Limitations of Methods: The Accuracy of the Values Measured for the Earth's/Sun's Orbital Elements in the Middle East, A.D. 800–1500, Part 2

Discussions and Results The relatively accurate observational data obtained by the early Islamic astronomers resulted in the good values for the length of the seasons and for the time intervals between successive mid-seasons that were achieved (Tables 1 and 2) and, consequently, as we shall see presently, the reasonable values for the solar eccentricity that were obtained in the Middle East during the medieval period. Since the accuracy of the observational data has already been discussed by Said and Stephenson,95 we turn our main attention to making comparisons between the methods and the corresponding recorded historical values.96 In order to reach the main goals defined at the beginning of the paper, it should be mentioned that, concerning the varying historical values for the solar orbital elements, we are confronted with a three-fold problem consisting of the following factors: (1) the sensitivity of methods and observational data; (2) the methods and theoretical errors due to the mismatch of the two models, eccentric and elliptical; and (3) the secular decrease in the eccentricity of the Earth. [...]taking the rate of the motion of the solar apogee to be equal to the rate of precession (l°/66y or l°/70y) remained as an assumption in nearly all the important zïjes written there in the late Islamic period.