The development of Babylonian lunar and planetary theory is based on the observation of periods, of variations in these periods as a function of position in the lunar or planetary orbit, and on casting these variations in strictly periodic arithmetic difference schemes by clever numerical manipulation.

In this paper I will limit myself to Babylonian lunar theory and - more specifically - to an investigation into the observational basis of the parameters used in the computation of the longitude of the Sun and the orbital velocity of the Moon (functions B and F in lunar ephemerides of system A and functions A and F of system B). Since function Φ of system A, whose exact interpretation is still enigmatic, has the same period as function F the results may also be relevant for a better understanding of function Φ.

The time frame for the early development of lunar theory is constrained by a few early texts. These texts show that functions F and Φ were fully developed by the middle of the 5th century while the other functions were still under construction or experimented with. The earliest known fully developed lunar ephemeris (system A) dates from 319 BC.

I will argue that the observational basis for the early Babylonian lunar and solar theories is formed by the observed periodicity in the heliacal rising of the star KAK-BAN (Sirius) of 334 synodic months (27 years) and by the observed periodicity in lunar eclipses (Saros) of 223 synodic months (about 18 years). In the course of time the Babylonian scholars became aware that these periods are not exact. I will show that by clever arithmetical manipulation of these two periods and their errors, the Babylonian scholars could have constructed the period relations on which the solar and lunar theories are based. The magnitude of the errors in the observed periods was estimated from the slow drift of the date of the Sirius risings in the lunar calendar and in the gradual evolution of the “Early Saros Scheme” by which the upper lines in the groupings of 7 or 8 consecutive lines in the scheme become depopulated and the lower lines become activated in the course of a few hundred years. Functions F and Φ of system A are the oldest elements of lunar theory and were probably developed late in the 6th century BC.