JRNTexas's idea is a good one. You have two images. A large backdrop with a hole cut out, and the part that's been cut out as a small rectangle image as the first image drawn, in place of where the hole exists. Essentially rendering these two would produce a complete backdrop, complete with details (does not have to be black). You can then render the moon between the small cut-out image and the large screen sized backdrop which is drawn last, creating the effect you are after
I drink tea, and in my spare time I write software.