The next morning, he was aboard a spaceship.

Literal

Next-morning, he [topic-は] spaceship [at-に] was-riding.

乗る ('to ride / board') takes に, not を — the に marks what you're in/on rather than marking it as a direct object. ~ている ('is riding') here describes the state of being aboard, not the act of boarding. 宇宙船 ('spaceship,' literally 'space-vessel') is a compound noun.