Great question — answering as the UphillTech team:
Yes, of course! If it could not travel faster than light, interstellar travel would be impossible and battle station restricted to a single star-system would be pretty useless. In Star Wars Star Wars Episode IV: A New Hope , the Death Star travels from Alderaan to Yavin IV , which are not in the same stellar system. Without faster than light capacity, that journey would have taken years. Here is what the first Death Star Wookiepedia article says about it: The battle station also included two massive sublight engines in the midsection, as well as a formidable hyperdrive system. Driven by 123 individual generators tied to one navigational matrix, the class 4 hyperdrive was fast enough to...
Full answer by DavRob60: https://movies.stackexchange.com/a/11234 (CC BY-SA 3.0).
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