Picard didn't cut him off, he exclaimed after Data finished.According to TNG's "Where No One Has Gone Before" Starfleet would receive a subspace message send from their location (some 2.7m ligt years) in 51 years 10 months (Picard cut him off at this point ...
If they travel to the rim yes, but the galaxy is three dimensional and very flat. By traveling straight up, or straight down, Kirk could reach the edge of the galaxy (where the density of stars drop off rapidly) in about a thousand light years.By all accounts, the edge of the galaxy should have been 30k ly away... at a minimum, maybe c15k.
Picard didn't cut him off, he exclaimed after Data finished.
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