I don't know how you got 2000LY is it mentioned in the episode? Have to check that.
The 2,000ly distance is spoken in the episode First Contact, when Troi & Picard introduce themselves to the Malcorian astronomer Mirasta:
The episode takes place about half a season on from Family, which is on Earth and the Enterprise has certainly not been travelling full speed away from their homeworld all that time. Perhaps 6,000c is appropriate?TROI: We come from a federation of planets. Captain Picard is from a planet called Earth, which is over two thousand light years from here. I'm from another planet called Betazed.
That's not exactly what happened: The Enterprise is flung 7,000ly from their previous position, at which point Data states that the distance to nearest starbase at maximum warp is two years, seven months, three days, eighteen hours - let's call that 948 days in total.Remember, we can't make warp speeds for TNG onwards too fast as according to the episode Q Who it would take the Enterprise D almost 3 years to cross 7000LY.
However, we have no way of knowing exactly how far away the E-D was in relation to Starbase 185. The Enterprise may well be on deep space exploration duties - as indeed seems to be case in Pen Pals, the episode just prior to Q-Who.
Regarding travel times:
7,000ly in 948 days = 2,697c
8,000ly in 948 days = 3,082c
9,000ly in 948 days = 3,468c
10,000ly in 948 days = 3,853c
I don't think it is out of the question that the Enterprise could be a few thousand light years away from SB185. According to Tom Paris in The 37s, Warp 9.9 is 4billion MPS (21,473c), whereas Kim in Manoeuvres gave one of Voyager's speeds as 2billion KMS (6,671). Laforge in Booby Trap compares Leah Bram’s working model to the real E-D, which he says has “tens of thousands of light years on it”. The E-D was launched approx 2½ years previously – if she has just 25,000ly on the clock this means she travelled an average of 10,000ly a year.
So, even if the Enterprise kept up high speed for some time, once in the Selcundi Drema sector they spend 6 weeks in Pen Pals on a research mission, time enough for the Warp Engines to recover.
An interesting fact about that 7,000ly figure - it is also the distance from Jouret-4 (one of the Federation's outermost colonies and the one which opens BOBW). So, is Jouret-4 also the (former) location of SB185, or is it just a curious coincidence?
