma Anu Enlil XIV and Other Early Astronomical Tables’, Archiv für Orientforschung, 38–39 (1991–1992), 52–73.

⁴H. Hunger and D. Pingree (note 2).

⁵The letters are edited in S. Parpola, Letters from Assyrian and Babylonian Scholars (Helsinki, 1993) (earlier edition S. Parpola, Letters from Assyrian Scholars to the Kings Esarhaddon and Assurbanipal. Part 1: Texts (Neukirchen-Vluyn, Germany, 1970), with a detailed commentary in S. Parpola Letters from Assyrian Scholars to the Kings Esarhaddon and Assurbanipal. Part 1: Commentaries and Appendicies (Neukirchen-Vluyn, Germany, 1983). The reports are edited in H. Hunger, Astrological Reports to Assyrian Kings (Helsinki, 1992).

⁶All datable Astronomical Diaries are edited in A.J. Sachs and H. Hunger, Astronomical Diaries and Related Texts from Babylonia, vols 1–3 (Vienna, 1988, 1989, 1996), and the Excerpt Texts in H. Hunger, Astronomical Diaries and Related Texts from Babylonia, vol. 5 (Vienna, 2001). Publication of the Goal-Year Texts is forthcoming from Hunger. For the classification of astronomical texts from Babylon, see A. Sachs, ‘A Classification of the Babylonian Astronomical Tablets of the Seleucid Period’, Journal of Cuneiform Studies, 2 (1948), 271–90, H. Hunger, ‘Non-Mathematical Astronomical Texts and Their Relationships’, in Ancient Astronomy and Celestial Divination, edited by N.M. Swerdlow (Cambridge, MA, 1999) and H. Hunger and D. Pingree, Astral Sciences in Mesopotamia (Leiden, Netherlands, 1999). Copies of many astronomical texts of all kinds are published in A. Sachs, Late Babylonian Astronomical and Related Texts (Providence, RI, 1955).

⁷For TU 11, see L. Brack-Bernsen and H. Hunger, ‘TU 11: A Collection of Rules for the Prediction of Lunar Phases and of Month Lengths’, SCIAMVS 3 (2002), 3–90; for BM 45728, see J.P. Britton, ‘Treatments of Annual Phenomena in Cuneiform Sources’, in Under One Sky: Astronomy and Mathematics in the Ancient Near East, edited by J.M. Steele and A. Imhausen (Münster, Germany, 2002), 21–78; for Atypical Text E, see O. Neugebauer and A. Sachs, ‘Some Atypical Astronomical Cuneiform Texts I’, Journal of Cuneiform Studies 21 (1967), 183–218.

⁸The primary publication of mathematical astronomical texts is O. Neugebauer, Astronomical Cuneiform Texts (London, 1955).

⁹O. Neugebauer, A History of Ancient Mathematical Astronomy (Berlin, 1975), 545.

¹⁰O. Neugebauer (note 9), 547.

¹²N.M. Swerdlow, The Babylonian Theory of the Planets (Princeton, NJ, 1998), 34.

¹¹This question is formulated in greater detail by F. Rochberg-Halton, ‘Between Observation and Theory in Babylonian Astronomical Texts’, Journal of Near Eastern Studies, 50 (1991), 107–20.

¹³N.M. Swerdlow (note 12), 34.

¹⁴BM 36609+ is published with commentary in N.A. Roughton, J.M. Steele and C.B.F. Walker, ‘A Late Babylonian Normal and Ziqpu Star Text’, Archive for History of Exact Sciences, 58 (2004), 537–572.

¹⁵J.M. Steele, ‘Planetary Latitudes in Babylonian Mathematical Astronomy’, Journal for the History of Astronomy 34 (2003), 269–89; A. Jones, ‘A Study of Babylonian Observations of Planets Near Normal Stars’, Archive for History of Exact Sciences, 58 (2004), 475–536.

¹⁶J.M. Steele (note 15), 283–86.

¹⁷A. Jones (note 15), 520.

¹⁸J. Epping, Astronomisches aus Babylon (Freiburg im Breisgau, 1889).

¹⁹Diary –136 B Rev. 14’, BM 41004 (=‘Atypical Text E’) Rev 1ff.

²⁰A. Jones (note 15), 481–91.

²¹A. Jones (note 15).

²²C. Bezold, A. Kopff, and F. Boll, Zenit- und Äquatoriangestirne am babylonischen Fixternhimmel (Heidelberg, Germany, 1913), 8.

²³E. Weidner, Handbuch der babylonischen Astronomie (Leipzig, Germany, 1915), 46–49; J. Schaumberger, Sternkunde und Sterndienst in Babel 3. Ergänzungscheft zum Ersten und Zweitren Buch (Münster, Germany, 1935), 321–22; B.L. van der Waerden, ‘Babylonian Astronomy. II. The Thirty-Six Stars’, Journal of Near Eastern Studies 8 (1949), 16–17.

²⁴E. Reiner and D. Pingree, Babylonian Planetary Omens, vol. 2 (Malibu, 1981), 17–18; H. Hunger and D. Pingree (note 6), 61.

²⁵W.G. Lambert, ‘Babylonian Astrological Omens and Their Stars’, Journal of the American Oriental Society, 107 (1987), 93–96; W. Horowitz, Mesopotamian Cosmic Geography (Winona Lake, IN, 1998), 165–66 and 252–56.

²⁶F.R. Stephenson and C.B.F. Walker, Halley's Comet in History (London, 1985), 19–20.

²⁷D. Brown, Mesopotamian Planetary Astronomy–Astrology (Groningen, Netherlands, 2000), 92–93.

²⁸E. Weidner (note 23), 121–23; F.R. Stephenson and C.B.F. Walker (note 26), 15–17.

²⁹J.M. Steele and J.M.K. Gray, ‘A Study of Babylonian Observations Referring to Zodiacal Signs’, forthcoming.

³⁰F. Rochberg, The Heavenly Writing: Divination, Horoscopy, and Astronomy in Mesopotamian Culture (Cambridge, 2004), 130–131.

³¹Known from two copies: BM 36737 + 36850 and 47912 which are from the same tablet but do not join, and BM 36599 + 36941. See texts B, C, and D of A. Aaboe and A. Sachs, ‘Two Lunar Texts of the Achaemenid Period from Babylon’, Centaurus, 14 (1969), 1–22 and A. Aaboe, J.P. Britton, J.A. Henderson, O. Neugebauer and A. Sachs, Saros Cycle Dates and Related Babylonian Astronomical Texts (Philadelphia, PA, 1991), 68–71.

³²For example, A. Aaboe et al. (note 31), text E, A. Aaboe and A. Sachs (note 31), text A and probably O. Neugebauer and A. Sachs (note 7), text C.

³³L. Brack-Bernsen and J.M. Steele, ‘Babylonian Mathemagics: Two Mathematical Astronomical–Astrological Texts’, in Studies in the History of the Exact Sciences in Honour of David Pingree, edited by C. Burnett, J.P. Hogendijk, K. Plofker and M. Yano (Leiden, 2004), 95–125.

³⁴H. Hunger and D. Pingree (note 6), 145–46.

³⁵Sexagesimal places are conventionally indicated by commas with a semicolon separating units from fractions.

³⁶F.X. Kugler, Sternkunde und Sterndienst in Babel (Münster, Germany, 1907), i, 39.

³⁷E. Weidner, Gestirn-Darstellungen auf babylonischen Tontafeln (Graz, Austria, 1967); U. Koch-Westenholz, Mesopotamian Astrology: An Introduction of Babylonian and Assyrian Celestial Divination (Copenhagen, 1995), 165–66.

³⁸R. Wallenfels, ‘Zodiacal Signs Among the Seal Impressions from Hellenistic Uruk’, in The Tablet and the Scroll: Festschrift for W.W. Hallo, edited by M.E. Cohen (Bethseda, MD, 1993), 281–89.

³⁹A similar view has been presented by L. Brack-Bernsen and H. Hunger, ‘The Babylonian Zodiac: Speculations on its Invention and Significance’, Centaurus 41 (1999), 280–92; D. Brown, ‘The Cuneiform Conception of Celestial Space and Time’, Cambridge Archaeological Journal, 10 (2000), 103–22; F. Rochberg (note 30), 129, and others.

⁴⁰L. Brack-Bernsen and J.M. Steele (note 33).

⁴¹E. Reiner, Astral Magic in Mesopotamia (Philadelphia, PA, 1995), 115.

⁴²A. Aaboe and A. Sachs (note 31), Text B col. v.

⁴³On the relationship between these two tablets, see N.A. Roughton, J.M. Steele, and C.B.F. Walker (note 14) 564–65.

⁴⁴A. Sachs, ‘A Late Babylonian Star Catalgue’, Journal of Cuneiform Studies, 6 (1952), 146–50; N.A. Roughton, J.M. Steele, and C.B.F. Walker (note 14), Appendix A.

⁴⁵Uniquely, and for reasons not understood, two positions are given for the Rear Foot of the Lion: 30 (Leo) and 1 Virgo.

⁴⁶N.A. Roughton, J.M. Steele, and C.B.F. Walker (note 14).

⁴⁷J.M. Steele, ‘Remarks on the Sources for the Lunar Latitude Section of Atypical Astronomical Cuneiform Text E’, Archiv für Orientforschung, in press.

⁴⁸V. Donbaz and J. Koch, ‘Ein Astrolab der Dritten Generation: NV 10’, Journal of Cuneiform Studies, 47 (1995), 63–84 with a transliteration of the obverse of LBAT 1502 on p. 76.

⁴⁹J.M. Steele (note 47).

⁵⁰L. Brack-Bernsen and H. Hunger, ‘On ‘the Atypical Astronomical Cuneiform Text E’: A Mean Value Scheme for Predicting Lunar Latitude’, Archiv für Orientforschung, in press.

⁵¹N.M. Swerdlow (note 12), 34.

⁵²N.M. Swerdlow (note 12), 34.

⁵³P.J. Huber, ‘Ueber den Nullpunkt der babylonischen Ekliptic’, Centaurus, 5 (1958), 192–208.

⁵⁴For further examples of overlapping data in a Diary and an Almanac, see H. Hunger and D. Pingree (note 6), 163.

⁵⁵A. Jones (note 15), 526–27.

⁵⁶For example, J.M. Steele and J.M.K. Gray (note 29), and unpublished studies by A. Jones and J.P. Britton.

⁵⁷J.M. Steele and J.M.K. Gray (note 29).

⁵⁸O. Neugebauer, ‘The Alleged Babylonian Discovery of the Precession of the Equinoxes’, Journal of the American Oriental Society, 70 (1950), 1–8.

⁵⁹O. Neugebauer, ‘Studies in Ancient Astronomy VII: Magnitudes of Lunar Eclipses in Babylonian Mathematical Astronomy’, Isis, 36 (1945), 10–15.

⁶⁰See B.L. van der Waerden, Anfänge ser Astronomie (Groningen, 1966), 145 and A. Aaboe and J.A. Henderson, ‘The Babylonian Theory of Lunar Latitude and Eclipses According to System A’, Archives Internationales d'Histoire des Sciences 25 (1975), 196–211, where these assumptions (formulated in modern terms) are demonstrated to underlie column E.

⁶¹O. Neugebauer (note 8), 191 and 199.

⁶²C.B.F. Walker, ‘Astronomical Tablets’, in Cuneiform Texts in the Metropolitan Museum (New York, 2005), ii, 344–45.

⁶³A. Aaboe et al. (note 31), text D; A. Aaboe, ‘Remarks on the Theoretical Treatment of Eclipses in Antiquity’, Journal for the History of Astronomy, 3 (1972), 105–18.

⁶⁴J.P. Britton, ‘An Early Function for Eclipse Magnitudes in Babylonian Astronomy’, Centaurus, 32 (1989), 1–52.

⁶⁵ Contra O. Neugebauer (note 8), 551. See also D. Brown (note 39), 114.

⁶⁶See, for example, J.M. Steele, Observations and Predictions of Eclipse Times by Early Astronomers (Dordrecht, The Netherlands, 2000), 27–28; C.B.F. Walker, ‘Achaemenid Chronology and the Babylonian Sources’, in Mesopotamia and Iran in the Persian Period: Conquest and Imperialism 539–331 BC, edited by J. Curtis (London, 1997), 17–25; and P.J. Huber and S. De Meis, Babylonian Eclipse Observations from 750 BC to 1 BC (Milan, 2004), 1–2.

⁶⁷J.P. Britton (note 64), 12–13.

⁶⁸O. Neugebauer and A. Sachs (note 7); L. Brack-Bernsen and H. Hunger (note 50).

⁶⁹L. Brack-Bernsen and H. Hunger (note 50).

⁷⁰K.P. Moesgaard, ‘The Full Moon Serpent: A Foundation Stone of Ancient Astronomy?’, Centaurus, 24 (1980), 51–96.

⁷¹J.M. Steele, ‘Four Procedure Texts Concerning Jupiter's Latitude and Synodic Motion from Babylon’, SCIAMVS, 6 (2005), 33–51.

⁷²O. Neugebauer and A. Sachs (note 7); J.M. Steele (note 15).

⁷³O. Neugebauer and A. Sachs (note 7), 208; followed by J.M. Steele (note 15), 275.

⁷⁴W. Horowitz (note 25), 119–20.

⁷⁵R. Wallenfels (note 38), 287.

⁷⁶A. Sachs, ‘Babylonian Horoscopes’, Journal of Cuneiform Studies 6 (1952), 49–75. See F. Rochberg-Halton, ‘TCL 6 13: Mixed Traditions in Late Babylonian Astrology’, Zeitschrift für Assyriologie 77 (1987), 207–28 for the correct reading of MI-ŠÌR as mi- . Cf. Hunger's comments to TU 11 Obv. 18 in L. Brack-Bernsen and H. Hunger (note 7), 19.

⁷⁷A. Sachs (note 76), 74. See also F. Rochberg-Halton (note 76), 222 fn. 15.

⁷⁸F. Rochberg-Halton (note 76).

⁷⁹F. Rochberg (note 30), 142.

⁸⁰J.M. Steele (note 15).

⁸¹Identified and photograph published by W. Horowitz, ‘Astronomical Cuneiform Texts in the Birmingham City Museum’, in Wisdom, Gods and Literature: Studies in Assyriology in Honour of W.G. Lambert, edited by A.R. George and I. Finkel (Winona Lake, IN, 2000), 311–14. A full edition of BCM A.1845–1982.2+ is being prepared by J.P. Britton, W. Horowitz, and J.M. Steele.

⁸²O. Neugebauer (note 8), 196.

⁸³A. Sachs (note 6).

⁸⁴L. Brack-Bernsen, Zur Entstehung der babylonischen Mondtheorie: Beobachtung und theortische Berechnung von Mondphasen (Stuttgart, Germany, 1997); L. Brack-Bernsen and H. Hunger (note 2002).

⁸⁵For the ACT texts, see O. Neugebauer (note 8); for MMA 86.11.363, see C.B.F. Walker (note 62).

⁸⁶My translation more or less follows O. Neugebauer (note 8), 234–35.

⁸⁷O. Neugebauer (note 8), 234.

⁸⁸BM 47734 has been identified by C.B.F. Walker who generously provided me with a copy of his unpublished transliteration.

⁸⁹See figures 1–5 in J.M. Steele (note 15).

⁹⁰The term used to describe the paths of the Moon and the planets in MUL.APIN is KASGAL to be read as the Akkadian word . This is a different term than is used to describe the fixed-width paths of the Moon and planets through the zodiac found in late texts: mālak. See W. Horowitz (note 25), 256–58.

⁹¹On the parallel treatment of solar and lunar eclipses, see A. Aaboe (note 63); J.P. Britton (note 64) and J.M. Steele, ‘Eclipse Predication in Mesopotamia’, Archive for History of Exact Sciences, 54 (2000), 421–51.

⁹²O. Neugebauer (note 8), 593.

⁹³D. Duke, ‘Hipparchus’ Coordinate System’, Archive for History of Exact Sciences, 56 (2002), 427–33.