Anomalistic Month (Babylonian lunar theory)

an-uh-muh-LIS-tik MUNTH

babylonian: anomalistic month (modern term; Babylonian texts give the parameter as the integer-relation 9 anomalistic months = 248 days or 6247 synodic = 6695 anomalistic months)

Definition

The anomalistic month is the period of return of the Moon to the same point of its varying orbital velocity — equivalently the interval between successive perigees, or the cycle of the Moon’s daily speed. Late Babylonian mathematical astronomy used two values: the convenient round 27;33,20 days (embedded in the relation 9 anomalistic months = 248 days), and the more accurate 27;33,16,26,54 days derived internally from Columns F and G of the lunar ephemerides. Neugebauer notes the Babylonians treated the round value as a deliberate approximation of the accurate one.

In Tradition

Neugebauer, Rochberg, and Hunger-Pingree concur in treating the anomalistic month as one of the foundational period-parameters of Babylonian lunar theory. Neugebauer reports that the Babylonian astronomers of the third or fourth century BCE already knew empirically that the anomalistic month is longer than the sidereal month — a distinction that forced a more complex lunar model and, in his account, supplied the empirical basis on which Greek lunar theory built.

In Practice

A reader of a Babylonian lunar ephemeris identifies the anomalistic-month parameter in Column F (daily lunar velocity), modelled as a linear zigzag function bounded by extremal velocities 11;6,35 and 15;14,35 degrees/day around a mean of 13;10,35°/day, with a number-period of 248 days = 9 anomalistic months. The monthly ephemerides use the alternate relation 4,29 anomalistic months = 4,11 synodic months for the same parameter. System A Column Φ embeds a longer-period relation 6247 synodic months = 6695 anomalistic months — the parameter Rochberg notes is preserved in P. Oxy. 4139, the earliest such Babylonian lunar-period attested in a surviving Greek text. The 248-day / 9-anomalistic-month relation is the parameter Jones [1983] traces through Greek arithmetical papyri into Tamil Vakyam eclipse-computation and onward through Eurasia.

Historical Origin

Attested across the Seleucid-period ACT lunar corpus from Babylon and Uruk (c. 250-50 BCE), in P. Oxy. 4139, and in the Tamil Vakyam corpus. The 251 synodic = 269 anomalistic-month relation is credited to "Kidenas" (Kidinnu) by an early-3rd-century CE Ptolemy commentator. Modern treatments: Neugebauer, *Exact Sciences* (1957/1969) Ch. V §52 + Ch. VI §74 + Appendix I; *Selected Essays* (1983) essay [36] p. 443; Rochberg, *Heavenly Writing* (2004) p. 272; Hunger-Pingree, *Astral Sciences* (1999) pp. 243, 257-258.

Definition

In Tradition

In Practice

Historical Origin

Further Reading