As in English, does the Ukrainian word "зірки" refer to the celestial bodies as well as celebrities?
That's true! However, if you want to ask "Which stars do you know" (as in "movie stars") you'd say "Яких зірок ти знаєш?"
Hmm, I don’t understand why the endings would change. Would you mind explaining?
які зірки is a Nominative case, яких зірок is a Genitive case.
I'm not entirely sure why it feels right to use genitive talking about celebrities, but I think we use it every time talking about animate objects.
Яких котів ти знаєш?
Яких лікарів ти знаєш?
Які машини ти знаєш?
Які мови ти знаєш?
If I find a rule I'll link it here, can't think of one now.