She's not the moon, she's not Kaguya-hime. She's just a girl who ended up taking the immortality elixir from the end of the story about Kaguya-hime, the Tale of the Bamboo Cutter. At least, I'm pretty heavily convinced that's the case with all of the evidence presented as of this chapter and volume (especially the end-of-volume Q&A sessions). People are jumping to conclusions about her real nature, but it's nowhere near as fantastical as you think, I guarantee you.
The real issue is actually that immortality. If she's immortal- If she instantly heals wounds or recovers from illnesses as was stated in a recent chapter... can you imagine how virtually impossible sex would actually be for Tsukasa? Think what that would mean for her hymen and the excruciating pain or potentially impassible nature of her cavity down there. What if trying to have sex would crush or destroy Nasa's manhood? There's too many potential issues when you factor in such an extreme healing factor like that with a female physiology. I'm probably not even scratching the surface.
Not to mention the fact that if she remains immortal, she can't grow old with Nasa like a normal married couple would. She's currently stuck at a physical age of 16. This is not tenable in the long-term.
The moon rock potentially only really has bearing towards finding a solution to Tsukasa's immortality, or it's merely just a fancy souvenir. Either way, it came from the Apollo program, I guarantee you. There's no way it has nearly the ramifications you all have been thinking. The leaps of logic to explain it any other way than it being something gathered from modern space program efforts are too great.