Indeed. Actually the cosmology of Middle Earth (which is the first part of 'The Silmarillion' and barely mentioned in TLOTR) does require, to put it charitably, a certain suspension of disbelief. I'm paraphrasing somewhat... (spoilers)
The creator, Eru / Ilúvatar creates a great theme and the Ainur (spirits) are then invited to create a music from it. The evil Morgoth (Sauron's boss) sows discord by breaking Eru's harmony. Eru then stops the music and the various spirits manifest in the world (Arda) created from it. The world is initially illuminated by stars and then the light from two great trees. Which Morgoth destroys, although their light bearing fruit are used to create the Sun and the Moon. The Valar (the most powerful good Ainur) create the westerly island Valinor, which (after a lot of misery which forms the main subject of the Silmarillion) Ilúvatar eventually makes inaccessible by sending a great wave, changing the shape of all the lands of Middle-earth.
Hence my comment that plate tectonics (or whatever geological processes were understood in the early 20th C) wasn't an overarching concern for Tolkien. But once he'd made this world, he made sure that the LOTR characters would see the same phase of the moon at their respective parts of the story.