Kāshī’s Lunar Measurements

Jamshīd Ghiyāth al-Dīn al-Kāshī (d. 22 June 1429 ad) measured the fundamental parameters of Ptolemy’s lunar model (the radius of the epicycle, and the mean motions in longitude and anomaly) from his observations of the lunar eclipses of 2 June 1406, 26 November 1406, and 22 May 1407 at Kāshān. He presents his data and his process of computations in the prolegomenon to the Khāqānī zīj (1413 - 1414 ad). His data make up the third of four surviving full accounts of lunar measurements carried out during the late medieval Islamic period. Kāshī’s error in the time of the maximum phase of the second eclipse is only ~ –8 minutes, an achievement that bears witness to his skill in making tolerably precise astronomical observations and also shows that the simple water and sand clocks available to him were relatively accurate. His input data include theoretical values for the longitude of the Sun and of the lunar ascending node, which he derives from the Īlkhānī zīj (Maragha, ca. 1270 ad), based, in the solar theory, upon Ibn Yūnus’ (1009 ad) Ḥākimī zīj. Kāshī computes a value of ~ 5;17 for the epicycle radius; this does not represent an improvement over Ptolemy’s 5;15, but is more precise than other values measured in medieval Islamic astronomy. He uses Muḥyī al-Dīn al-Maghribī’s (d.1283 ad) last value for the mean lunar longitudinal motion (measured from the latter’s observations at Maragha between 1262 and 1275 ad) and Hipparchus’ value for the mean motion of the Moon in anomaly in order to compute the mean lunar motions in longitude and in anomaly respectively in the time intervals between his triple eclipses. As a result, his final values for the motional parameters of the Moon remain very close to those of his two predecessors.