Weirdly, Cloud Atlas also stars Halle Berry. I really like the movie of Cloud Atlas, myself. I've read the book at least three times, but I don't remember anything about the Moon?
It's in the movie adaption of The Time Machine. In the book though he just arrives in the future and the moon is already gone (Chapter XIV The Further Vision https://www.gutenberg.org/cache/epub/35/pg35-images.html).
I think I read cloud atlas and the time machine, and watched the time machine movie around the same time, and got everything mixed up.
That was a fun afternoon reading through bits of books until I could figure out what I was remembering.