The orbital elements of each planet are the eccentricity and the direction of the apsidal
line of its orbit defined by the ecliptic longitude of either of its apses, i.e., the two
points on its orbit where the planet is either furthest from or closest to the Earth,
which are called the planet’s apogee and perigee. In the geocentric view of the solar
system, the eccentricity of Venus is a bit less than half of the solar one, and its apogee
is located behind that of the Sun. Ptolemy correctly found that the apogee of Venus is
behind that of the Sun, but determined the eccentricity of Venus to be exactly half the
solar one. In the Indian Midnight System of Āryabhata (b. ad 476), the eccentricity of
Venus is assumed to be half the solar one, and also the longitudes of their apogees are
assumed to be the same. This hypothesis became prevalent in early medieval Middle
Eastern astronomy (ad 800–1000), where its adoption resulted in large errors of more
than 10° in the values for the longitude of the apogee of Venus adopted by Yahyā b.
Abī Mansūr (d. ad 830), al-Battānī (d. ad 929), and Ibn Yūnus (d. ad 1007). In Western
Islamic astronomy, it was used in combination with Ibn al-Zarqālluh’s (d. ad 1100) solar
model with variable eccentricity, which only by coincidence resulted in accurate values
for the eccentricity of Venus. In late Islamic Middle Eastern astronomy (from ad 1000
onwards), Āryabhata’s hypothesis gradually lost its dominance. Ibn al-A‘lam (d. ad 985)
seems to have been the first Islamic astronomer who rejected it. Late Eastern Islamic
astronomers from the middle of the thirteenth century onwards arrived at the correct
understanding that the eccentricity of Venus should be somewhat less than half of the
solar one. Its most accurate medieval value was measured in the Samarqand observatory
in the fifteenth century. Also, the values for the longitude of the apogee of Venus show
a significant improvement in late Middle Eastern Islamic works, reaching an accura