Eclipse prediction by Islam astronomers in medieval Islam

from observations of two sets of three lunar eclipses in the Late Medieval Islamic Period. The first trio consists of the lunar eclipses of 7 March 1262, 7 April 1270 and 24 January 1274, observed by Muḥyī al-Dīn al-Maghribī from the Maragha Observatory (in north-western Iran), 

and the second includes those of 2 June and 26 November 1406, and 22 May 1407, observed by Jamshīd Ghiyāth al-Dīn al-Kāshī from Kāshān (in central Iran). 

The results are that al-Maghribī‟ s values for the magnitudes of these eclipses agree excellently with modern data, and his values for the times when the maximum phases occurred agree to within five minutes with modern values. 

Al-Kāshī‟ s values for the times of the maximum phases show a rather larger divergence from modern data, varying from about ten minutes to about one hour. 

The errors in all six values both astronomers computed from their own solar parameters for the longitude of the Sun at the instant of the opposition of the Moon to the Sun in these eclipses remain below ten minutes of arc. 

The motivation for doing these observations was to measure the lunar epicycle radius r in the Ptolemaic model. Al-Maghribī achieved r= 5; 12 and al-Kāshī r≈ 5; 17, 1 in terms of the radius of an orbit of R= 60 arbitrary units. It is argued that comparing with modern theory, neither of these two medieval values can be considered an improvement on Ptolemy‟ s value of r= 5; 15.

Qiblat

Ramadan

SM Mozaffari

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