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This question is bugging me for some time now. in ST:VOY journey back to the Alpha Quadrant would have taken more than seventy years since Voyager would have to pass 70,000 light years.

Same wiki says United Federation of Planets is one of the most powerful interstellar states in known space, it encompassed 8,000 light years

Does it mean that it would take full eight years to cross it? If not how many than and why the discrepancy is speed?

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Three Months. According to the DS9 episode Valiant, the training cruise of the ship was to "circumnavigate the entire Federation" and Collins said that

The training cruise was supposed to last three months.

Bear in mind, the vessel was limited to warp 3.2 until Nog fixed the engines.

Why the speed discrepancy? Because it's Star Trek.

In Where No One Has Gone Before, the Enterprise is hurled 2,700,000 light years to the far side of Triangulum. Data says it will take over 300 years to return ship and crew to Federation space. This breaks down to approximately 9,000 light years per year at maximum warp.

At that speed, Voyager should have been home, without outside assistance, in less than 8 years but it is often repeated that it will take them 75 years to travel 70,000 light years meaning Voyager travels less than 1,000 light years per year...This implies that the Enterprise is more than 9 times faster at maximum warp.

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    Warp speed is as fast as the plot needs it to be at any given time – geewhiz Jan 2 '18 at 15:50
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    It also bears mentioning that maximum warp cannot be maintained for extended periods of time and normal cruising speed for a Galaxy Class Starship is Warp 6. Data's calculation may not have taken that into effect while the Voyager calculation probably did account for it. Warp 6 is NOT 2/3 as fast as Warp 9. All the scales I've seen are somewhat exponential. – geewhiz Jan 2 '18 at 15:55
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    Note that "circumnavigating" implies making a round-trip around something. On a planet (eg: Earth) that can be simply crossing around it once. However, for a 3-dimensional (non-curved) map, that would imply to me that the ship traveled around the perimeter of their territory. That would be a much longer trip than simply crossing it like the question asked. So this answer only really gives an upper-bound, and the answer itself should probably be significantly less.. – T.E.D. Jan 2 '18 at 17:50
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    All travel in Star Trek is at speed of plot. The meaning of the warp numbers varies from series to series and unfortunately from episode to episode. And that's true even in the later series, where they had technical manuals and rulebooks to guide the writers. Fundamentally, the writers in star trek have no grasp of how large the distances involved in space travel are. This isn't just a problem with warp travel- I can't even count the number of episodes where non-warp shuttlecraft travel interstellar distances in hours or minutes. – Jim W Jan 2 '18 at 17:57
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    @VanjaVasiljevic Star Trek originally didn't even have sequential/chronological Star Date timestamps. It wasn't until the show gained popularity that they started to try and nail down things like a coherent time line, distances, maximum speeds, and so on. And they still often get it wrong. Point being, Star Trek is not a fictional historical record of actual events, and each episode should be taken on its own merit as a form of entertainment. Continuity is not this franchise's strong suit. – phyrfox Jan 2 '18 at 18:59

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