...As regards "Amok Time", Kirk may or may not be on course towards Altair originally, or even on a course in that general direction. He's intent on making it to Altair in time, yes, but perhaps he intends to stop at Celtair and Beltair first, and a further stop at Vulcan isn't out of the question, either. Perhaps the diversion to Vulcan, only adding those 2.8 light days, is from the current course towards Celtair (and thus away from Altair), and not from the final leg between Beltair and Altair?
This sort of a zigzag setup would make much better sense of the situation where seven days are removed from the schedule. Just drop the visits to Celtair and Beltair altogether and go straight for the designated goal, rather than try and add to your speed. The infinitesimal disturbance of the Vulcanian stop-and-go shouldn't affect an increased-speed dash along an already intended course much (and indeed would affect it even less than in the original situation, since the ship would be covering those 2.8 ld at higher speed and thus in shorter time). But going to Vulcan would be wholly out of the question if the only way to lose those seven days were to drastically alter course.
Timo Saloniemi
That makes a lot of sense. If the Enterprise was on a zig zag course between several star systems before reaching Altair, it might not have been heading on a line from some star to Altair when the decision to divert to Vulcan was made.
I wonder if there is any pair of stars A & B such that diverting slightly from a straight line between them to visit 40 Eridani would add only 2.8 light days to the total journey traveled?
It is easy to calculate the maximum possible speed of the Enterprise on the last leg of the journey, from Altair to Vulcan. Since the Vulcan star system must be between 16.0 and 17.0 light years from Earth, and since Altair is itself one of those stars, being about 16.73 light years from Earth, the maximum possible distance between Vulcan and Altair would be about 33.73 light years. Make it an even 34 light years, or about 12,418.5 light days.
When McCoy says that Kirk has to get Spock to Vulcan soon, he says:
MCCOY: Jim, you've got to get Spock to Vulcan.
KIRK: Bones, I will, I will. As soon as this mission is
MCCOY: No! Now. Right away. If you don't get him to Vulcan within a week eight days at the outside, he'll die. He'll die, Jim.
That implies that McCoy believes that the time necessary to reach Altair, plus the time that the Enterprise is ordered to spend at Altair for the ceremonies, which McCoy may have learned, since it might be public information and his close friend Kirk might have told him, plus the time to get from Altair to Vulcan, would be more than eight days and probably more than seven days.
When Kirk ask Admiral Komack for permission to divert to Vulcan before going to Altair:
KIRK: Sir, the delay would be, at most, a day. I can hardly believe that
If Kirk intended to stay in the Vulcan system for only two hours at most, or 0.08333 days, and if he told Admiral Komack that the delay wold be, at most, a day, that implies that the journey from Vulcan to Altair should have taken at least
about one day. If Kirk knew the voyage from Vulcan to Altair would take only 0.1 day, he would have told Komack that the delay would be, at most a quarter of a day, for example.
So if the voyage from Vulcan to Altair, a distance of no more than 12,418.5 light days, took 0.5 days, the speed would be at most 24,837 times c, the speed of light.
If the voyage from Vulcan to Altair would take 1 day, the speed would be at most 12,418.5 c,
If the voyage from Vulcan to Altair would take 2 days, the speed would be at most 6,209.25 c.
If the voyage from Vulcan to Altair would take 3 days, the speed would be at most 4,139.5 c.
If the voyage from Vulcan to Altair would take 4 days, the speed would be at most 3,104.625 c.
If the voyage from Vulcan to Altair would take 5 days, the speed would be at most 2,483.7 c.
If the voyage from Vulcan to Altair would take 6 days, the speed would be at most 2,069.75 c.
If the voyage from Vulcan to Altair would take 7 days, the speed would be at most 1,774.0714 c,
If the voyage from Vulcan to Altair would take 8 days, the speed would be at most 1,523.3125 c.
If the voyage from Vulcan to Altair would take 9 days, the speed would be at most 1,379.8333 c.
If the voyage from Vulcan to Altair would take 10 days, the speed would be at most 1,241.85 c,
If the voyage from Vulcan to Altair would take 11 days, the speed would be at most 1,128.9545 c.
If the voyage from Vulcan to Altair would take 12 days, the speed would be at most 1,034.875 c.
If the voyage from Vulcan to Altair would take 13 days, the speed would be at most 955.26923 c.
If the voyage from Vulcan to Altair would take 14 days, the speed would be at most 887.03571 c.
If the voyage from Vulcan to Altair would take 15 days, the speed would be at most 827.9 c.
If the voyage from Vulcan to Altair would take 16 days, the speed would be at most 776.15625 c.
If the voyage from Vulcan to Altair would take 17 days, the speed would be at most 730.5 c.
If the voyage from Vulcan to Altair would take 18 days, the speed would be at most 689.91666 c.
If the voyage from Vulcan to Altair would take 19 days, the speed would be at most 653.60526 c.
If the voyage from Vulcan to Altair would take 20 days, the speed would be at most 620.925 c.
And so on.
And if the Vulcan system is a lot less than 34 light years from Altair, the speed necessary would be considerably slower. Of the stars known to be 16 to 17 light years from Earth like Vulcan is, 70 Ophiuchi is is said to be 7.772 light years from Altair, and 40 Eridani is said to be 29.69 light years from Altair.
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