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star trek - Why would Voyager require 75 years to return home?


The Star Trek: Voyager Wikipedia article says:



(...) show is initially set on the other side of the Milky Way galaxy, 75,000 light-years from Earth (...) and (...) Voyager to make the estimated 75-year journey home.




This is confirmed by Captain Janeway, who says in the first episode, that (I don't have access to direct quotation) "even with maximum speed, our travel home will take approximately 75 years" (unless they find some "shortcuts"). The general assumption here is, that Voyager will be travelling approximately 75 years until it reach Earth.


In Warp drive Wiki article, The Next Generation onwards section it is said that:



The Intrepid-class starship Voyager has a maximum sustainable cruising speed of warp 9.975.



According to my calculations (correct me, if I'm wrong), 9.975 warp is around 1680 times light speed. This theoretically means, that traveling entire year with constant maximum speed would allow Voyager to pass 1680 light years, not 1000 (not mentioning these shortcuts, they used like subspace corridors, trans-warp technology etc.).


This means, that Voyager would actually need only around 45 years to reach home (pass 75,000 light years distance). It would be impossible to travel all the time at maximum speed, but that would be compensated by using "extra additions" (subspace corridors, trans-warp etc.).


What am I missing?



Answer




They were (presumably) using the old warp scale. From later in the Wikipedia article you linked:



Exact velocities were given in a few episodes, one being "Relativity", where Kathryn Janeway describes Voyager's velocity at warp factor 9.975. Voyager was about 70,000 light-years away from home, and crew would often use "75 years" as the time it would take to get back home at top speed. This means the Voyager series used the old method of Warp calculation. 70,000/9.9753 is roughly 71 years. Accounting for delays to refuel, repair, restock and downtime, 75 years is a logical rounding.



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