BM 76829, a fragment from the mid-section of a small tablet from Sippar in Late Babylonian script, preserves what remains of two new unparalleled pieces from the cuneiform astronomical repertoire relating to the zodiac. The text on the obverse assigns numerical values to sectors assigned to zodiacal signs, while the text on the reverse seems to relate zodiacal signs with specific days or intervals of days. The system used on the obverse also presents a new way of representing the concept (...) of numerical ‘zero’ in cuneiform, and for the first time in cuneiform, a system for dividing the horizon into six arcs in the east and six arcs in the west akin to that used in the Astronomical Book of Enoch. Both the obverse and the reverse may describe the periodical courses of the sun and moon, in a similar way to what is found in astronomical texts from Qumran, thus adding to our knowledge of the scientific relationship between the two cultures. (shrink)

In this study I attempt to provide an answer to the question how the Babylonian scholars arrived at their mathematical theory of planetary motion. Although no texts are preserved in which the Babylonians tell us how they did it, from the surviving Astronomical Diaries we have a fairly complete picture of the nature of the observational material on which the scholars must have based their theory and from which they must have derived the values of the defining parameters. Limiting the (...) discussion to system A theory of the outer planets Saturn, Jupiter and Mars, I will argue that the development of Babylonian planetary theory was a gradual process of more than a century, starting sometime in the fifth century BC and finally resulting in the appearance of the first full-fledged astronomical ephemeris around 300 BC. The process of theory formation involved the derivation of long “exact” periods by linear combination of “Goal–Year” periods, the invention of a 360° zodiac, the discovery of the variable motion of the planets and the development of the numerical method to model this as a step function. Longitudes of the planets in the Babylonian zodiac could be determined by the scholars with an accuracy of 1° to 2° from observations of angular distances to Normal Stars with known positions. However, since the sky is too bright at first and last appearances of the planets and at acronychal rising for nearby stars to be visible, accurate longitudes as input for theoretical work could only be determined when the planets were near the stationary points in their orbits. In this study I show that the Babylonian scholars indeed based their system A modeling of the outer planets on planetary longitudes near stations, that their system A models of Saturn and Jupiter provided satisfactory results for all synodic phenomena, that they realized that their system A model of Mars did not produce satisfactory results for the second station so that separate numerical schemes were constructed to predict the positions of Mars at second station from the model at first station, and finally that their system A model for Mars provided quite poor predictions of the longitude of Mars at first and last appearances over large stretches of the zodiac. I further discuss ways in which the parameters of the system A models may have been derived from observations of the outer planets. By analyzing contemporaneous ephemerides from Uruk of four synodic phenomena of Jupiter from the second century BC, I finally illustrate how the Babylonian scholars may have used observations of Normal Star passages of planets to choose the initial conditions for their ephemerides. (shrink)

In this study I attempt to provide an answer to the question how the Babylonian scholars arrived at their mathematical theory of planetary motion. Although no texts are preserved in which the Babylonians tell us how they did it, from the surviving Astronomical Diaries we have a fairly complete picture of the nature of the observational material on which the scholars must have based their theory and from which they must have derived the values of the defining parameters. Limiting the (...) discussion to system A theory of the outer planets Saturn, Jupiter and Mars, I will argue that the development of Babylonian planetary theory was a gradual process of more than a century, starting sometime in the fifth century BC and finally resulting in the appearance of the first full-fledged astronomical ephemeris around 300 BC. The process of theory formation involved the derivation of long “exact” periods by linear combination of “Goal–Year” periods, the invention of a 360° zodiac, the discovery of the variable motion of the planets and the development of the numerical method to model this as a step function. Longitudes of the planets in the Babylonian zodiac could be determined by the scholars with an accuracy of 1° to 2° from observations of angular distances to Normal Stars with known positions. However, since the sky is too bright at first and last appearances of the planets and at acronychal rising for nearby stars to be visible, accurate longitudes as input for theoretical work could only be determined when the planets were near the stationary points in their orbits. In this study I show that the Babylonian scholars indeed based their system A modeling of the outer planets on planetary longitudes near stations, that their system A models of Saturn and Jupiter provided satisfactory results for all synodic phenomena, that they realized that their system A model of Mars did not produce satisfactory results for the second station so that separate numerical schemes were constructed to predict the positions of Mars at second station from the model at first station, and finally that their system A model for Mars provided quite poor predictions of the longitude of Mars at first and last appearances over large stretches of the zodiac. I further discuss ways in which the parameters of the system A models may have been derived from observations of the outer planets. By analyzing contemporaneous ephemerides from Uruk of four synodic phenomena of Jupiter from the second century BC, I finally illustrate how the Babylonian scholars may have used observations of Normal Star passages of planets to choose the initial conditions for their ephemerides. (shrink)