How does the Sun appear to revolve around the Earth?

Considering that the Sun always rises in the East but at different angles, how could you tell it had moved? Did people who used the geocentric model just use the stars and constellations opposite the Sun throughout the year to jump to the conclusion that the Sun is moving?
But what about astrologers who said the [...]

How far would the Sun have to be to appear as dim as the moon?

The Sun appears 400,000 time brighter than the full Moon in our sky. How far from the Sun (in AU) would you have to go for the Sun to appear only as bright as the full Moon appears in our nighttime sky? Compare your answer with the radius of Neptune’s orbit.