Hi Mytran,
My apologies for the late comments
Mytran said:
ARENA
...
Incidentally, this is also the same episode where, having been stopped at the edge of the Metron solar system, Spock declares that Kirk could be out there anywhere "within a thousand cubic parsecs of space". I suppose Spock could just be using flowery language, but that seems very large for a solar system!
According to the dialogue it doesn't specify where the Enterprise is stopped but we can guess that it wasn't at the edge of the system because the Gorn was heading away from it and the Enterprise was closing on the Gorn.
KIRK: Our position.
DEPAUL: Two two seven nine pl, sir. Uncharted solar system at two four six six pm.
KIRK: Is it on the alien's course?
DEPAUL: No, sir. He's headed away from it.
...
UHURA: No, sir. It's from that solar system ahead.
...
KIRK: Mister Sulu, is the alien still heading away from that solar system?
SULU: Yes, sir. We're closing, sir.
...
SPOCK: We're being held in place, Captain, apparently from that solar system.
KIRK: This far out? That's impossible.
With this in mind, 1,000 cubic parsecs is 10x10x10 parsecs or 32x32x32 LY. That could indicate that they were stopped many light years away from the Metron system and Spock's estimate is based on the space around the system.
Regarding "Breads and Circuses", the average speed for the TOS Enterprise to cover 1/16th of a parsec approaching from outside of a system is about 200,000c. 200,000c for interstellar travel is consistent with the speeds presented in "That Which Survives" and "Obsession".
The drift speed of the wreckage is about 0.03c to cover 0.2LY (1/16 parsec). Since we don't know how exactly the Beagle was destroyed (it was damaged by meteors), it is reasonable that her wreckage left the system at 0.03c either by explosion or some other means.
In "Where Silence Has Lease" there are too many cuts to determine how long they they took to record 1.4 parsecs or whether they were still at Warp 2 for the entire duration. If they were going anywhere close to the speed listed in Voyager's "The 37's" it's possible to cover 4.5 LY in a few hours.
"Maneuvers" had a speed of about 6600c and "The 37's" upwards to 21,000c. That's between 18 LY/day to 58 LY/day so in Voyager traveling parsecs doesn't sound prohibitively long.
At this point I'm not so sure parsec needs to be redefined. I do think the TNG warp formulas don't make sense though
