If a ship travels at warp 9.5 (TNG-era warp scale) and encounters no resistance or gravitational affects that change its velocity, and assuming infinite fuel is available, how far does it travel in 123 days?

Frame of reference:

In the episode "Remember Me" of TNG's 4th season, Dr Crusher is stuck inside an experimental warp bubble by Wesley.

After the rest of the crew disappears she decides to try to get to Tau Alpha C from where she is, and asks the computer how long it would take at warp 9.5 to reach there. The computer responds that it would take 123 days. Synopsis.

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    I assumed it was because 123 days is almost exactly one-third of a year. – Valorum Jan 21 '15 at 15:33
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    It would travel the distance between the Enterprise and Tau Alpha C. – Lightness Races in Orbit Jan 21 '15 at 17:26
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    @Nerrolken Tau is a Greek letter and almost certainly does not refer to the constellation Taurus, from which Aldebaran gain is designation of Alpha Tauri ("brightest star in Taurus"). – ApproachingDarknessFish Jan 21 '15 at 20:05
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    "If there's nothing wrong with me, maybe there's something wrong with the universe." -- Dr. Beverly Crusher, greatest line ever uttered on television (or, possibly, anywhere) – David Conrad Jan 21 '15 at 22:37
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    The Enterprise and other starships travel at the speed of plot. – Mark Jan 22 '15 at 2:31

That's actually a surprisingly hard question to answer. Assuming we use the standard logarithmic scale offered in the TNG Technical Manual, then you're looking at Warp 9.5 being approximately 1800-2000 times the speed of light. In 123 days, assuming no malfunction and unlimited fuel, you could therefore travel 606 light years:

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This tallies quite nicely with the Warp Speed calculations in the (unpublished) Voyager Technical Manual which refers to Warp 9.6 as being around 1900 times the speed of light

enter image description here

Unfortunately, nothing in life is that easy. The TNG Manual stresses that your speed is highly variable due to the interstellar medium you're traveling through, not just resistance and gravitation but also changes in subspace.

The actual values are dependent upon interstellar conditions, e.g., gas density, electric and magnetic fields within the different regions of the Milky Way galaxy, and fluctuations in the subspace domain. Starships routinely travel at multiples of c, but they suffer from energy penalties resulting from quantum drag forces and motive power oscillation inefficiencies.

With regard to the episode TNG : Remember Me, it's important to note that when Dr. Crusher asks the computer how far Tau Alpha C is from her present location, she's in a pocket dimension created by her own mind. There's no specific confirmation that this figure is in any way accurate.

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    @MrDobilina - Discussed at length here. Basically they retconned in later episodes to say that they can only sustain high warp for approx 12 hours due to the need for fuel. Also, Voyager was not fully fitted out yet. – Valorum Jan 21 '15 at 15:45
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    @Wikis however it would explain why TOS enterprise could get from UFP space to the edge of the galaxy in one episode ;) – MrDobilina Jan 21 '15 at 15:47
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    @MrDobilina - Warp speed in Star Trek is highly inconsistent. MST3K mantra in full operation - It's just a show. Relax. – Valorum Jan 21 '15 at 15:50
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    @Hypnosifl - Also, they were spouting complete crap in the early episodes. That doesn't help. – Valorum Jan 21 '15 at 16:10
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    @Hypnosifl - Also, Janeway stops every week to pick up a camera crew and have an adventure. – Valorum Jan 21 '15 at 19:22

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