Logically, the spaceship would be considered to be sovereign soil, and treated just like an embassy. The child of foreign parents born on a U.S. spaceship MIGHT have a claim on U.S. citizenship, but not a strong claim.
Suggest you think up an analogy question that will present an actual analogous issue.
Can you not do this without my help for the purposes of answering the question? Use a hot air balloon for all I care, dodging the point by invoking irrelevant technicalities is not the behavior of someone who has an actual rebuttal.