The apparent sun is the true sun as seen by an observer on Earth.

For that reason, average daytime (disregarding cloud effects) is longest in polar areas, where the apparent Sun spends the most time around the horizon.

Yoga - EM of the angular relationship between Sun and Moon( Apparent Moon plus Apparent Sun).

This gives an apparent movement of the Sun eastward with respect to the stars at a rate of about 1 /day, which is one apparent Sun or Moon diameter every 12 hours.

On the other hand, Wei Pu realized that the old calculation technique for the mean sun was inaccurate compared to the apparent sun, since the latter was ahead of it in the accelerated phase of motion, and behind it in the retarded phase.

Shen hypothesized that rays of sunlight refract before reaching the surface of the earth, hence people on earth observing the sun are not viewing it in its exact position, in other words, the altitude of the apparent sun is higher than the actual altitude of the sun.

When Zhang Xiu reached adulthood (at around the age of 19), he, along with Zhuge Ke, Gu Tan and Chen Biao, were appointed by Sun Quan as zhongshuzis (中庶子; an aide to the crown prince) to the heir apparent Sun Deng.