On the Babylonian Sighting-Criterion for the Lunar Crescent and its Implications for Egyptian Lunar Data
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References
1. See e.g. Odeh M. Sh., “New criterion for lunar crescent visibility”, Experimental astronomy, xviii (2004), 39–64, p. 39.
2. Fatoohi L. J., Stephenson F. R., Al-Dargazelli S. S., “The Babylonian first visibility of the lunar crescent: Data and criterion”, Journal for the history of astronomy, xxx (1999), 51–72, p. 60.
3. Neugebauer O., Astronomical cuneiform texts: Babylonian ephemerides of the Seleucid period for the motion of the Sun, Moon, and the planets, i (London, 1955), 43.
4. Brack-Bernsen L., Hunger H., “TU 11, a collection of rules for the prediction of lunar phases and of month lengths”, SCIAMVS, iii (2002), 3–90, pp. 39 and 66.
5. Ossendrijver M., Babylonian mathematical astronomy: Procedure texts (New York, 2012), 161–78 and 195–202.
6. Fotheringham J. K., “On the smallest visible phase of the Moon”, Monthly notices of the Royal Astronomical Society, lxx (1910), 527–30; Maunder E. W., “On the smallest visible phase of the Moon”, Journal of the British Astronomical Association, xxi (1911), 355–62; Schoch K., “Astronomical and calendrical tables”, in Langdon S., Fotheringham J. K. (eds), The Venus Tablets of Ammizaduga: A solution of Babylonian chronology by means of the Venus observations of the First Dynasty (Oxford, 1928), 95; Neugebauer P. V., Astronomische Chronologie, ii (Berlin and Leipsig, 1929), Table E21.
7. Table E21 provided by Schoch K., in Neugebauer, op. cit. (ref. 6).
8. Bruin F., “The first visibility of the lunar crescent”, Vistas in astronomy, xxi (1977), 331–58.
9. Schaefer B. E., “Visibility of the lunar crescent”, Quarterly journal of the Royal Astronomical Society, xxix (1988), 511–23.
10. Yallop B. D., “A method for predicting the first sighting of the new crescent Moon”, NAO technical note, no. 69 (1997).
11. Krauss R., “Babylonian crescent observation and Ptolemaic-Roman lunar dates”, PalArch's journal of Egypt/Egyptology, ix/5 (2012), 1–95.
12. Ibid., 10–22.
13. See e.g. Krauss R., “Lunar dates”, in Hornung E., Krauss R., Warburton D. A. (eds), Ancient Egyptian chronology (Leiden, 2006), 395–431; Huber P. J., “The astronomical basis of Egyptian chronology of the second millennium BC”, Journal of Egyptian history, iv (2011), 172–227; Gautschy R., “Die Monddaten aus dem Archiv von Illahun: Chronologie des Mittleren Reiches”, Zeitschrift für Ägyptische Sprache und Altertumskunde, clxxviii (2011), 1–19; and Gautschy R., “Chronology of the Egyptian New Kingdom revisited”, Current research in Egyptology, xiii (2013), 55–69.
14. Standish E. M., “JPL planetary and lunar ephemerides, DE405/LE405”, Jet Propulsion Laboratory Interoffice Memorandum 312.F (1998).
15. Espenak F., Meeus J., Five millennium canon of solar eclipses: −1999 to +3000 (2000 BCE to 3000 CE), Revision 1.0 (2007 May 11), http://eclipse.gsfc.nasa.gov/SEcat5/deltatpoly.html.
16. Morrison L. V., Stephenson F. R., “Historical values of the Earth's clock error ΔT and the calculation of eclipses”, Journal for the history of astronomy, xxxv (2004), 327–36, p. 332. The ΔT values calculated in such a way assume a value for the Moon's secular acceleration of −26 arcsec/cy2. I, however, use a slightly different value of −25.826 arcsec/cy2 to be consistent with the value that was used for the construction of the lunar ephemeris (J. Chapront, M. Chapront-Touzé, G. Francou, “A new determination of lunar orbital parameters, precession constant and tidal acceleration from LLR measurements”, Astronomy & astrophysics, ccclxxxvii (2002), 700–9, p. 705 Table 7). Thus, a small correction to ΔT has been applied to the values derived from the polynomial expressions.
17. Yallop, op. cit. (ref. 10).
18. The topocentric threshold values were obtained by performing geocentric as well as topocentric calculations for approximately 1000 available observations: the Babylonian observations collected by Stern S. (“The Babylonian month and the new Moon: Sighting and prediction”, Journal for the history of astronomy, xxxix (2008), 22–30) and modern observations published by Odeh (op. cit. (ref. 1)).
19. Sachs A. J., Hunger H. (eds), Astronomical diaries and related texts from Babylonia, i: Diaries from 652 B.C. to 262 B.C. (Vienna, 1988); ii: Diaries from 261 B.C. to 165 B.C. (1989); iii: Diaries from 164 B.C. to 61 B.C. (1996); iv: Undated diaries (still unpublished); v: Lunar and planetary texts (2001); vi: Goal year texts (2006); vii: Almanacs and normal star almanacs (still unpublished). I thank Hermann Hunger for making a state-of-the-art version of the still unpublished Almanacs available to me.
20. Since the main aim of the paper is establishing the lower limit of crescent visibility prediction, all accounts with larger lagtimes can be disregarded.
21. Brack-Bernsen and Hunger, op. cit. (ref. 4), 34.
22. For an explanation why these formulae are very good approximations see Brack-Bernsen and Hunger, op. cit. (ref. 4), 34–5.
23. Krauss, op. cit. (ref. 11), 19–22.
24. Yallop, op. cit. (ref. 10), 6–11.
25. Schoch, op. cit. (ref. 6), 95; Schoch K. in Neugebauer, op. cit. (ref. 6), Table E21; Krauss, op. cit. (ref. 11), 59–60.
26. Yallop, op. cit. (ref. 10), 4.
27. Krauss, op. cit. (ref. 11), 70–6.
28. Odeh, op. cit. (ref. 1), 44–60.
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