A study of Babylonian planetary theory. I: The outer planets (Q1714466)

The author addresses the question how Babylonian astronomers constructed the tables for the phenomena of the outer planets using what modern scholars call ``System A''. This model uses a ``step function'' to represent the variable velocity of the planets among the fixed stars. While these tables are well understood, we have no documentation how their inventors used the observational material contained in the \textit{Astronomical diaries} to arrive at the parameters of the tables. As the author says, ``How did the Babylonian astronomers proceed from observation to theory?'' The author gives a very clear overview of the Babylonian method to compute planetary phenomena, as applied to the outer planets. He then investigates how the Babylonians could have found the positions of the planets at their characteristic phenomena. In the \textit{Diaries}, such positions are related to fixed stars near the ecliptic. For observing the stations the difficulty is the slow motion of the planets near their stationary points; for the first and last visibilities, the brightness of the sky near these phenomena makes stars practically invisible so that the planet's distance from a star could not be observed. The author assumes that observations at the first station were used because the Babylonian model for Mars produces the best fit to reality for the first stations. For the other phenomena of Mars, the fit is much worse, in spite of a special correction introduced in some tables. The two-zone step function used for the System A model of Jupiter and Saturn delivers results accurate within the Babylonian observational possibilities. For the initial conditions of the planetary tables the author quotes a suggestion by P. Huber that four of the tables for Jupiter phenomena used observations from the years 108 and 109 of the Seleucid era to derive their initial conditions. The author then inspects to remaining fragments of a \textit{Diary} for this year and finds that the only suitable observation of Jupiter that occurred at this time was its first station near the star Beta Virginis.