Eclipse Prediction in Mesopotamia

Archive for History of Exact Sciences

Volumn 54, Issue 5, 2000, Pages 421-454

  Steele, John M ^a  

^a NONE

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EID: 26444539932     PISSN: 00039519     EISSN: 14320657     Source Type: Journal    
DOI: 10.1007/s004070050007     Document Type: Article

References (99)

1. Those tablets of Einnna Aim Enlil concerned with lunar eclipses have been edited by R Rochberg-Halton, Aspects of Babylonian Celestial Divination: The Lunar Eclipse Tablets of Enuma Ann Enlil, Archiv für Orientforschung Beiheft 22 (Horn, 1988).
2. The Substitute King Ritual is discussed by S. Parpola, Letters from Assyrian Scholars to the Kings Esarhaddon and Assurbanipal, Part II: Commentary and Appendices, Alter Orient und Altes Testament 5/2 (Neukirchen-Vluyn, 1983), xxii-xxxii, and
3. J. Bottéro, Mesopotamia: Writing, Reasoning, and the Cods (University of Chicago Press, Chicago, 1992), 138-155. For examples of texts describing rituals involving the playing of a kettledrum,
4. see P.-A. Beaulieu and J. P. Britton, "Rituals for an Eclipse Possibility in the 8th Year of Cyrus," Journal of Cuneiform Studies 46 (1994), 73-86,
5. and D. Brown and M. Linssen, "BM 134761 = 1965-10-14, 1 and the Hellenistic Period Eclipse Ritual from Uruk," Revue d'AssyrioIogique et d'Archéologie Orientale (forthcoming).
6. By contrast, in China if an event was predicted before it occurred then its significance as an omen was reduced. See N. Sivin, "Cosmos and Computation in Early Chinese Mathematical Astronomy," T'oung Pao 55 (1969), 1-73.
7. See A. Sachs, "Babylonian Observational Astronomy," Philosophical Transactions of the Royal Society of London 276 (1974), 43-50.
8. It is worth noting that while we have no evidence that the Babylonians possessed a physical theory of eclipses, all of the concepts used in the following discussion (syzygy, nodes, anomaly, etc.) were, or became, familiar to them.
9. The situation for solar eclipses is complicated by the fact that, due to the relative sizes of the Earth, moon and sun, the moon's umbral shadow only falls on a small part of the Earth's surface. Thus the prediction of solar eclipses for any given site requires knowledge of the geometry of the Earth-moon-sun system, and of the geographical location on the Earth's surface of the observation site. There is no evidence that the Babylonian astronomers were able to take this into account. Instead, I agree with Aaboe in suggesting that the Babylonians may have been content to distinguish between those conjunctions at which solar eclipses \\erepossible, and to exclude those at which they were not. See A. Aaboe, "Remarks on the Theoretical Treatment of Eclipses in Antiquity," Journal for the History of Astronomy 3 (1972), 105-118.
10. Here and elsewhere I am transcribing sexagesimal numbers using commas to separate places and a semicolon to separate integers from fractions.
11. I am here following the discussion given by J. P. Britton, "An Early Function for Eclipse Magnitudes in Babylonian Astronomy," Centaiirus 32 (1989), 1-52. For further details I refer the reader to his article.
12. More generally, this time interval is a very complicated function dependent upon a number of factors including the moon's longitude, latitude and velocity, and the visibility conditions. See O. Neugebauer, The Exact Sciences in Antiquity (Brown University Press, Providence, 1957), 107-110, and
13. L. Brack-Bernsen and O. Schmidt, "On the Foundations of the Babylonian Column : Astronomical Significance of Partial Sums of the Lunar Four," Centaums 37 (1994), 183-209.
14. Because the moon's orbit is not exactly circular its distance from the Earth varies. The average interval between successive closest approaches to the Earth is known as an anomalistic month and is equal to 27.5545 days.
15. As has often been noted, the term "Saros" is modern. To the Babylonians this period was simply called 18 MU.MES "18 years." See O. Neugebauer, The Exact Sciences in Antiquity (Brown University Press, Providence, 1957), 141-143 for a history of the term "Saros."
16. Throughout this paper, magnitudes are given as a fraction of the lunar or solar diameter, and local times in hours and decimals.
17. For details of these eclipse periods, see J. P. Britton, "An Early Function for Eclipse Magnitudes in Babylonian Astronomy," Centaitnts 32 (1989), 1-52.
18. Earlier astronomical records are preserved from Babylon, but, with the exception of a single diary from 652 BC, they are all contained in compilations which were probably made at a later date.
19. The letters have been edited most recently by S. Parpola, Leiters from Assyrian and Babylonian Scholars (Helsinki University Press, Helsinki, 1993). All translations of the letters will be taken from this edition and quoted by their LABS number.
20. This is a revised version of Parpola's earlier edition, Letters from Assyrian Scholars to the Kings Esarhaddon and Assurbanipal, Part 1: Texts, Alter Orient und Altes Testament 5/1 (Neukirchen-Vluyn, 1970).
21. See also his commentary Letters from Assyrian Scholars to the Kings Esarhaddon and Assurbanipal, Part 11: Commentary and Appendices, Alter Orient und Altes Testament 5/2 (Neukirchen-Vluyn, 1983).
22. The reports have been edited most recently by H. Hunger, Astrological Reports to Assyrian Kings (Helsinki University Press, Helsinki, 1992). All translations of the reports will be taken from this edition and quoted by their ARAK number.
23. This edition supersedes R. C. Thompson, The Reports of the Magicians and Astrologers of Nineveh and Babylon in the British Museum (London, 1900).
24. H. Hunger, Astrological Reports to Assyrian Kings (Helsinki University Press, Helsinki, 1992), xvi.
25. See U. Koch-Westenholz, Mesopotamian Astrology (Museum Tusculanum Press, Copenhagen, 1995), 105.
26. Christopher Walker has since examined the tablet and confirmed that a reading of 5 is quite possible.
27. ACh. Sin 3, 26.
28. See F. X. Kugler and J. Schaumberger, Sternkunde und Sterdienst in Babel. Ergänzungen HI (Aschendorffsche Verlagsbuchhandlung, Münster, 1935), 251 ,
29. and F. RochbergHalton, Aspects of Babylonian Celestial Divination: The Lunar Eclipse Tablets of Enüma Aim Enlil, Archiv für Orientforschung Beiheft 22 (Horn, 1988), 41 on which my translation is based.
30. Parpola, Letters from Assyrian Scholars to the Kings Esarhaddon andAssurbanipal, Part II: Commentary and Appendices, Alter Orient und Altes Testament 5/2 (Neukirchen-Vluyn, 1983), 51.
31. The use of the 47-month eclipse period by the Assyrian scholars was also claimed by B. L. van der Waerden, Science Awakening II: The Birth of Astronomy (Noordhoff, Leiden, 1974), 118-119.
32. The dates proposed by Parpola in Letters from Assyrian Scholars to the Kings Esarhacldon and Assurbanipal, Part II: Commentary and Appendices, Alter Orient und Altes Testament 5/2 (Neukirchen-Vluyn, 1983) for many of the texts containing only eclipse predictions cannot be justified.
33. See, for example, S. De Meis and H. Hunger, Astronomical Dating of Assyrian and Babylonian Reports (Istituto Italiano per 1'Africa e l'Oriente, Rome, 1998)
34. and D. R. Brown, Neo-Assyrian and Neo-Babylonian Planetary Astronomy-Astrology (747-612 BC) (Styx, forthcoming), Appendix 2.
35. It may eventually be possible to determine whether eclipse periods were being used by the scholars, but first it will be necessary to systematically redate all of the letters. This is no small task and it would take me far beyond the scope of this article to even attempt to redate those letters including references to eclipses.
36. In Enüina Amt Enlil the omen associated with an eclipse depends in part upon the watch (a third of a day or night) in which it took place. Since the eclipses were being reported for divination there was no need for the scholars to record the time of the eclipse more precisely.
37. These are the so called "Lunar Six" described by A. Sachs, "A Classification of the Babylonian Astronomical Tablets of the Seleucid Period," Journal of Cuneiform Studies 2 (1948), 271-290.
38. The ACT texts have largely been published by O. Neugebauer, Astronomical Cuneiform Texts (Lund Humphries, London, 1955). For references to texts published subsequently (mostly by Aaboe, Neugebauer and Sachs), see
39. O. Neugebauer, A History of Ancient Mathematical Astronomy (Springer-Verlag, Berlin, 1975). When discussing the ACT texts I will follow the terminology established by Neugebauer and assume some knowledge of the methods of Babylonian mathematical astronomy.
40. The term NMAT (Non-Mathematical Astronomical Texts) was coined by A. Aaboe, "Observation and Theory in Babylonian Astronomy," Centaiims 24 (1980), 14-35.
41. These descriptions are based upon those given by A. Sachs, "A Classification of the Babylonian Astronomical Tablets of the Seleucid Period," Journal of Cuneiform Studies 2 (1948), 271-290
42. and "Babylonian Observational Astronomy," Philosophical Transactions of the Royal Society of London 276 (1974), 43-50,
43. and H. Hunger, "Non-mathematical Astronomical Texts and Their Relationships," in N. M. Swerdlow (ed.) Ancient Astronomy and Celestial Divination (The MIT Press, Cambridge, forthcoming). For further details I refer the reader to these articles.
44. Most of the extant texts have been catalogued by A. J. Sachs, Late Babylonian Astronomical and Related Texts (Brown University Press, Providence, 1955).
45. Copies of many of these tablets drawn by T. G. Pinches and J. N. Strassmaier were published in this work.
46. The identity of the Babylonian astronomers is not fully known. In the Hellenistic period at least they held the title tupsar Emimci Ami Enlil "Scribe of (the great omen series) Enüma Anu Enlil" and were employed in the Esagila temple as astrologer-astronomers.
47. See F. Rochberg, "The Cultural Locus of Astronomy in Late Babylonia," in H. D. Galter (ed.), Die Rolle der Astronomie in den Kulturen Mesopotamiens (Grazer Morgenländische Studien, Graz, 1993), 3145.
48. A number of modern terms have been adopted to describe these individuals - none of which are very satisfactory - including "scribe," "astrologer," and "astronomer." For convenience I will use "astronomer," with the proviso that the astrological roles of these individuals are not forgotten.
49. All of the dateable Diaries have been published by A. J. Sachs and H. Hunger, Astronomical Diaries and Related Texts from Babylon, Volumes I-IH (Österreichischen Akademie der Wissenschaften, Vienna, 1988-1996). Translations of Diaries will be quoted from this work.
50. The eclipse records in the Goal-Year texts, together with many of the records from the Diaries and the Eclipse Texts, have been edited by P. J. Huber, Babylonian Eclipse Observations: 750 BC to 0 (Unpublished manuscript, 1973).
51. These texts of individual phenomena will shortly be published by A. J. Sachs and H. Hunger, Astronomical Diaries and Related Texts from Babylon, Volume V (Österreichischen Akademie der Wissenschaften, Vienna, forthcoming).
52. The Horoscopes have been published by F. Rochberg, Babylonian Horoscopes, Transactions of the American Philosophical Society 88/1 (Philadelphia, 1998).
53. The first discussion of this terminology was, I believe, by F. X. Kugler, "Zur Erklärung der Babylonischen Mondtafeln I: Mond- und Sonnenfinsternisse," Zeitschrift für Assyriologie 15 ( 1906), 178-209.
54. More recently, see A. J. Sachs and H. Hunger, Astronomical Diaries and Related Texts from Babylon, Volume I (Österreichischen Akademie der Wissenschaften, Vienna, 1988), 23.
55. J. M. Steele and F. R. Stephenson, "Lunar Eclipse Times Predicted by the Babylonians," Journal for the History of Astronomy, 28 (1997) 119-131 and
56. J. M. Steele, "Solar Eclipse Times Predicted by the Babylonians," Journal for the History of Astronomy, 28 (1997) 131-139.
57. In the first of these papers I speculated that one motivation for predicting the time of the beginning of the eclipse, rather than the moment of syzygy, was that if the prediction was to be used for religious purposes then it seems likely that the moment when the eclipse would begin would be the most useful time to predict. This has now been confirmed by the description of an eclipse ritual on BM 134761 which explains that the period of ritual lamentation during an eclipse begins at the moment of first contact and continues until the middle of the eclipse.
58. See D. Brown and M. Linssen, "BM 134761 = 1965-10-14, 1 and the Hellenistic Period Eclipse Ritual from Uruk," Revue d'Assyriologique et d'Archéologie Orientale (forthcoming).
59. J. P. Britton, "An Early Function for Eclipse Magnitude in Babylonian Astronomy," Centaurus 32 (1989), 1-52.
60. See also O. Neugebauer, A History of Ancient Mathematical Astronomy (Springer-Verlag, Berlin, 1975), 504-505.
61. A. Aaboe, "Remarks on the Theoretical Treatment of Eclipses in Antiquity," Journal for the History of Astronomy 3 (1972), 105-118.
62. P.-A. Beaulieu and J. P. Britton, "Rituals for an Eclipse Possibility in the 8th Year of Cyrus," Journal of Cuneiform Studies 46 (1994), 73-86.
63. C. B. F. Walker, "Achaemenid Chronology and the Babylonian Sources," in J. Curtis (ed.), Mesopotamia and Iran in the Persian Period: Conquest and Imperialism 539-331 BC (British Museum Press, London, 1997), 17-25.
64. A full discussion of the structure and layout of all the Eclipse Texts is given in my appendix to A. J. Sachs and H. Hunger, Astronomical Diaries and Related Texts from Babylon, Volume V (Österreichischen Akademie der Wissenschaften, Vienna, forthcoming).
65. These dates have been taken from the list of eclipse records in J. M. Steele, Observations and Predictions of Eclipse Times by Early Astronomers (forthcoming), Appendix 1.
66. In this and the following tables, dates of full and new moons have been taken from H. H. Goldstine, New and Full Moons 1001 BC to AD 1651 (American Philosophical Society, Philadelphia, 1973).
67. For columns 8 and 9 the tablet LBAT *1420 fully determines the layout of the table, but the important point is that by reconstructing the whole table as described above, we can see that this same layout extends beyond these two columns.
68. The Diaries for those months are unfortunately not preserved, so we cannot be sure whether these two eclipses were observed or not.
69. The Saros Canon and related texts have been published by A. Aaboe, J. P. Britton, J. A. Henderson, O. Neugebauer, and A. J. Sachs, Saros Cycle Dates and Related Babylonian Astronomical Texts, Transactions of the American Philosophical Society 81/6 (Philadelphia, 1991).
70. In fact, the small fragment LBAT *1425 agrees with both of the two schemes.
71. J. P. Britton, "Scientific Astronomy in Pre-Seleucid Babylon," in H. D. Galter (ed.), Die Rolle der Astronomie in den Kulturen Mesopotamiens (Grazer Morgenländische Studien, Graz, 1993), 61-76.
72. Perhaps the theoretical Text L which has an unusual distribution into 8-7-7-8-8 groups may fall into this category. On this text, see A. Aaboe, J. P. Britton, J. A. Henderson, O. Neugebauer, and A. J. Sachs, Sams Cycle Dates and Related Babylonian Astronomical Texts, Transactions of the American Philosophical Society 81/6 (Philadelphia, 1991), 35-62.
73. First published as Texts B, C, and D by A. Aaboe and A. J. Sachs, 'Two Lunar Texts of the Achaemenid Period from Babylon," Centaurus 14 (1969), 1-22, and
74. published with an additional fragment as Text S by J. P. Britton, "An Early Function for Eclipse Magnitude in Babylonian Astronomy," Centaurus 32 (1989), 1-52.
75. In addition, a tablet from Nippur, CBS 11901, contains a prediction of a solar eclipse on -424 October 23. This tablet was last discussed in its entirety by F. X. Kugler, Sternkunde und Sterdienst in Babel. Ergänzungen 11 (Aschendorffsche Verlagsbuchhandlung, Münster, 1914), 233-234.
76. I have here accepted the corrections to the Solar Saros proposed by A. Aaboe, J. P. Britton, J. A. Henderson, O. Neugebauer, and A. J. Sachs, Saros Cycle Dates and Related Babylonian Astronomical Texts, Transactions of the American Philosophical Society 81/6 (Philadelphia, 1991 ). Uncorrected, the Solar Saros contains not the expected 8-7-8-7-8 distribution of eclipses, but an 8-8-6-8-8 distribution. It should be noted that any correction applied is in some ways arbitrary.
77. This effectively confirms the placing of the five month interval between rows 17 and 18 in the final part of the lunar Saros table.
78. For a detailed discussion of these methods, see O. Neugebauer, Astronomical Cuneiform Texts (Lund Humphries, London, 1955), 41-85
79. and "Studies in Ancient Astronomy VII: Magni-tudes of Lunar Eclipses in Babylonian Mathematical Astronomy," his 36 (1945), 10-15,
80. 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), 181-222, and the references therein.
81. A. Aaboe, "A Computed List of New moons for 319 BC to 316 BC from Babylon: BM 40094," Del Kongelige Danske Vldenskabemes Selskab Matematisk-fysiske Meddeleser 37/3 (1960).
82. F. N. H. Al-Rawi and A. R. George, "Enuma Anu Enlil XIV and Other Early Astronomical Tables," Archiv für Orientforsclnmg 38-39 (1991-1992), 52-73.
83. H. Hunger and D. Pingree, MUL.APIN: An Astronomical Compendium in Cuneiform, Archiv für Orientforschung Beiheft 24 (Hom, 1989).
84. A. Livingstone, Mystical and Mythological Explanatory Works of Assyrian and Babylonian Scholars (Oxford University Press, Oxford, 1986).
85. See, most recently, D. Brown, J. Fermor and C. Walker, "The Water Clock in Mesopotamia," Archiv für Orientforschiing (forthcoming) with references to earlier discussions.
86. A copy of TU 11 (=AO 6455) was published by R Thureau-Dangin, Tablettes d'Uriik, Textes Cuneiform du Louvre 6 (Paris, 1922). A full edition with translation and commentary is currently being prepared by H. Hunger and L. Brack-Bemsen.
87. See L. Brack-Bemser, "Goal-Year Tablets: Lunar Data and Predictions," in N. M. Swerdlow (ed.) Ancient Astronomy and Celestial Divination (The MIT Press, Cambridge, forthcoming).
88. A more detailed discussion of the possible role of the lunar six in predicting eclipses will have to wait for further investigations of TU 11 and related texts.
89. Chinese astronomers of the first millennium AD used simple relationships between magnitude and duration in their calendrical systems. For example, in the Ta-yen-Ii magnitudes were calculated on a scale of 1 to 15, and from these the duration of a lunar eclipse was obtained by adding to it 2 k'o if the magnitude was less than 5, 4 k'o if it was less than 10, and 5 k'o if it was greater than 10. For solar eclipses, 2 k'o was simply added to the magnitude to give the duration. The k'o was a unit of time such that there are 100 k'o in a day. For details, see K. Yabuuti, "Astronomical Tables in China from the Han to the T'ang Dynasties," in K. Yabuuti (éd.), Chûgokii Chûsei Kagakit Gijiitsnslii No Kenkyû (Tokyo, 1963)445-492.
90. K. P. Moesgaard, 'The Full Moon Serpent: A Foundation Stone of Ancient Astronomy," Centaums 24 (1980), 51-96.
91. On these individuals, see F. Rochberg, "The Cultural Locus of Astronomy in Late Babylonia," in H. D. Galter (ed.), Die Rolle der Astronomie in den Kulturen Mesopotamiens (Grazer Morgenländische Studien, Graz, 1993), 31-45
92. and "Scribes and Scholars: the tiipSar Enûma. Ami Enlil" in H. Neumann (ed.), Fs. Oelsner (Berlin, forthcoming).
93. H. H. Goldstine, New and Full Moons 1001 BC to AD 1651 (American Philosophical Society, Philadelphia, 1973). Goldstines times contain some error due to his not making sufficient allowance for long-term variations in the Earth's rate of rotation, but this is generally less than about 0.2 hour which is insignificant for the present purposes.
94. This is partly caused by the convention of recording the time relative to sunrise or sunset. Both System A and System B ephemerides have a column C which contains the supposed length of the day at each syzygy. This column is based upon the ratio of 3:2 for the longest to the shortest night, which is not exact for Babylon. Errors in column C are propagated directly to column M, the time of syzygy. See O. Neugebauer, A History of Ancient Mathematical Astronomy (Springer-Verlag, Berlin, 1975), 366-371.
95. J. M. Steele and F. R. Stephenson, "Lunar Eclipse Times Predicted by the Babylonians," Journal for the History of Astronomy, 28 (1997) 119-131 and
96. J. M. Steele, "Solar Eclipse Times Predicted by the Babylonians," Journal for the History of Astronomy, 28 (1997) 131-139.
97. J. M. Steele, F. R. Stephenson and L. V. Morrison, 'The Accuracy of Eclipse Times Measured by the Babylonians," Journal for the History of Astronomy, 28 (1997) 337-345.
98. A. J. Sachs and H. Hunger, Astronomical Diaries and Related Texts from Babylon, Volume I (Österreichischen Akademie der Wissenschaften, Vienna, 1988), 25.
99. I hope discuss some of these questions in detail in a forthcoming article.