In "Arena" the Metrons stopped the Gorn ship and the pursuing Enterprise, and took Captain KIrk and the Gorn Captain to a world to fight.
On the bridge of the Enterprise, McCoy doesn't think Spack is doing enough to find KInk.
So what makes Mr. Spock say that Kirk is somewhere in a thousand cubic parsecs of space instead of somehwere in a hundred cubic parsecs of space or somwhere within a million cubic parsecs of space, or soe other volume of space?
So what would a thousand cubic parsecs of space be like? A parsec is approximatley 3.2626 light years, so a cubic parsec is approimately 34.697011 cubic light years. A thousand cubic parsecs would be 34,697.011 cubic light years.
If the "thousand cubic parsecs" was in a cube shape, each side of that cube would be 10 parsecs or 32.626 light years long.
If the "thousand cubic parsecs" was in a sphere shape, the radius of the sphere would be about 6.2035 parsecs or about 20.2333 light years, and the diameter of the sphere would be about 12.407 parsecs or about 40.4666 light years.
The Enterprise was scanned from a solar system ahead of the Enterprise but behind the fleeing Gorn Ship:
At that time the Gorn ship has passed beyond the scanning solar system and that solar system is still ahead of the Enteprise. The scanning solar system is somewhere on a line from the Etneprise to the Gorn Ship, and between the btwo spacehips. And probably not exactly on the line but off to one side of it by an unspecified amout.
Then the Gorn ship slows and stops. And then the Enterprise slows and stops.
So the Enterprise is too far from the scanning solar system for any technology that Kirk knows about to hodl the ship in place. Part of that distance may be the sizeways distance by which that solar system is offset from the past and future path of the Enterprise. Part of that distanc emay be the distance of that solar sysem along the projected path of the Enterprise.
And if part of the distance Kirk considers to be too great for any technology to affect the Enterpris eis along the projected path of the Enterprise, has the Enterprise already passed the solar system in pursuit of the Gorn ship? Or is the Enterprise still getting closer to the solar system as it pursues the Gorn Ship?.
The Enterprise seems to stop very soon after the Uhura says the solar system is ahead of the Enteprise.
And I think that it is unlikely that the Enterprise moves past "that solar system ahead" in just a few minutes of dialog and action.
So I think that the scanning solar system is still ahead of the Enterprise and behind the Gorn ship, off to the side from the line between the two ships. Other people might want to assume the Enteprise has passed that solar system by the time it stops.
One possible reason why Spock might think that the volume of space where Kirk could be might have a volume of 1,000 cubic parsecs would be if the Gorn ship was stopped 10 parsecs or 32.626 light years ahead of the Enterprise and Spock assumed the Metrons could have sent to Kirk to anyplace within a cubical volume of space 10 parsecs wide.
Another possible reason why Spock might think that the volume of space where Kirk could be might have a volume of 1,000 cubic parsecs would be if the Gorn ship was stopped 12.407 parsecs or 40.4666 32.626 light years ahead of the Enterprise and Spock assumed the Metrons could have sent to Kirk to anyplace within a spherical volume of space 12.407 parsecs wide.
Or maybe Spock calculated the possible volume of space from the distances between the two ships and the solar system which scanned the Enterprise. Possibly both ships were the same distance from that solar system. Or possibly one ship was farther from the solar system.
So Spock might have calculated the volume of a sphere with a radius equal to the distance from the scanning solar system fo both of the ships, or to the farther ship if one ship was farther from the system.
Thus the Enterprise could have been 10 parsecs or 32.626 light years from the Gorn ship when they stopped, or 12.407 parsecs or 40.4666 light years, or possibly less than 12.407 parsecs or 40.4666 light years if both ships were 6.2035 parsecs or 20.23333 lightyears from the solar system and the distance between the ships was the third side of a equl side sided triangle.
Before the Enterprise was stopped, Sulu counted down the distance to the stopped Gorn ship.
Assuming that Sulu took 0.5 to 2.0 seconds ro say each number, the range would change from 1810 to 1550 in about 3 to 12 seconds. Thus the Enteprise would have closed from 1810 units to 1550 units in 3 to 12 seconds. The Enterprise would have traveled about 0.1436464 of the oriignal distance between it and the Gorn ship in 3 to 12 seconds, which would be .0.1677419 of the remaining distance.
If the remaining distance was 0.1 light year, or 3,155,760 light seconds, the Enterprise would have travelled 529,353.17 light seconds in 3 to 12 seconds, at about 44,112.764 to 176,451.05 times the speed of light.
If the remaining distance was 1 light year, or 31,557,600 light seconds, the Enterprise would have travelled 5,293,531.7 light seconds in 3 to 12 seconds, at about 441,127.64 to 1,764,510.5. times the speed of light.
If the remaining distance was 2 light years, or 63,115,200 ight seconds, the Enterprise would have travelled 10,578,063.57 light seconds in 3 to 12 seconds, at about 882,255.2972 to 3,526,021.19 4,4501,764,510.5. times the speed of light.
If the remaining distance was 10 light years, or 315,576,000 light seconds, the Enterprise would have travelled 52,935,317 light seconds in 3 to 12 seconds, at about 4,411,276.4 to 17.645,105. times the speed of light.
So apparently in "Area" Warp Factor Eight should be somewhere betwen tens of thosuands and tens of millions of times the speed of light.
On the bridge of the Enterprise, McCoy doesn't think Spack is doing enough to find KInk.
MCCOY: Now, you're the one that's always talking about logic. What about some logic now? Where's the Captain, Mister Spock?
SPOCK: He's out there, Doctor. Out there somewhere in a thousand cubic parsecs of space, and there's absolutely nothing we can do to help him.
So what makes Mr. Spock say that Kirk is somewhere in a thousand cubic parsecs of space instead of somehwere in a hundred cubic parsecs of space or somwhere within a million cubic parsecs of space, or soe other volume of space?
So what would a thousand cubic parsecs of space be like? A parsec is approximatley 3.2626 light years, so a cubic parsec is approimately 34.697011 cubic light years. A thousand cubic parsecs would be 34,697.011 cubic light years.
If the "thousand cubic parsecs" was in a cube shape, each side of that cube would be 10 parsecs or 32.626 light years long.
If the "thousand cubic parsecs" was in a sphere shape, the radius of the sphere would be about 6.2035 parsecs or about 20.2333 light years, and the diameter of the sphere would be about 12.407 parsecs or about 40.4666 light years.
The Enterprise was scanned from a solar system ahead of the Enterprise but behind the fleeing Gorn Ship:
.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: Captain, sensors report we're being scanned.
KIRK: By the alien ship?
UHURA: No, sir. It's from that solar system ahead.
At that time the Gorn ship has passed beyond the scanning solar system and that solar system is still ahead of the Enteprise. The scanning solar system is somewhere on a line from the Etneprise to the Gorn Ship, and between the btwo spacehips. And probably not exactly on the line but off to one side of it by an unspecified amout.
Then the Gorn ship slows and stops. And then the Enterprise slows and stops.
SCOTT: I don't know, sir, but whatever it is, we canna move.
SPOCK: We're being held in place, Captain, apparently from that solar system.
KIRK; This far out? That's impossible.
SPOCK: We are being held.
So the Enterprise is too far from the scanning solar system for any technology that Kirk knows about to hodl the ship in place. Part of that distance may be the sizeways distance by which that solar system is offset from the past and future path of the Enterprise. Part of that distanc emay be the distance of that solar sysem along the projected path of the Enterprise.
And if part of the distance Kirk considers to be too great for any technology to affect the Enterpris eis along the projected path of the Enterprise, has the Enterprise already passed the solar system in pursuit of the Gorn ship? Or is the Enterprise still getting closer to the solar system as it pursues the Gorn Ship?.
The Enterprise seems to stop very soon after the Uhura says the solar system is ahead of the Enteprise.
UHURA: No, sir. It's from that solar system ahead.
KIRK: Any interference? Resistance?
UHURA: No, sir, Just scanning beams. It's on an unusual wave length.
KIRK: Mister Spock?
SPOCK: It would appear someone is curious about us.
KIRK: Mister Sulu, is the alien still heading away from that solar system?
SULU: Yes, sir. We're closing, sir.
KIRK: Lieutenant Uhura, anything further on those scanning beams?
UHURA: There's no hostility, sir. They're not tractors or weapons of any sort, Just increasing in intensity. Steady. Regular. It's growing stronger, sir.
SULU: Captain!
KIRK: Yes, what is it?
SULU: The alien. It's slowing down. Warp five, four, two. It's going sublight, sir. Sir? It's stopped dead in space.
KIRK: He may be turning to fight.
SULU: No, sir. They're just dead out there.
KIRK: Are you sure?
SULU: Yes, sir. Unmoving.
KIRK: Then we've got them. Go to Red Alert. Prepare to fire phaser banks. Sensors, lock on. Mister Sulu, continue closing. Mister Spock, lock phasers into computer. Computers will control attack.
SPOCK: Computer lock ready, Captain. All systems standing by.
SULU: Range is one eight one zero. One seven six zero. Range is one seven zero zero. One six four zero. Range is one five nine zero. One five five zero and closing, sir.
(Suddenly, the ship decelerates, and everyone hangs on to something as the lights dim.) SULU: Warp six, warp five, four, warp three, warp one. Sublight, Captain. We're stuck, Captain. It's impossible, but. It's impossible.
KIRK: From warp eight? Have you lost your mind?
And I think that it is unlikely that the Enterprise moves past "that solar system ahead" in just a few minutes of dialog and action.
So I think that the scanning solar system is still ahead of the Enterprise and behind the Gorn ship, off to the side from the line between the two ships. Other people might want to assume the Enteprise has passed that solar system by the time it stops.
One possible reason why Spock might think that the volume of space where Kirk could be might have a volume of 1,000 cubic parsecs would be if the Gorn ship was stopped 10 parsecs or 32.626 light years ahead of the Enterprise and Spock assumed the Metrons could have sent to Kirk to anyplace within a cubical volume of space 10 parsecs wide.
Another possible reason why Spock might think that the volume of space where Kirk could be might have a volume of 1,000 cubic parsecs would be if the Gorn ship was stopped 12.407 parsecs or 40.4666 32.626 light years ahead of the Enterprise and Spock assumed the Metrons could have sent to Kirk to anyplace within a spherical volume of space 12.407 parsecs wide.
Or maybe Spock calculated the possible volume of space from the distances between the two ships and the solar system which scanned the Enterprise. Possibly both ships were the same distance from that solar system. Or possibly one ship was farther from the solar system.
So Spock might have calculated the volume of a sphere with a radius equal to the distance from the scanning solar system fo both of the ships, or to the farther ship if one ship was farther from the system.
Thus the Enterprise could have been 10 parsecs or 32.626 light years from the Gorn ship when they stopped, or 12.407 parsecs or 40.4666 light years, or possibly less than 12.407 parsecs or 40.4666 light years if both ships were 6.2035 parsecs or 20.23333 lightyears from the solar system and the distance between the ships was the third side of a equl side sided triangle.
Before the Enterprise was stopped, Sulu counted down the distance to the stopped Gorn ship.
SULU: Range is one eight one zero. One seven six zero. Range is one seven zero zero. One six four zero. Range is one five nine zero. One five five zero and closing, sir.
Assuming that Sulu took 0.5 to 2.0 seconds ro say each number, the range would change from 1810 to 1550 in about 3 to 12 seconds. Thus the Enteprise would have closed from 1810 units to 1550 units in 3 to 12 seconds. The Enterprise would have traveled about 0.1436464 of the oriignal distance between it and the Gorn ship in 3 to 12 seconds, which would be .0.1677419 of the remaining distance.
If the remaining distance was 0.1 light year, or 3,155,760 light seconds, the Enterprise would have travelled 529,353.17 light seconds in 3 to 12 seconds, at about 44,112.764 to 176,451.05 times the speed of light.
If the remaining distance was 1 light year, or 31,557,600 light seconds, the Enterprise would have travelled 5,293,531.7 light seconds in 3 to 12 seconds, at about 441,127.64 to 1,764,510.5. times the speed of light.
If the remaining distance was 2 light years, or 63,115,200 ight seconds, the Enterprise would have travelled 10,578,063.57 light seconds in 3 to 12 seconds, at about 882,255.2972 to 3,526,021.19 4,4501,764,510.5. times the speed of light.
If the remaining distance was 10 light years, or 315,576,000 light seconds, the Enterprise would have travelled 52,935,317 light seconds in 3 to 12 seconds, at about 4,411,276.4 to 17.645,105. times the speed of light.
So apparently in "Area" Warp Factor Eight should be somewhere betwen tens of thosuands and tens of millions of times the speed of light.
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