The correct pair of verbs to complete the sentence is:
knows; are
So the full sentence would read: "Sean or Stacey knows when shuttles or other space vehicles are launched."
Here's the reasoning:
- When using "or" to connect subjects, the verb agrees with the closer subject in a compound subject. In this case, "Stacey" is the closer subject to the verb "knows."
- "Shuttles or other space vehicles" is a plural subject, so the correct form of the verb is "are."