There are two versions.

In St Thomas Aquinas, the daily motion of the Universe around Earth is an ongoing direct act of God. Angels of Sun and Moon are moving the visible bodies backwards in relation to this, so as to get around the Zodiac in either a sidereal or tropical Year or a sidereal or tropical Month.

In Riccioli, the angels moving Sun and Moon are moving Westward, through empty space, and so are the stars, each moved by an angel, and the reason Sun and Moon get around the Zodiac is that the stars move Westward faster and the Sun and Moon lag behind.

One can compare the theories so that to St Thomas Aquinas God is so to speak "driving a train" and angels of Sun and Moon "walking backwards through the train", while to Riccioli, they are on their own.

The theory of St Thomas would require either solid crystalline spheres (as he believed himself, following the Ancients) or sth replacing them, like the aether or a solidified solidarically rotating portion of it.

The theory of Riccioli requires Empty Space