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.

中文翻译：

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巴比伦行星理论研究一、外行星

在这项研究中，我试图回答巴比伦学者如何得出行星运动数学理论的问题。虽然巴比伦人告诉我们他们是如何做到的，但没有保存任何文本，但从幸存的天文日记中，我们对观测材料的性质有了相当完整的了解，学者们必须以此为基础，并从中得出他们的理论定义参数的值。将讨论限制在外行星土星、木星和火星的系统 A 理论上，我认为巴比伦行星理论的发展是一个多世纪的渐进过程，从公元前五世纪的某个时间开始，最终导致出现公元前 300 年左右第一个完整的天文星历。理论形成的过程包括通过“目标-年份”周期的线性组合推导出长“精确”周期、360°黄道带的发明、行星可变运动的发现以及数值方法的发展将此建模为阶跃函数。巴比伦黄道带中行星的经度可以由学者通过观察到已知位置的正常恒星的角距离来确定，精度为1°到2°。然而，由于在行星第一次和最后一次出现时天空太亮，并且在缩写上升时无法看到附近的恒星，因此只有当行星靠近其轨道上的静止点时才能确定作为理论工作输入的准确经度。在这项研究中，我表明巴比伦学者确实将他们的外行星系统 A 模型建立在靠近站点的行星经度上，他们的土星和木星系统 A 模型为所有会合现象提供了令人满意的结果，他们意识到他们的系统 A 模型火星的第二站没有产生令人满意的结果，因此构建了单独的数值方案来根据第一站的模型预测第二站火星的位置，最后他们的系统 A 模型对火星的经度预测非常差火星第一次和最后一次出现在黄道十二宫的大片区域。我进一步讨论了系统 A 模型的参数可能是从外行星的观测中推导出来的方式。