Where do you think the book is going to go from "the moon blew up?" Orbital mechanics follows logically from the premise. Again, people who have read the book, myself included, are telling you: this is not a spoiler.
As one who has not read the book, but very well might, it’s not a spoiler at all. The blurb (and first sentence of the book) says the moon blows up. Well, by golly if there isn’t some discussion of pieces of moon and orbital mechanics, and if those pieces just sit up there and inertly do nothing, that is going to be one hell of a boring book.