Okay so here's my guess as to what happens:
Tsukasa is, as her name implies, some sort of moon goddess/alien. We've seen that she's got some sort of superhuman ability, from when she saved his life and got hit by a truck and wasn't hurt at all. Not to mention, she can read minds. That's also probably one of the reasons she loves Nasa-kun - what he says outwardly matches with what he thinks internally, which she was probably referencing when she said he'd never lied to her.
She's probably some kind of Japanese national secret as well. We've seen the moon rock called her 'moonstone', so we know she has a strong connection to the moon - not to mention the fact that the story is based on Kaguya-hime who was taken from Earth to the Moon.
And early on, Nasa talks about how he'd never stand by as the woodcutter and emperor did, and let her be taken away. He'd go fight for her.
And so that's my prediction (as of Chapter 17) of what will happen. My guess? Alien life or something exists on the moon, and Tsukasa will be forced to return there - perhaps as a sort of arranged marriage to a moon god or something. Consider that the alternate name of this is "Fly me to the moon" and the MC's name is literally NASA.
To get his wife back, he will go back to school, spend several years becoming an astronaut (realistically we're looking at about 10+ years), and will literally fly to the moon to retrieve his wife.
Also, I would just like to say thank the freakin' heavens for an MC that isn't a blubbering pile of shit. Actually able to confess properly, kisses his wife, etc. A real main character and good person! I'm really looking forward to where this goes.