Hi there, @staylor98 ...
Sounds like a great question for your students. I can see why using the "Ordering" question type would be the most appropriate for this kind of question. However, I don't think that question type will work just exactly for your needs. What would you think of making your question a "Matching" question instead? Here is an example I created from my own sandbox course using New Quizzes:


From a student perspective, they would have drop-down lists where they would have to choose the name of the planet based on its location relative to the Sun. The only downside to this is that if a student chooses Mercury, for example, for the first response...then Mercury is still a choice for the other drop-down lists...if that matters to you. The drop-down lists do not eliminate choices that have already been used by the student.
Hopefully this might be a workable solution for you. Keep us posted here in the Community...thanks!