<><><> start of synopsis ><><><><><>
The theory that the Muslim astronomers borrowed from Ptolemy predicted that the apparent relative diameters of the sun and moon as seen during eclipses of the sun would vary twice as much as is actually observed. The reason for this error is that they did not know that gravity causes the smaller body to travel faster when it is nearer to the larger body.
The Tusi couple does not make any sense, but accidentally nearly agrees with measurements of the changes in the apparent relative diameters of the sun and moon as seen during eclipses.
<><><> end of synopsis ><><><><><>
Al-Tusi’s Tusi couple model makes no logical sense, but accidentally nearly agrees with measurements of the changes in the apparent diameter of the sun as seen during eclipses.
VARIATION IN APPARENT DIAMETER OF THE SUN
Al-Battani (858 – 929) copied the Greek model that the sun moved in a perfectly circular path at constant speed around the Earth, with the Earth not precisely at the center of this circle.
He calculated the path of the orbit of the sun around the Earth, and the annual variation in the distance between the Earth and the sun. From this he predicted the percentage variation in the apparent diameter of the sun as seen during eclipses. But observations of eclipses of the sun showed that the apparent size of the sun varied by about only half as much as he predicted.
The reason for the error in the theory al-Battani copied from the Byzantine Christian astronomer Ptolemy was the assumption of constant speed. It was not until Christian European mathematicians worked out the mathematical formulas of gravity that it was discovered that the Earth moves faster when it is closer to the sun.
THE TUSI COUPLE
Al-Tusi (1201 – 1274) in his Tusi-couple model, placed the sun on the rim of a circle rolling at uniform speed along the inside of a circle with twice the diameter.
Al-Tusi’s model had the side benefit of being the first theory to correctly predict the observed annual variation in the apparent diameter of the sun during solar eclipses. But al-Tusi insisted on a perfectly round epicycle for Mercury, because Allah made perfect circles moving at constant speed.
Al-Tusi’s ideas probably did not reach Europe and did not influence European astronomers.
COMBINING OVAL MERCURY PATH WITH TUSI COUPLE
Ibn al-Shatir (1304 – 1375) and Ali Qushji (1403 – 1474) proposed a theory that better agreed with observations by copying the al-Tusi model but reviving the oval epicycle of Mercury.
Image by Nasir al-Din Tusi, in an Arabic manuscript in the Vatican Library, via Wikimedia Commons.
Image credit https://commons.wikimedia.org/wiki/File:Tusi_couple.jpg