Eclipse Prediction and the Length of the Saros in Babylonian Astronomy

The Saros cycle of 223 synodic months played an important role in Late Babylonian astronomy. It was used to predict the dates of future eclipse possibilities together with the times of those eclipses and underpinned the development of mathematical lunar theories. The excess length of the Saros over a whole number of days varies due to solar and lunar anomaly between about 6 and 9 h. We here investigate two functions which model the length of the Saros found in Babylonian sources: a simple zigzag function with an 18‐year period presented on the tablet BM 45861 and a function which varies with the month of the year constructed from rules found on the important procedure text TU 11. These functions are shown to model nature very well and to be closely related. We further conclude that these functions are the likely source of the Saros lengths used to calculate the times of predicted eclipses and were probably known by at latest the mid‐sixth‐century BC.     

On the Babylonian Lunar Theory: A Construction of Column Φ from Horizontal Observations

We demonstrate that column Φ in System A of the Babylonian moon ephemerides can be derived from such horizontal phenomena as were observed and recorded by the Babylonians. Combining four of the so-called ‘Lunar Six’ in such a way that the effects of the oblique ascension are eliminated, we obtain a curve which oscillates, indeed, with the exact period and the approximate amplitude of Φ. Our curve (which we call S?) also contains oscillations with the approximate period of the Saros and allows us to find the period relation which is underlying column Φ. Herewith it has been shown for the first time that the length of the anomalistic month can be derived from horizontal observations.     

Instrumentation in Astronomy III

Two-wavelength holography and phase-shifting interferometry are combined to measure the phase contours of deep wavefronts and surfaces, such as those produced by aspherics, with a variable sensitivity. When interference fringes are very closely spaced, the phase data contain high frequencies where 2 ~ ambiguities cannot be resolved. In this technique, the surface is tested at a synthesized longer equivalent wavelength. The phase of the wavefront is calculated modulo 2φ using phase-shifting techniques at each of two visible wavelengths. The difference between these two phase sets is the phase of the wavefront as it would be measured at λ_eq=λ₁λ₂/|λ₁ ? λ₂ |, assuming that 2π ambiguities can be removed at λ_eq. This technique enables surfaces to be contoured to an accuracy of λ_eq/100.     

Algebra and Geometry in the Old Babylonian Period: Matters Concerning Reeds

Abstract.   One of the mathematical topics examined in the Old Babylonian period consisted of calculating the size of a reed which was used to measure either a longitude or the perimeter of a rectangle or trapezium. These subjects were solved, probably, applying the geometric construction called completing the square. In this paper, we analyse the problem texts on the tablets AO 6770 (5), Str 368, VAT 7532, and VAT 7535.     

Astronomy in the twentieth century

This paper is based on theSource Book in Astronomy and Astrophysics 1900–1975 which is considered representative of the pioneer research work in the field. The distribution of important scientific achievements over a certain period, their distribution by subject area and sources, single or multiple authorship and age of techniques relevant to these areas are quantitatively examined. In some cases results are obtained as known from the analysis of the overall output of the sciences (including astronomy). As regards, however, the frequency of published important papers and the role of the latest technique pioneer achievements differ significantly from the total of scientific publications.