A study of Babylonian planetary theory III. The planet Mercury (2021) Teije deJong

https://www.academia.edu/126021122/A_study_of_Babylonian_planetary_theory_III_The_planet_Mercury_2021_?rhid=41533914141&swp=rr-rw-wc-170578636&nav_from=518796bb-d04a-4365-89f3-87222d6462b7 In this series of papers I attempt to provide an answer to the question how the Babylonian scholars arrived at their mathematical theory of planetary motion. Papers I and II were devoted to system A theory of the outer planets and of the planet Venus. In this third and last paper I will study system A theory of the planet Mercury. Our knowledge of the Babylonian theory of Mercury is at present based on twelve Ephemerides and seven Procedure Texts. Three computational systems of Mercury are known, all of system A. System A 1 is represented by nine Ephemerides covering the years 190 BC to 100 BC and system A 2 by two Ephemerides covering the years 310 to 290 BC. System A 3 is known from a Procedure Text and from Text M, an Ephemeris of the last evening visibility of Mercury for the years 424 to 403 BC. From an analysis of the Babylonian observations of Mercury preserved in the Astronomical Diaries and Planetary Texts we find: (1) that dates on which Mercury reaches its stationary points are not recorded, (2) that Normal Star observations on or near dates of first and last appearance of Mercury are rare (about once every twenty observations), and (3) that about one out of every seven pairs of first and last appearances is recorded as "omitted" when Mercury remains invisible due to a combination of the low inclination of its orbit to the horizon and the attenuation by atmospheric extinction. To be able to study the way in which the Babylonian scholars constructed their system A models of Mercury from the available observational material I have created a database of synthetic observations by computing the dates and zodiacal longitudes of all first and last appearances and of all stationary points of Mercury in Babylon between 450 and 50 BC. Of the data required for the construction of an ephemeris synodic time intervals t can be directly derived from observed dates but zodiacal longitudes and synodic arcs λ must be determined in some other way. Because for Mercury positions with respect to Normal Stars can only rarely be determined at its first or last appearance I propose that the Babylonian scholars used the relation λ t −3;39,40, which follows from the period relations, to compute synodic arcs of Mercury from the observed synodic time intervals. An additional difficulty in the construction of System A step