Whoa! Time out!
The Castle, and its associated Habitats, are in a four-year orbit beyond Mars. The only thing they are orbiting is the Sun!
We use the Sun to reflect from our solar mirror with a complicated clockwork mechanism that gives each Habitat its allotment of sunshine for our growing plants, which give us food and oxygen.
And that mechanism supports each Habitat having its own time zone, eight hours different from its neighbor.
(So, if you're a morning person, and it's already afternoon, you can pop over to the next Habitat for your coffee.)
*whine*
(I get SOOO confused!)