Yeah, and to be going past the star field as fast as is depicted on most episodes (old AND new) you would have to be traveling at about 15 light years per second, which works out to more than 473,000,000 times the speed of light. That's four hundred, seventy three MILLION times the speed of light. I think that they did not think this through when they came up with the warp figures. At about 31 light years per second we are talking a BILLION times light speed. You would need about that speed to account for the rate at which you sometimes see stars moving in the viewscreen on Star Trek episodes.
HOWEVER, our galaxy is about 100,000 light years across. If you really could travel at 31 light years per second, you would cross the entire galaxy in about 55 minutes!!!! Even if you were going 1 light year per second (which would be a CRAWL on the viewscreen), it would still take only about 30 hours to cross the galaxy.
1 light year per second is STILL 31,557,600 times the speed of light.
Warp 9 = 729 times the speed of light, or 43,288 times slower than 1 light year per second. At warp 9 it would take 2 days and almost 4 hours to reach our nearest star at 4.3 light years away. I suspect that you could stare out the viewscreen all day and not detect any movement in the star field at warp factor 9. At warp 2, it would take 337.7 days to reach Alpha Centauri.
But they never listen to me.......