Mean Synodic Month (Babylonian lunar theory)

MEEN sih-NOD-ik MUNTH

babylonian: mean synodic month / m = 29;31,50,8,20 days (modern label; the Babylonian texts carry the value as a sexagesimal computed in Column G of the System B lunar ephemerides)

Definition

The mean synodic month is the average interval from one Sun-Moon conjunction to the next — the average lunar month — and the empirical anchor on which the Babylonian System A and System B lunar ephemerides are built. The value derived in System B from Column G of the lunar ephemerides is m = 29;31,50,8,20 days. Neugebauer singles it out as one of the genuine Babylonian contributions to Greek astronomy: it is fundamental to Hipparchus’s lunar theory, recorded in Ptolemy’s *Almagest* IV,2, and survives into the eleventh-century Toledan Tables.

In Tradition

Neugebauer, Rochberg, and Hunger-Pingree concur in treating the mean synodic month as the abscissa-unit of the lunar ephemerides — each successive line of a Babylonian lunar Ephemeris is spaced by exactly one mean synodic month, with the date entry in the first column denoting not a whole calendar month but the moment of the mean conjunction falling at its end. The same value m = 29;31,50,8,20 days underlies the molad-interval of the Jewish calendar, a Babylonian inheritance transmitted to Maimonides via the Almagest.

In Practice

A reader of a Late Babylonian lunar Ephemeris identifies the mean synodic month as the line-spacing of the table: each row covers one synodic month, and Column G carries the value as a derived sexagesimal quantity. The variations of the actual time between consecutive new crescents around this mean value were, for Neugebauer, "the decisive achievement of Babylonian mathematical astronomy" — modelled by Columns A through K of the System B lunar ephemerides, each tracking a specific quantity (solar velocity, lunar velocity, lunar latitude, length of daylight, etc.) that determines the genuine excursion of a particular lunation from the mean. The mean synodic month sits at the top of the dependency chain: the period-relation 6247 synodic = 6695 anomalistic months, the Saros 223 synodic months, and the Metonic 235 synodic = 19 years are all framed in mean-synodic-month units.

Historical Origin

Attested across the Seleucid-period ACT lunar Procedure Texts and Ephemerides from Babylon and Uruk (c. 250-50 BCE). Transmitted via Hipparchus to Ptolemy’s *Almagest* IV,2; transmitted via the Almagest to Maimonides and the Jewish-calendar molad; transmitted to the eleventh-century Toledan Tables. Modern critical treatments: Neugebauer, *The Exact Sciences in Antiquity* (1957/1969) Ch. V §52 pp. 111-122; *Astronomy and History: Selected Essays* (1983) essay [6] p. 163 and essay [34] p. 386; Hunger-Pingree, *Astral Sciences in Mesopotamia* (1999) Ch. II §C4.

Definition

In Tradition

In Practice

Historical Origin

Further Reading