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Starship Phasers

In "The Tholian Web", after the initial encounter where the Enterprise shot the Tholian ship with phasers, they said it then moved out of range. I forget if they said what that range distance was. I don't have the ep handy; maybe someone else can check.

Robert
 
The first Tholian ship closed to 90,000 km, and the two ships then exhanged fire. The exchange ended in both ships being damaged, but not in either of them explicitly maneuvering out of range. Indeed, Spock seemed to consider the Tholians "disabled", unable to fire, perhaps unable to maneuver. And Scotty said he "couldn't do a thing with the Enterprise", suggesting she was totally unable to move as well.

Then the second Tholian ship arrived, and the two started spinning the web "just beyond phaser range". Apparently, the first ship had been repaired to some degree... But no, we never learn how far the web is being created, nor how far "just beyond phaser range" might be.

Timo Saloniemi
 
The hero vessel retreated from the Romulans at "emergency warp" for at least a minute (the time we saw on screen) and probably two (the estimate Sulu gave), without slowing down or flying in circles. That gives the two vessels a hefty separation, certainly in excess of one lightsecond.

A little over two minutes, so yes there is a considerable separation at that point.

Kirk then gives chase to the Romulans at less than maximum warp, again becoming a sensor ghost to them. He may have closed some of that distance there, but not down to a lightsecond, it seems - because he then orders maximum warp to catch the Romulans before they cross the Neutral Zone border, definitely much faster than the speed of the Romulans, and still fails to appreciably decrease range within the next twenty seconds of action (which involves phaser fire fired from a distance Stiles increduously considers "this distance?").

The main argument for a distance greater than one lightsecond is that Kirk doesn't overshoot the Romulans while firing, despite maintaining maximum warp. Luckily for us, his earlier retreat at maximum warp allows for that.

Timo Saloniemi

Some time passes between the retreat and the resuming of pursuit. The engines are even offline for a period. They resume following the Romulan for a while until they come close to the neutral zone. There is acceleration and some firing at which time the Rom pops the nuclear mine. There is nothing here to imply that they did not close the range that was opened during the retreat. Matter of fact it seems that they are once again at a range similar to previous weapons exchanges....the Roms are just over the Neutral Zone boundry and the Feds have stopped or are flying parallel to the border as they fire (they never crossed the zone, but flew at max warp only 20 secs out). They certainly were not at millions of Kms as they were after the emergency warp retreat....a few hundred thousand maybe, but thats about all.
 
The phaser range was also covered on-screen in one of the TNG episodes.
I think it was called 'The Wounded'.

In any event, a battle ensued and the USS Pheonix (I think that was the name of the Fed ship) that chased the Cardassian cargo ship closed within 300 000 Km and it was confirmed through dialogue on the Enterprise's bridge that was the weapons range.

Of course Weapons range is a broad term ... they could have meant torpedoes and not phasers, but taking into account what we witnessed of Trek technology, phaser 'should' have a maximum range of 300 000km, while torpedoes (in-universe wise) would probably have a very large range ... and capable of being fired at warp speeds (so visually speaking, torpedoes would appear as an after flash from being fired from the tube, and the same second hit the other ship - unless warp strafing maneuvers are used).
 
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