Lunar Theory (Babylonian mathematical astronomy)

LOO-nar THEE-uh-ree

babylonian: lunar theory (modern Assyriological label for the ACT lunar Procedure Text + Ephemeris corpus; the Babylonian scribes give the system without a name)

Definition

The Babylonian lunar theory is the body of mathematical-astronomical technique by which Late-Babylonian scribes predicted lunar phenomena — first visibility of the new crescent (defining the start of each calendar month), eclipses, the Lunar Six time-intervals around full moon, and the variable length of the synodic month. Neugebauer treats it as "undoubtedly the most characteristic section of the whole development of Babylonian astronomy" and, in essay [6], proposes that the planetary theory was modelled on it: the lunar theory pursued the length of the lunar month, the planetary theory pursued the laws governing consecutive synodic phenomena, by the same arithmetical means.

In Tradition

Neugebauer reads the Babylonian lunar theory as both the most refined achievement of Babylonian arithmetical astronomy and the ancestral template on which the planetary theory was built — a finding Hunger-Pingree and Rochberg accept. The theory had to master the variable velocity of both Sun and Moon and the seasonally varying ecliptic-horizon angle, because the month begins with the new crescent’s first visibility and predicting month length requires modelling both motions plus local-horizon geometry.

In Practice

A reader of the ACT lunar corpus identifies the System A vs System B framing of a given Procedure Text or Ephemeris by inspecting the column structure: System A holds solar velocity constant within ecliptic zones via step functions (lunar ephemerides ACT 1-99); System B varies it linearly via zigzag functions (ACT 100-199). The full lunar System B Ephemeris carries up to eighteen columns each realising a specific computational function of time — solar velocity (Column A), lunar latitude (Column E), daily lunar velocity (Column F), length of daylight, eclipse magnitude, and so on. The theory’s output is the predicted moment of conjunction or opposition, the lunar-six time intervals, and the eclipse possibility for each month within the planning horizon. Hunger-Pingree note the Saros 223-synodic-month relation as Column Φ of System A, enabling eclipse prediction over the 18-year cycle.

Historical Origin

Attested across the Seleucid-period ACT lunar corpus from Babylon and Uruk (c. 250-50 BCE); colophons attribute System A to Nabu-rimannu (per Schnabel) and System B to Kidinnu (via the teršītu attribution). Modern treatments: Neugebauer, *Astronomical Cuneiform Texts* (1955); *Exact Sciences* (1957/1969) Ch. V §§44-55 pp. 99-122; *Selected Essays* (1983) essay [6] p. 130; Hunger-Pingree, *Astral Sciences* (1999) Ch. II §C4; Rochberg, *Heavenly Writing* (2004) §§4.2.4 + 7.4.2.

Definition

In Tradition

In Practice

Historical Origin

Further Reading