An early system A-type scheme for Saturn from Babylon (Q6171826)

The authors have found two small tablet fragments in the British Museum, which together with two previously known fragments, all come from a single tablet. The additional pieces give sufficient information that a plausible reconstruction of the overall astronomical text can be considered. Two main types of systems for computing dates and positions of astronomical phenomena are known for Babylonian mathematical astronomy, System \(A\), using step functions, and System \(B\), using linear zigzag functions. The authors transliterate and translate the remaining visible signs (parts of the fragments are damaged), reconstruct and analyze the contents. The current fragments bear witness to a previously-unknown variant of System \(A\) for Saturn, which the authors name System \(A_0\). The authors explain the details of this variant, and compare it with other known schemes, including the standard System \(A\), which this text predates. The completed text appears to cover an entire 59-year cycle of Saturn, and contains dates running from around 390 BC to 330 BC. Very unusually, the computed predictions of astronomical phenomena are glossed by observations comparing the predicted date and position with that observed. These glosses enable the authors to conclude that the tablet was written late in the cycle it covers. The authors also offer detailed comparisons of the predicted and observed events with modern synthetic projections, showing that the early System \(A_0\), although quite accurate, was not as good as the later System \(A\).