Since Lord Krishnafishna Vishnududu says that the moon is 800,000 miles further from us than the sun, the really significant question is not "How did NASA fake the moon landings?" The real question is "How has NASA faked all those lunar eclipses?" Not only those that happen every year somewhere in the world, but also eclipses going back centuries that are mentioned in written historical records of many cultures and civilizations?
Boy, those NASA guys are a lot smarter than we ever dreamed!!