How did Ptolemy explain the daily rising and setting of the Sun, Moon, and stars?
Ptolemy explained the daily rising and setting of the Sun, Moon, and stars through his geocentric cosmological framework, which he detailed in his work the Almagest.1
He argued that Earth is a stationary sphere positioned at the center of the universe. Surrounding Earth is a vastly larger celestial sphere that rotates at a perfectly uniform rate. As this celestial sphere revolves around the stationary Earth, it carries the Sun, Moon, planets, and stars with it, which results in their observed daily risings and settings.21
While this rotation accounts for the daily motion, Ptolemy also described the Sun, Moon, and planets as traveling backward against the rotation of the celestial sphere over longer periods, such as the Sun tracing the ecliptic throughout the year.1