The Babylonian lunar three in calendrical scrolls from Qumran

Studies on the Ancient Exact Sciences in Honor of Lis Brack-Bernsen, 2017

In this investigation, I sketch the way in which Babylonian astronomers may have derived the basic parameters of their lunar theory. I propose that the lunar velocity period of 6247 synodic months which underlies the construction of functions Φ and F of system A is derived by fitting a multiple of the Saros period of 223 synodic months within an integer number of solar years using the -year Sirius period relation. I further suggest that the lunar velocity period of 251 synodic months used to construct function F of system B is a direct derivative of the -month period. I also briefly discuss the origin of the periods of the solar velocity function B (of system A) and of the solar longitude function A (of system B) suggesting that the periods of these functions may have been derived from a refined version of the -year Sirius period. I finally discuss the timeframe of the possible stepwise development of these early lunar and solar functions.

Journal of Ancient Judaism , 2013

This paper re-examines 4QcryptA Lunisolar Calendar (4Q317), a scroll from Qumran in an esoteric Hebrew script with many emendations that aligns the moon’s daily waxing and waning to a 364-day calendar. It seeks to ascertain whether the calendar may be exegetically related to the Creation and also discusses the text’s arithmetical relationships with the cycles of the priestly courses from Qumran, possible intertextual allusions to other lunar calendars in the Dead Sea Scrolls (4QDaily Prayers [4Q503], 4QAstronomical Enocha-bar [4Q208–4Q209]), biblical passages, and parallels with another Mesopotamian calendar text. The first transcription of the largest fragments using a Cryptic A font is here published with a commentary (in the Appendix), focusing on the text’s unusual scribal features. A reconsideration of the calendar’s structure with a new arrangement of its dates is presented. [Please note there is a Hebrew transcription error in the Appendix, p.87 at 4Q317 frags 1+1a, line 9: the penultimate letter is cryptic waw, not a tav]

Centaurus, 2000

in G. Selz and K. Wagensonner (ed.), The Empirical Dimension of Ancient Near Eastern Studies – Die empirische Dimension altorientalischer Forschungen (Wien: LIT Verlag, 2011), 111-130

At the heart of the Babylonian lunar theory known as System A is Column Φ, a function that represents the length of the Saros assuming that the solar velocity is at its maximum, and from which all functions that reflect the moon's anomalistic motion are derived. In this paper we discuss the Q-polygon for analysing linear zig-zag functions and apply it to Column Φ. We show that using multiples of the smallest difference between Φ values provides a convenient way of calculating the change in Φ over long periods. We use this approach to analyse the Φ and related numbers on the so-called Atypical Text C. We draw attention to our new reading of some of the Φ-values and related numbers. These new readings show that the Φ-values are closely connected to the other, related, numbers in the text, and they make it obvious that there is a connection between the Φ-numbers, the 14-month anomalistic period and the truncated version of Φ, which was used for finding Λ and G from Φ.  We thank warmly Hermann Hunger for his careful collation of the lunar part of BM 36601, and John Britton for reading the manuscript and useful discussions. John Steele's work was supported by a Royal Society University Research Fellowship, and Lis Brack-Bernsen thanks the Deutsche Forschungsgemeinschaft for supporting her research.

Journal for the History of Astronomy xlv Vol. i, 2014

This paper is part of an ongoing debate regarding the theory raised a year ago by Dennis Duke and Matthew Goff in an attempt to re-explain the numerical values found in the Aramaic Astronomical Book (AAB). According to their proposal, the composers of the AAB or their sources computed the times of lunar visibility and invisibility using the phenomenon of lunar elongation. In this article, I accept Duke and Goff's argument that their theory does not contradict the data preserved in the fragments of the scrolls of the AAB. However, I demonstrate that their theory is unnecessarily complicated and that their proposal both ignores knowledge of physics available to the authors of the AAB while making use of knowledge that neither the authors of the AAB nor their sources obtained. Therefore, I suggest accepting Duke and Goff's theory as a modern explanation of the astronomy of the AAB, but not as a historical reconstruction.

2023

The ancient Egyptians celebrated the wAgj feast, an integral part of the Osirian cult. Data from the Illahun archive evidence that there were two instances of it: a fixed one, which fell on a specific civil date, and a movable one associated with a specific phase of the moon. There is disagreement about the lunar day and month on which the movable feast took place. The aggregation of the Illahun lunar dates into a ‘date net’ indicates that the disagreement is due both to peculiarities of the datasets of previous studies and to the incorrect numeration of lunar days in Parker’s list, which has been the standard for more than 70 years. Analysis of the lists of lunar days from the Ptolemaic Period also reveals the erroneous position of one of the days; when it is set to the proper position, the symmetry of the phases relative to the day of full moon improves. Based on the corrected numeration of lunar days, it is concluded that the movable wAgj in the original list fell on the 17th day of the second month after the emergence of Sopdet (the heliacal rising of Sirius in modern terms). Further research is needed to examine the effect of the proposed correction on the chronology of the Middle Kingdom.

SCIAMVS 11 (2010), 211-239

In memory of John P. Britton SCIAMVS 11(2010), 211-239 fragments, and the staff of the Department of the Middle East student room at the British Museum. Photographs are copyright the British Museum. Lunar Tables Text A: BM 42876 (= 81-7-1, 640) Contents: System A new and full moon ephemeris for SE 180. Transcription: Plate 1. Photograph: Plate 10. This small fragment preserves the upper left corner of a standard lunar ephemeris for SE 180. The ephemeris overlaps with Text B below, but the appearance of the two tablets suggests that they are not part of the same tablet but duplicate ephemerides covering the same year. Text B: BM 40754 + 44196 (= 81-4-28, 29 + 81-7-1, 1957)

Dead Sea Discoveries, 2014

This article puts forth a mathematical and astronomical model that helps explain the structure of the Aramaic Astronomical Book (aab; 4Q208–211), in particular the sequences of fractions in 4Q208 and 4Q209. The article confirms and builds upon Drawnel’s reconstruction of this highly formulaic composition. The model proposed here demonstrates that the numerous fractions of the aab, although they seem bewildering and incomprehensible to many readers today, constitute genuine and authentic astronomical knowledge. While there are parallels between the aab and Mesopotamian astronomical texts, especially the Enūma Anu Enlil, they do not necessarily indicate that the author of the aab had direct or extensive access to centers of astronomical knowledge in Babylon.