Directions of Obscuration in Babylonian Eclipse Records

Neugebauer P. V. Hiller R. , “Spezieller Kanon der Mondfinsternisse für Vorderasien und Ägypten von 3450 bis 1 v. Chr.”, Astronomische Abhandlungen, ix (1934), 1–46, p. 3.

Sachs A. J. Hunger H. (eds), Astronomical diaries and related texts from Babylonia (6 vols, Vienna, 1988–2006).

Huber P. J. De Meis S. , Babylonian eclipse observations from 750 BC to 1 BC (Rome and Milan, 2004), 13.

Hunger H. , Lunar and planetary texts , vol. v of Sachs Hunger (eds), op. cit. (ref. 2) (hereafter H5), 13.

Standish E. M. , “JPL planetary and lunar ephemerides, DE405/LE405”, Jet Propulsion Laboratory interoffice memorandum 312.F (1998).

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.

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 ( Chapront J. Chapront-Touzé M. Francou G. , “A new determination of lunar orbital parameters, precession constant and tidal acceleration from LLR measurements”, Astronomy and 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.

All data of the solar eclipses together with maps covering the geographical region between (20°N, 5°O), (20°N, 50°O), (50°N, 5°O) and (50°N, 50°O), which were especially designed for the needs of historians, are available online at http://www.gautschy.ch/∼rita/archast/solec/solec.html.

Huber De Meis , op. cit. (ref. 3), 1.

Hunger , op. cit. (ref. 4).

I thank Kurt Locher for bringing this to my attention.

See e.g. The Full Moon Atlas, http://www.lunarrepublic.com/atlas/.

In such a way ecliptic position angles can be measured with a deviation of ±5°, depending on whether the eclipse occurred near the ascending or descending lunar node.

Neugebauer Hiller , op. cit. (ref. 1), 3.

Huber De Meis , op. cit. (ref. 3), 13.

PB_cal or PE_cal deviates less than 5° from the mathematical degree range for the following lunar eclipses: −500 Nov 08, −602 Oct 28, −345 Jan 14, −134 Mar 21, −98 Oct 06 and −97 Mar 31. For ecliptic position angles XB_cal or XE_cal the deviation from the mathematical degree range amounts to less than 5° for the lunar eclipses of: −576 Jun 14, −423 Sep 29, −405 Apr 15, −345 Jan 14, −316 Dec 13, −162 Mar 31, −119 Jun 02, and −75 Jan 28. For the solar eclipses this applies for XB_cal or XE_cal for: −322 Oct 07, and −189 Mar 14.

Huber De Meis , op. cit. (ref. 3), 22.

The calculated magnitudes depend on the choice of the shadow enlargement method. There are two different formulations available and the resulting small magnitude difference between these two methods is difficult to observe because the edge of the umbral shadow is poorly defined. The choice of the shadow enlargement method is important only in limiting cases where a small change in magnitude can shift an eclipse from one type to another as is the case for the lunar eclipse of −378 Apr 17.

Sometime between Hipparchus and Ptolemy such a true ecliptic coordinate system was developed ( Steele J. M. , “Celestial measurements in Babylonian astronomy”, Annals of science, lxiv (2007), 293–325, p. 320).

Jones A. , “A study of Babylonian observations of planets near normal stars”, Archive for the history of exact sciences , lviii (2004), 475–537, p. 498. Steele , op. cit. (ref. 19), 319.