WARNING! I HAVE BEEN TOLD THIS POST IS NOT FOR THE MATH PHOBIC OR THOSE WITH SHORT ATTENTION SPANS! My post # 12 dated January 5, 2017 is a much better post to start this thread on. Space and time are connected. Suppose that some of the creators wanted to make Star Trek: the Motion Picture the most scientifically accurate and realistic Star Trek production yet. One way they might have done so would have been to remember high school problems about calculating distance and time. remember? Problems like: "If Train A leaves from City C at a speed of 50 miles per hour and Train B leaves from City D at the same time at a speed of 60 miles per hour, and the cities are 220 miles apart, when will the two trains pass each other - or crash if they're on the same track?" So maybe the creators of Star Trek: the Motion Picture decided to make V'Ger's trip to Earth and the Enterprise's trip to intercept V'Ger scientifically plausible and do the necessary calculations. Star Trek: the Motion Picture opens with three Klingon ships fighting V'Ger and then shows the Epsilon IX station intercepting the Klingon messages. [Epsilon IX - interior] LIEUTENANT: Our sensor drone is intercepting this on Quad L fourteen. BRANCH: That's in Klingon boundaries. Who are they fighting? LIEUTENANT: Unknown, sir. TECHNICIAN: I have an exterior visual. (the battle cruisers are destroyed by energy bolts from the Cloud) LIEUTENANT: We've plotted a course on that Cloud, Commander. It will pass into Federation space fairly close to us. BRANCH: Heading? LIEUTENANT: Sir, it's on a precise heading for Earth! So we can imagine a line and V'ger travelling on that line toward Earth. Somewhere between V'ger's current position and Earth there is the Federation Border. Epsilon IX is probably very close to the spot here V'Ger's path crosses the Federation border. Since V'Ger fought the Klingons inside Klingon boundaries, there is also a Klingon border between V'ger and Earth. Possibly there is one border, between Federation and Klingon space, as there is in many regions of space, or possibly the Klingon and Federation borders are separated by unclaimed space between them in this region of space. The next scene shows Spock's Kolinahr failure, probably but not certainly after the previous scene. The Next scene is at starfleet Headquarters. Kirk has certainly heard about V'Ger heading toward Earth: KIRK: Here? At Starfleet? The Enterprise is in final preparation to leave dock. SONAK: Which will require twenty more hours at minimum. KIRK: Twelve! I'm on my way to a meeting with Admiral Nogura which will not last more than three minutes. Report to me on the Enterprise in one hour. SONAK: Report to you, sir? KIRK: It is my intention to be on that ship following that meeting. Report to me in one hour. The next scene is in an orbiting complex. SCOTT:SCOTT: Those departure orders, twelve hours, Starfleet cannot be serious. KIRK: Why aren't the Enterprise transporters operating, Mister Scott? SCOTT: A wee problem, sir, really. Just temporary. Admiral, we have just spent eighteen months redesigning and refitting the Enterprise. How in the name of hell do they expect to have her ready in twelve hours? KIRK: Take me over, please. [Travel Pod] SCOTT: She needs more work, a shakedown. KIRK: Mister Scott, there's an alien object with unbelievable destructive power less than three days away from this planet. ...The only starship in interception range is the Enterprise. Ready, or not, she launches in twelve hours. So now, an unknown time after V'ger was first detected in Klingon space by Epsilon IX, it is less than three days from Earth, though probably more than 2.5 days. Kirk goes to the bridge and orders the crew to assemble on the rec deck at 0400 hours. Soon after the bridge scene is the transporter accident to Commander Sonak, about an hour after Stardate 7410.2. When the crew is on the rec deck Kirk plays the recordings of V'ger. KIRK: That's all we know about it, except that it's now fifty-three point four hours away from Earth. Enterprise is the only Federation starship that stands in its way. Our orders are to intercept, investigate, and take whatever action is necessary, ...and possible. Then they get the message of V'ger destroying Epsilon IX at about the time it crosses the Federation border. KIRK: External view! (Epsilon IX is destroyed in the same way as the Klingon battle cruisers) KIRK: Viewer off. ...Pre-launch countdown will commence in forty minutes. Since we don't know how long the Pre-launch countdown lasts, this moment is probably more than one hour and less than eleven hours and twenty minutes, after Kirk talked to Sonak and Spock. Thus at Stardate 7410.2 V'ger was about 54.4 to 64.7333 hours (2.266 to 2.69 days), or less from Earth. Later Enterprise launches: KIRK: Impulse power, Mister Sulu. Ahead, warp point five. ...Departure angle on viewer. SULU: Departure angle. KIRK: Viewer ahead. (external space, Enterprise passes Jupiter) Captain's log, stardate 7412.6. one point eight hours from launch. In order to intercept the intruder at the earliest possible time, we must now risk engaging warp drive while still within the solar system. DECKER: Captain, assuming we have full warp capability, accelerating to warp seven on leaving the solar system will bring us to IP with the intruder, twenty point one hours. If the Enterprise did launch in 12 hours, stardate 7412.6 should be 2.4 stardate units and 13.8 hours after Kirk talked to Sonak and Scott, thus making about 5.75 hours per stardate unit in this era. If the Enterprise will intercept V'ger in 20.1 hours at warp factor seven, and the official TOS warp scale is used and warp seven is 343 times the speed of light, Enterprise will intercept V'ger at a point 6,894.3 light hours from Earth. Since a light year is defined as the distance light travels in a Julian calendar year, 365.25 days long, there are 8,766 light hours in a light year. So the projected intercept point is about 0.786 light years from Earth. But when they try to go to warp an engine imbalance creates a wormhole,. Then Kirk says: KIRK: That object out there is less than two days from Earth. We need to intercept while it still is out there. If it is less than 48 hours but more than 20.1 hours from Earth this should be about 5.4 to 33.1 hours after the rec deck scene. Spock comes aboard, and by stardate 7413.4, about 18.4 hours after Kirk talked to Sonak and Scott on stardate 7410.2, has corrected the engine imbalance. Captain's log, stardate 7413.4. Thanks to Mister Spock's timely arrival, and assistance, we have the engines rebalanced into full warp capacity. Repair time less than three hours, ...which means we will now be able to intercept intruder while still more than a day from Earth. SULU: Warp point eight, ...point nine, ...warp two, ...warp five, ...warp six, ...warp seven, sir. So now the projected intercept point is more than a day from Earth. Thus they will intercept V'Ger when V'Ger is between 24 and 48 hours, possibly between 24 and 36 hours, from Earth at V'gr's speed. Later when they arrive at V'Ger and have managed to call off it's attack: KIRK: That thing is twenty hours away from Earth. We know nothing about it yet. I don't see how they spent at least 4 hours travelling alongside V'ger in the few onscreen minutes after intercepting it. Later: Captain's log, stardate 7414.1. Our best estimates place us some four hours from Earth. No significant progress thus far reviving Ilia memory patterns within the alien probe. This remains our only means of contact with our captor. This should be about 3.9 stardate units, or about 22.425 hours after Kirk talked to Sonak and Scott on Stardate 7410.2. And that doesn't add up to at least 53.4 hours from Earth in the rec deck room scene. If the rec deck scene is 53.4 hours from Earth and is between stardates 7410.2 and 7412.6, and stardate 7414.1 is 4 hours from Earth, stardate 7414.1 is about 49.4 hours after the rec deck scene, and there should be about 12.6666 to 32.333 hours in a stardate unit. And some time later: [Enterprise bridge] UHURA: A faint signal from Starfleet, sir. Intruder Cloud has been located on their outer monitors for past twenty-seven minutes. ...Cloud dissipating rapidly as it approaches. SULU: Starfleet reports forward velocity has slowed to sub-warp speed. We are three minutes from Earth's orbit. One other point: KIRK: Gentlemen. At last report you were on Vulcan. Apparently to stay. McCOY: Yes, you were undergoing the Kolineer discipline. KIRK: Sit down. SPOCK: If you are referring to the Kolinahr, Doctor, you are correct. McCOY: Well, however it's pronounced, Mister Spock, it's the Vulcan ritual supposed to purge all remaining emotions. KIRK: The Kolinahr is also the discipline you broke ...to join us. Will you, please, ...sit down! SPOCK: On Vulcan I began sensing a consciousness of a force more powerful than I have ever encountered. Thought patterns of exactingly perfect order. I believe they emanate from the intruder. I believe it may hold my answers. This seems to prove that Spock was on Vulcan or in the Vulcan Solar system when he sensed V'ger. KIRK: Mister Scott! Shall we give the Enterprise a proper shakedown? SCOTT: I would say it's time for that, sir, aye. We can have you back on Vulcan in for days, Mister Spock. SPOCK: Unnecessary, Mister Scott. My task on Vulcan is completed. So the rebuilt Enterprise can reach Vulcan in "four days", or about 3.0 to 5.0 days. At warp 6 a ship could travel 1.77 light years in 3 days, 2.36 light years in 4 days, and 2.956 light years in 5 days. At warp 7 a ship could travel 2.817 light years in 3 days, 3.756 light years in 4 days, and 4.695 light years in 5 days. At warp 8 a ship could travel 4.205 light years in 3 days, 5.607 light years in 4 days, and 7.01 light years in 5 days. It seems to me that they would travel faster when trying to intercept V'ger than on a shakedown cruise, so it doesn't seem likely Scott would calculate the travel time to Vulcan using warp 8 instead of warp 7. It seems to be generally agreed that Vulcan is 40 Eridani: According to Gene Roddenberry, James Blish and multiple other background sources, the Vulcan system was the star 40 Eridani A. One official source that suggested this proposal was the 1980 reference work Star Trek Maps (pp. 25-26). An alternative possibility, included in the equally official Star Trek Spaceflight Chronology (first published in 1979), was that Vulcan's sun was Epsilon Eridani. Roddenberry favored 40 Eridani, due to the comparative ages of the two systems. In a letter printed in Sky and Telescope magazine in July 1991, Roddenberry wrote, "Based on the history of life on Earth, life on any planet around Epsilon Eridani would not have had time to evolve beyond the level of bacteria. On the other hand, an intelligent civilization could have evolved over the aeons on a planet circling 40 Eridani. So the latter is the more likely Vulcan sun." He also made the presumption that the planet orbits the primary star. [12] This association was continued in the books The Worlds of the Federation (p. 18) and Star Trek: Star Charts (p. 58). Both sources cite Vulcan as the second planet in the system, which Star Charts (pp. 19 & 45) places in Sector 005 in the Beta Quadrant. MiscellaneousEdit But the most certain thing Memory Alpha could say was" Location Edit Vulcan was located "a little over" sixteen light years from Earth. Vulcan was located near Andoria. (ENT: "The Andorian Incident", "Home") In the 2270s, a Constitution-class heavy cruiser traveling at warp speed from Earth could reach Vulcan in four days. (Star Trek: The Motion Picture) http://memory-alpha.wikia.com/wiki/Vulcan_(planet) 40 Eridani is about 16.45 plus or minus 0.07 light years, or 16.38 to 16.52 light years. To travel that distance in "four days" - 3.0 to 5.0 days - requires a speed of 1,196.559 to 2,011.31 times the speed of light. That is about 2.337 to 9.311 times as fast as the official TOS warp factors 6, 7, and 8. Possibly TMP uses a new warp scale in which warp seven is about 1,196.559 to 2,011.31 times the sped of light. Maybe Scotty calculated the trip time to Vulcan knowing that certain unspecified factors would enable the Enterprise in much less time that according to the warp formula. Presumably Spock's Vulcan shuttle used the same warp factors and/or unknown additional factors to enable it to make the trip from Vulcan to near Earth in the same time as Scott calculated. Thus Spock would have left Vulcan three to five days before meeting the Enterprise. And we might suppose that Spock left Vulcan two to five days before stardate 7410.2 when Kirk talked to Sonak and Scott. Thus at V'ger's speed it was probably roughly approximately (53.4 plus 48=101.4) to (72 + 120 = 192) hours, or 4.225 to 8 days, from Earth When Spock left Vulcan. When the Enterprise launched, V'ger was less than 3 days minus half a day from Earth, or 1.5 days to 2.5 days from Earth. It was also at least 40 minutes (0.666 hours) less than 53.4 hours from Earth, or less than 52.734 hours or 2.197 days from Earth. When the Enterprise tried to enter warp 1.8 hours (or 0.075 days) after launch, V'ger was between 1.425 and 2.197 days from Earth. If the Enterprise would intercept V'ger after travelling 20.1 hours (or 0.8375 days) at warp seven, V'ger would have traveled 20.1 hours (or 0.8375 days) toward Earth at it's speed. 20.1 hours (or 0.8375 days) would be 0.3812 to 0.5875 of the total time V'Ger needed to reach Earth. V'ger would have traveled 0.3812 to 0.5875 of its remaining distance to Earth while the Enterprise traveled 20.1 hours at warp seven. If the Enterprise is using the official TOS warp formula, it should expect to intercept. V'ger about 0.786 light years from Earth. But possibly they plan to travel at warp factor seven and somehow travel 1,196.559 to 2,011.31 times the speed of light, as in Scott's calculated travel time from Earth to Vulcan. in that case they would expect to intercept V'ger at a distance of about 2.743 to 4.611 light years from Earth. Then they have the wormhole problem and turn off the warp engines. After a few minutes Kirk says that V'Ger is less than 2 days (48 hours) from Earth. But obviously more than the 0.8375 days (20.1 hours) they expected to intercept V'ger in. Thus when the Enterprise tried to enter warp V'ger should have been between 1.425 and 2.000 days from Earth. Thus intercepting V'ger in 0.8375 days would mean traveling somewhere between 0.441875 and 0.5877 of the distance V'ger has to travel to Earth. After some time Spock comes aboard, and after repair time of less than three hours, or about 2.5 to 3.0 hours, Enterprise is ready to go to warp. This could be about 2.5 to 4.0 hours after the first attempt to go to warp. Thus V'ger should be about 1.2584 to 1.896 days from Earth when they go to warp the second time. And Kirk says they will intercept V'Ger while it is still more than a day from Earth (about 1.0 to 2.0 days). If they originally planned to intercept V'ger between 0.441875 and O.5877 of the distance V'ger had still to travel to Earth, V'ger would travel between 0.558125 and 0.4123 of the total distance to Earth during that period. Thus the Enterprise would travel between about 0.7917 and 1.4254 times as far, and thus between about 0.7917 and 1.4254 times as fast as V'ger. Similarly V'Ger would travel between about 0.701 and 1.263 times as fast as the Enterprise. As written above, V'ger should be about 1.2584 to 1.896 days from Earth when they go to warp the second time. And Kirk says they will intercept V'Ger while it is still more than a day from Earth (about 1.0 to 2.0 days). Thus the Enterprise should travel for less than 0.2584 to 0.896 days to intercept V'ger more than 1.000 days from Earth. Half of 1.2584 to 1.896 days is 0.6292 to 0.948 days. If the Enterprise and V'ger traveled at the same speed they would meet halfway between them after 0.6292 to 0.948 days. And V'ger would be less than a day from Earth, not more than a day. If V'ger has 1.2584 to 1.896 days to travel and the Enterprise meets V'ger when V'ger still has more than 1.001 days to travel, then the Enterprise travels at least 1.118 to 3.387 times as fast as V'ger. Thus it seems that the Enterprise should be travelling about 1.118 to 1.4254 times as fast as V'ger, and thus that V'ger should be travelling 0.701 to 0.894 times as fast as the Enterprise. If the Enterprise travels at the official TOS warp factor Seven, or 343 times the speed of light, V'Ger's speed should be about 240.4 to 306.6 times the speed of light. The Enterprise should intercept V'Ger about 1.0 to 2.0 days from Earth at a point about 0.658 to 1.679 light years from Earth. V'ger should cross the Federation border and destroy Epsilon IX 53.4 hours (2.225 days) from Earth about 1.464 to 1.867 light years from Earth. And farther away than the Enterprise reaches it, of course. V'ger should be less than three days from Earth (about 2.0 to 3.0 days) on stardate 7410.2, and thus about 1.316 to 2.518 light years from Earth. But this is before V'Ger crosses the Border, and so 1.464 to 2.518 light years from Earth. And Spock Should have left Vulcan about 2.0 to 5.0 days before stardate 7410.2. This should be when V'ger is about 4.225 to 8.000 days from Earth, and thus about 2.364 to 6.715 light years from Earth. But if Spock's Vulcan Shuttle and the Enterprise could travel at speeds of about 1,196.559 to 2,011.31 times the speed of light between Earth and Vulcan, maybe the Enterprise travels at 1,196.559 to 2,011.31 times the speed of light when travelling at warp seven to intercept V'Ger. So if V'ger travels at 0.701 to 0.894 times the Enterprise's speed of 1,196.559 to 2,011.31 times the speed of light, V'ger would travel 838.787 to 1,789.111 times the speed of light. The Enterprise should intercept V'Ger about 1.0 to 2.0 days from Earth at a point about 2.296 to 9.796 light years from Earth. V'ger should cross the Federation border and destroy Epsilon IX 53.4 hours (2.225 days) from Earth about 5.292 to 10.898 light years from Earth. And farther away than the Enterprise reaches it, of course. V'ger should be less than three days from Earth (about 2.0 to 3.0 days) on stardate 7410.2, and thus about 4.592 to 14.694 light years from Earth. But this is before V'Ger crosses the Border, and so 5.292 to 14.694 light years from Earth. And Spock Should have left Vulcan about 2.0 to 5.0 days before stardate 7410.2. This should be when V'ger is about 4.225 to 8.000 days from Earth, and thus about 9.702 to 39.186 years from Earth. And presumably V'Ger destroyed the Klingon ships within Klingon boundaries shortly before, or at the same time that Spock sensed Vger, and thus when V'ger was either about 2.364 to 6.064 light years from Earth, or about 9.702 to 39.186 light years from Earth. If V'Ger traveled at about 240.4 to 306.6 times the speed of light, it could travel about 72,120 to 122,640 light years in 300 to 400 years, the approximate time limits for its journey if there was no time travel involved. If V'Ger traveled at about 838.787 to 1,789.111 times the speed of light, it could travel about 251,636.1 to 715,644.4 light years in 300 to 400 years, the approximate time limits for its journey if there was no time travel involved. [SIZE=4]Edit:[/SIZE] [SIZE=3]Subject:[/SIZE]
Also assuming that the new engine design wasn't revolutionary and they changed the warp scale at that point. Also assuming that Mr. Scott was boasting about getting Spock back to Vulcan in four days, as oppose to apologizing that it would take them a few days to do a proper shakedown before they could drop him off at Vulcan.
Let's just deal with the really basic things here: Why would we assume that? TOS was never consistent with the "official" warp scale. Why would we expect the movies to be? Also, I think you're reading way too much into the "stardate" numbers. They don't really make sense, and never really did, so taking them too literally is an exercise in futility. It's like trying to figure out the weight of an assault rifle in an action movie based on the number of times you see it fire without reloading. It'll be amusing, but not a productive use of anyone's brainpower.
In "This Side of Paradise" https://en.wikipedia.org/wiki/Mira To travel about 220 light years - perhaps 200 to 240 - in 0.5 to 1.5 years requires a speed of about 133.33 to 480 times the speed of light. To travel the newer distance measurement of 299 plus or minus 32.89 light years in 0.5 to 1.5 years requires a speed of about 177.406 to 663.78 times the speed of light. Warp five is 125 times the speed of light, warp six is 216 times the speed of light, warp seven is 343 times the speed of light, warp eight is 512 times the speed of light. At classic warp six, the highest speed for extended travel, a ship could travel 200 to 300 light years in in 0.926 to 1.388 years. The distance to the Andromeda Galaxy is estimated to be 2,540,000 plus or minus 110,000 light years, or about 2,430,000 to 2,650,000 light years. In "By Any Other Name": Assuming that "Less than three hundred" years is between 250 and 300 years, the trip to Andromeda requires speeds of 8,100 to 10,600 times the speed of light. If travelling ten times as fast as Starfleet ships is enough to be "a leap far beyond" their speeds, starfleet ships should travel about 810 to 1,060 times the speed of light; if twenty times as fast is necessary to be "a leap far beyond", then starfleet ships should travel about 405 to 530 times the speed of light. At warp 6 to warp 8 it would take the Enterprise about 4,746.0937 to, 12,268.5 years to reach Andromeda. If Kirk meant the Enterprise would take at least 10,000 years, and not mere thousands of years, to reach Andromeda its speed would be no more than 243 to 265 times the speed of light. Thus in some episodes like "this Side of Paradise" and "By Any Other Name" TOS speeds are consistent with the official TOS warp formula. And as I said in my original post, perhaps some of the creators of Star Trek: The Motion Picture tired to make it as accurate as they could.
Well I'll try to make the stardates in The Motion Picture make sense relative to the passing hours. SHORT VERSION: it turns out that at least one of the stardate numbers disagrees with the others. It seems there are too many stardate units between 7410.2 and 7412.6, and between 7412.6 and 7413.4, and too few stardate units between 7413.4 and 7414.1. It would probably work out better if the stardates were 7410.32, 7411.6, 7412.4, and 7414.1 or 7415.1. It can work with the numbers 7410.2, 7412.6, 7413.4 if stardate 7414.1 is changed to a later stardate. So maybe Kirk was tired and stressed and said stardate 7414.1 by mistake. Or perhaps due to warp travel since the previous three stardates the stardate on the Enterprise was lower than that on Earth. WARNING! LONG VERSION FOLLOWS. NOT FOR MATH PHOBIC OR THOSE WITH SHORT ATTENTION SPANS. USEFUL FOR SOMEONE ATTEMPTING A TIMELINE OF ST:TMP. If there are about 2.5 to 3.0 days (60 to 72 hours) between stardate 7410.2 and V'Ger reaching Earth, and 4 hours between stardate 7414.1 and V'Ger reaching Earth, there must be about 56 to 68 hours between stardate 7410.2 and stardate 7414.1. So there must be about 14.358974 and 17.435897 hours per stardate unit. If the rec deck scene is 53.4 hours from Earth and is between stardates 7410.2 and 7412.6, and stardate 7414.1 is 4 hours from Earth, stardate 7414.1 is about 49.4 hours after the rec deck scene, and there should be about 12.6666 to 32.333 hours in a stardate unit. If V'Ger was more than 20.1 hours and less than 48 hours from Earth sometime between Stardate 7412.6 and stardate 7413.4, and four hours from Earth on Stardate 7414.1, there would be 16.1 to 44 hours in 0.7 to 1.5 stardate units, and thus 10.73333 to 62.857142 hours per stardate unit. If V'Ger is 1.0 to 2.0 days, or 24 to 48 hours from Earth at Stardate 7413.4 and 4 hours from Earth on stardate 7414.1 there are 20 to 44 hours in 0.7 stardate units and so 28.571428 to 62.857141 hours per stardate unit. If V'Ger is 2.5 to 3.0 days (60 to 72 hours) from Earth on stardate 7410.2 and 1.0 to 2.0 days (24 to 48 hours) from Earth on stardate 7412.6, and the 2 stardates are separated by at least 12 hours to launch plus 1.8 hour since launch, then there are 13.8 to 48 hrs in 2.4 stardate units and thus 5.75 to 20 hours per stardate unit. If V'Ger is 2.5 to 3.0 days (60 to 72 hours) from Earth on Stardate 7410.2 and 1.0 to 2.0 days (24 to 48 hours) from Earth on stardate 7413.4, and the 2 stardates are separated by at least 12 hours to launch plus 1.8 hour since launch, plus 2.5 to 3 hours to repair the engines, then there are 16.3 to 48 hrs in 3.2 stardate units and thus 5.09375 to 15 hours per stardate unit. If V'Ger is 1.0 to 2.0 days (24 to 48 hours) from Earth on stardate 7412.6, and 1.0 to 2.0 days (24 to 48 hours) from Earth on stardate 7413.4, and the 2 stardates are separated by at lest 2.5 hours to repair the Engines, then Stardate 7412.6 must be 25.5 to 48 hours before V'Ger reaches Earth, and stardate 7413.4 must be 24.0 to 45.5 hours before V'Ger reaches Earth. Thus there is a different of 2.5 to 24 hours in 0.8 stardate units and there are 3.125 to 30 hours in a stardate unit. Calculations involving the three stardates 7410.2, 7412.6, and 7413.4 produce stardate ranges that overlap at 5.75 to 15 hours per stardate unit. Calculations involving stardate 7414.1 with the other ones produce stardate ranges that are not so consistent. So maybe Kirk was tired and stressed and said stardate 7414.1 by mistake. Or perhaps due to warp travel since the previous three stardates the stardate on the Enterprise was lower than that on Earth. I'll try six hours per stardate unit; 0.25 days per stardate unit. 4 stardate units per day. 0.1666 stardate units per hours. Stardate 7410.2: V'ger less than three days (less than 72 hours and less than 12 stardate units from Earth. Kirk tells Sonak to beam aboard in one hour. Enterprise will launch in 12 hours about stardate 7412.2. V'Ger predicted to reach Earth about stardate 7420.2 to Stardate 7422.2. Sonak's accident about an hour later at Stardate 7410.3666. Later: V'Ger crosses border and destroys Epsilon IX. 53.4 hours (8.99644 stardate units) before V'Ger reaches Earth. V'Ger projected to reach Earth between stardates 7419.0996 and 7421.5964. 40 minutes later (0.111 stardate units later) Pre launch countdown begins. Later: Enterprise launches. Later: Stardate 7412.6. 1.8 hours (0.299988 stardate units) after launch. Launch should have been about Stardate 7412.3001, 0.1001 stardate units and 0.6006 hours after the predicted launch time. Projected time to intercept V'Ger 20.1 hours (3.349866 stardate units) about Stardate 7415.9498. Minutes later, V'Ger is less than 2 days (48 hours, 8.0 stardate units) from Earth. V'Ger will reach Earth before stardate 7420.6. Stardate 7413.4. Spock has arrived, engine repair took less than three hours (0.4998 stardate units) so began after stardate 7412.9002, They expect to reach V'ger when V'ger is more than a day from Earth, and so between stardates 7412.6 and 7416.6. Thus the trip should take less than 3.2 stardate units or 19.2 hours or 0.8 days. When they reach V'Ger after V'Ger's attack and before Ilia is taken, V'Ger is 20 hours (3.332 stardate units) away from Earth. So they reach V'Ger before stardate 7417.268. On Stardate 7414.1 They are estimated to be 4 hours (0.664 stardate units) from Earth. V'Ger should reach Earth about stardate 7414.7664. That is 4.5664 stardate units or 1.1416 days after stardate 7410.2. That doesn't fit with V'ger being 53.4 hours or 2.225 days from Earth in the meantime. The time 20 hours before reaching Earth would then be about 7411.4344, before they went into warp or launched. That doesn't work. Enterprise would have reached V'ger by about 7410.7664 also before they went into warp or launched. That doesn't work. With stardates 6 hours long Kirk's log should have said stardate 7419.1 instead of 7414.1. Thus either Kirk said the wrong number or something changes the stardates after going into warp. If there are about 12.666 to 32.333 hours in a stardate unit I'll try calculations with a stardate unit at 18 hours and at 15 hours and see if they make sense. At 18 hours per stardate unit: Stardate 7410.2: V'ger less than three days (less than 72 hours and less than 4 stardate units from Earth. Kirk tells Sonak to beam aboard in one hour. Enterprise will launch in 12 hours about stardate 7410.866. Sonak's accident about an hour later at Stardate 7410.255. Later: V'Ger crosses border and destroys Epsilon IX. 53.4 hours (2.966 stardate units) until V'Ger reaches Earth. V'Ger predicted to reach Earth about stardate 7413.166 to 7415.566. 40 minutes later (0.0833 stardate units later) Pre launch countdown begins. Later: Enterprise launches. Later . Stardate 7412.6. 1.8 hours after launch. Launch should have been about Stardate 7412.5 long after the predicted launch time. Projected time to intercept V'Ger 20.1 hours (1.116 stardate units) about Stardate 7413.71. Minutes later, V'Ger is less than 2 days (48 hours, 2.666 stardate units) from Earth. V'Ger will reach Earth before stardate 7415.266. Stardate 7413.4. Spock has arrived, engine repair took less than three hours (0.166 stardate units) so began after stardate 7413.23, They expect to reach V'ger when V'ger is more than a day from Earth, and so before stardate 7413.933. Thus the trip should take less than 0.703 stardate units or 12.654 hours. When they reach V'Ger after V'Ger's attack and before Ilia is taken, V'Ger is 20 hours (1.111 stardate units) away from Earth. So this is before stardate 7414.155. On Stardate 7414.1 They are estimated to be 4 hours from Earth. V'Ger should reach Earth about stardate 7414.3222. That is 4.1222 stardate units or 3.09165 days after stardate 7410.2. That will not work. V'ger should have been 20 hours from Earth about stardate 7413.2111. Enterprise should have reached V'ger by about stardate 7412.9889, but both are before their second attempt to go to Warp. This will not work. With stardates 18 hours long Kirk's log should have said 7414.9 or 7415.0 instead of 7414.1. Thus either Kirk said the wrong number or something changes the stardates after going into warp. At 15 hours per stardate unit (0.625 days per stardate unit,1.6 stardate units per day, 0.0666 stardate units per hour): Stardate 7410.2: V'ger less than three days (less than 72 hours and less than 4.8 stardate units from Earth. Kirk tells Sonak to beam aboard in one hour. Enterprise will launch in 12 hours about stardate 7410.279. Sonak's accident about an hour later at Stardate 7410.2666. Later: V'Ger crosses border and destroys Epsilon IX. 53.4 hours (3.55644 stardate units) before V'Ger reaches Earth. V'Ger predicted to reach Earth about Stardate 7413.7564 to 7416.1564. 40 minutes later (0.04435 stardate units later) Pre launch countdown begins. Later: Enterprise launches. Later . Stardate 7412.6. 1.8 hours (0.2157 stardate units) after launch. Launch should have been about Stardate 7412.3843 long after the predicted launch time. Projected time to intercept V'Ger 20.1 hours (1.339 stardate units) about Stardate 7413.9398. Minutes later, V'Ger is less than 2 days (48 hours, 3.2 stardate units) from Earth. V'Ger will reach Earth before stardate 7415.8. Stardate 7413.4. Spock has arrived, engine repair took less than three hours (0.199 stardate units) so began after stardate 7413.2, They expect to reach V'ger when V'ger is more than a day from Earth, and so before stardate 7414.2. Thus the trip should take less than 1 stardate unit or 15 hours or 0.625 days. When they reach V'Ger after V'Ger's attack and before Ilia is taken, V'Ger is 20 hours (1.3332 stardate units) away from Earth. So they reach V'Ger before stardate 7414.46. On Stardate 7414.1 They are estimated to be 4 hours (0.26664 stardate units) from Earth. V'Ger should reach Earth about stardate 7414.3664. That is 4.1664 stardate units or 2.604 days after stardate 7410.2. That works. V'ger should have been 20 hours from Earth about stardate 7413.0344. Enterprise should have reached V'ger by about stardate 7412.7664, but both are before their second attempt to go to warp. This will not work. With stardates 15 hours long Kirk's log should have said about 7415.2 or 7415.3 instead of 7414.1. Thus either Kirk said the wrong number or something changes the stardates after going into warp. If 18 hours has 3 problems and 15 hours has 1 problem, What about the minimum length of 12.6666 hours from my previous post? At 12.66666 hours per stardate unit (0.52775 days per stardate unit, 1.8947778 stardate units per day, 0.0789477 stardate units per hour): Stardate 7410.2: V'ger less than three days (less than 72 hours and less than 5.684 stardate units from Earth. Kirk tells Sonak to beam aboard in one hour. Enterprise will launch in 12 hours about stardate 7411.1473. Sonak's accident about an hour later at Stardate 7410.2789. Later: V'Ger crosses border and destroys Epsilon IX. 53.4 hours (4.2158071 stardate units) before V'Ger reaches Earth. V'Ger predicted to reach Earth about Stardates 7414.4158 to 7416.8158. 40 minutes later (0.0526265 stardate units later) Pre launch countdown begins. Later: Enterprise launches. Later . Stardate 7412.6. 1.8 hours (0.1421058 stardate units) after launch. Launch should have been about stardate 7412.458, 1.3105 stardate units or 16.55 hours after the predicted launch time. Projected time to intercept V'Ger 20.1 hours (1.5868487 stardate units) or about Stardate 7414.1868. Minutes later, V'Ger is less than 2 days (48 hours, 3.7895556 stardate units) from Earth. V'Ger will reach Earth between stardates 7414.4947 and 7416.2475. Stardate 7413.4. Spock has arrived, engine repair took less than three hours (0.2368431 stardate units) so began after stardate 7413.1632, They expect to reach V'ger when V'ger is more than a day from Earth, and so between stardates 7412.6 and 7414.3528. Thus the trip should take less than 0.9528 stardate units or 12.068736 hours or 0.502864 days. When they reach V'Ger after V'Ger's attack and before Ilia is taken, V'Ger is 20 hours (1.578954 stardate units) away from Earth. So they reach V'Ger between stardates 7412.9158 and 7414.6686. On Stardate 7414.1 They are estimated to be 4 hours (0.3157908 stardate units) from Earth. V'Ger should reach Earth about stardate 7414.4157. That is 4.2157 stardate units or 2.2249046 days after stardate 7410.2. That works. V'ger should have been 20 hours from Earth about stardate 7412.8368. Enterprise should have reached V'ger by about stardate 7412.521, but that is before their second attempt to go to warp. This will not work. With stardates 12.666 hours long Kirk's log should have said about 7415.8 or 7415.3 instead of 7414.1. Thus either Kirk said the wrong number or something changes the stardates after going into warp.
Thank god... Or maybe the writers never really put that much thought into what stardates actually mean -- never have, and never will -- and that going down the rabbit hole of the Stardate system is the quickest path to madness? I mean, maybe you've got that kind of sad desperation in your life, in which case, I wish you well. But there's a reason that even the most anal Trek nerds never look too closely at the Stardate Problem. It's not just TMP, it's literally ALL of Star Trek in every episode ever filmed, and smarter people than you have gone insane trying to make sense of them.
Here is what I hope will be a much, much shorter version of my first post on this thread. In Star Trek: The Motion Picture, after the Enterprise launches, Kirk makes a log: A few minutes later, after the failed attempt to go to warp: So when V'ger is between 24 and 48 hours from Earth, the Enterprise could reach V'Ger from Earth in 20.1 hours, at which point V'Ger would still be between 3.9 and 27.8 hours from Earth. Remembering high school math problems about finding the relative speed of objects, this means that Enterprise's predicted average speed would be between 0.1940 and 1.33830 of the predicted average speed of V'Ger. Later, when they are about to go to warp for the second time: So repair time was between about 2.5 and 3.0 hours, beginning either when Spock came aboard or right after the first attempt to go to warp. If we assume that this is 2.5 to 4 hours after the first attempt to go to warp, V'Ger must be between 20.0 to 45.5 hours from Earth. But V'ger will be more than 24 hours from Earth when they reach V'Ger hours in the future. The trip to reach V'Ger will take less than 20.1 hours since V'ger has been travelling toward Earth in the interval. Assuming that the travel time tor each V'ger will be over 5.0 hours and less than 20.1 hours long, they will reach V'Ger when it is between 24.0 and 40.5 hours from Earth. So the speed of the Enterprise should be between 1.1940 and 8.1 times that of V'Ger. At one time there is statement exactly how long V'Ger is from Earth. In the rec decks scene Kirk shows the destruction of the Klingon ships and says: The Epsilon IX is s destroyed by V'Ger and Kirk says: Forty minutes is 0.6666 hours. So if the Pre-launch countdown takes 10 seconds the rec deck scene is only 0.6666 hours before launch, which is 1.8 hours before the first attempt to go to warp. Thus V'Ger might be 50.9334 hours from Earth at the the first attempt to go to warp - except that V'Ger is 24 to 48 hours from Earth at that point. The earliest possible time for the rec deck scene is after stardate 7410.2 when Kirk tells Scott and Sonak that the Enterprise will launch in 12 hours and orders Sonak to board the Enterprise in one hour. Sonak suffers a transporter accident one our after Stardate 7410.2 and thus eleven hours before scheduled launch. The Rec deck scene is after Sonak's acccident and thus is between 0.6666 hours and 11 hours before launch and thus between 2.466 and 12.8 hours before the first attempt at warp. Thus V'gr should be 40.6 to 50.934 hours from Earth at the first attempt at warp. But V'Ger was 24 to 48 hours from Earth at the first attempt first attempt at warp. So thus V'ger was between 40.6 and 48 hours from Earth at the first attempt at warp, making the rec deck scene between 5.4 and 12.8 hours before launch, and the pre launch countdown between 4.734 and 12.1334 hours long. So if the Enterprise is predicted to reach V'Ger 20.1 hours after V;Ger is between 40.6 and 48 hours from Earth it will be when V'ger is between 20.5 and 27.9 hours, but more than 24 hours, from Earth. Thus the speed of the Enterprise should be 0.1940298 to 1.3880 times V'Ger's speed.
My first post was very long, so I'll try to be shorter this time. Where and when does Star Trek: The Motion Picture happen? On Earth, on Vulcan, and in outer space is where. But where and when do the outer space scenes happen? The short answer is: 1) If the Enterprise in Star Trek: The Motion Picture traveled at warp factor seven on the TOS scale: V'Ger would be 0.6765435 to 1.5729637 light years from Earth when the Enterprise reached it. V'Ger would be 1.5053092 to 1.749922 light years from Earth when it crossed the Federation border near station Epsilon IX. V'Ger would be 3.2640492 to 5.505373 light years from Earth when Spock started his journey from Vulcan to Earth - which may have been the same time V'Ger fought the Klingons. V'Ger could travel 74,132.256 to 114,905 light years in the 300 to 400 years that were the maximum length of its trip back to Earth from the Machine Planet if V'ger was rebuilt and sent immediately after been launched from Earth more than 300 years before. 2) If the Enterprise in Star Trek: The Motion Picture traveled at warp factor seven on the TNG scale: V'Ger would be 1.2941804 to 3.0089694 light years from Earth when the Enterprise reached it. V'Ger would be 2.8795512 to 3.3474784 light years from Earth when it crossed the Federation border near station Epsilon IX. V'Ger would be 6.2438984 to 10.531393 light years from Earth when Spock started his journey from Vulcan to Earth - which may have been the same time V'Ger fought the Klingons. V'Ger could travel 141,809.82 to 219,805.22 light years in the 300 to 400 years that were the maximum length of its trip back to Earth from the Machine Planet if V'ger was rebuilt and sent immediately after been launched from Earth more than 300 years before. 3) If the Enterprise in Star Trek: The Motion Picture traveled at the speeds needed in the described journey from Earth to Vulcan: V'Ger would be 2.3053763 to 9.4916659 light years from Earth when the Enterprise reached it. V'Ger would be 5.129462 to 10.559478 light years from Earth when it crossed the Federation border near station Epsilon IX. V'Ger would be 11.12251 to 33.220832 light years from Earth when Spock started his journey from Vulcan to Earth - which may have been the same time V'Ger fought the Klingons. V'Ger could travel 252,611.61 to 693,366.24 light years in the 300 to 400 years that were the maximum length of its trip back to Earth from the Machine Planet if V'ger was rebuilt and sent immediately after been launched from Earth more than 300 years before So there is a vast contrast between the immense length of V'Ger's journey and the comparatively short distances that the main events of the movie take place in. Note that even the farthest calculated distance for V"Ger when Spock began his journey to Earth - 33.220832 light years - is "only" a "mere" 195,292,810,000,000 miles, give or take a few billion. This may seem way too close to Earth. But possibly the interstellar laws and treaties in Star Trek allow interstellar realms like the federation to only claim space within a sphere with a relatively small radius around each star they rule. Thus a map of the Federation would look like hundreds or thousands of tiny spheres scattered across space. The same goes for the Klingon, Romulan, Cardassian, Breen, Tholian, Gorn, etc. etc. realms. And star systems belonging to different realms might be mixed up together. It is possible that the most distant Federation star system might be hundreds of times farther from Earth than the nearest Klingon star system. Note that: https://www.google.com/webhp?source...TF-8#q=distance+from+Bajor+to+Cardassia+Prime A distance that probably gave millions of Bajorans and Cardassians nightmares. So Cardassia let a colony planet only 5.25 light years from their capital planet become independent and then apply to join Cardassia's former and potentially future enemy, the Federation. If it's good enough for Cardassia it's good enough for the Federation. One advantage of events happening so close to Earth is that it should be very easy to identify the Klingon star system V'Ger passes by when it fights the Klingons. Explanation of the Distances 1) Relative Speeds After launch: After the failed attempt to go to warp, Kirk says just minutes later: So it will take the Enterprise 20.1 hours to reach V'Ger. Since V'Gr is 24.0 to 48 hours from Earth, they will reach V'Ger when V'Ger is still 3.9 to 27.9 hours from Earth. Thus the speed of Enterprise must be 0.1940298 to 1.3880597 times the speed of V'Ger. When they are about to try the warp drive again hours later: So because V'Ger is now closer to Earth than before, the Enterprise will take less than 20.1 hours to reach V'ger from very near Earth when V'ger is more than 24.0 hours from reaching Earth. So the speed of the Enterprise must be at least 1.1940298 time the speed of V'Ger. Together the 2 calculations prove the speed of the Enterprise is 1.1940298 to 1.3880597 times the speed of V'ger. Thus the speed of V'Ger must be 0.7204301 to 0.8375 times the speed of the Enterprise. 2) Absolute Speed of V'Ger: The Enterprise travels at warp factor seven during the movie. 1) If the official TOS warp scale is used, warp factor seven is 343 times the speed of light and the speed of V'Ger is between 247.10752 and 287.2625 times the speed of light. 2) If the official TNG warp scale is used, warp factor seven is 656.135 times the speed of light and the speed of V'Ger is between 472.6994 and 549.51306 times the speed of light. 3) if warp factor seven was the speed of the discussed trip from Earth to Vulcan, it would be about 1,168.8 to 2,069.75 times the speed of light, and the speed of V'Ger would be 842.0387 to 1,733.4156 times the speed of light. 3) Discussion of the hypothetical trip from Earth to Vulcan After V'Ger ascends to a higher plane: Vulcan is said to be 16 light years from Earth in the Enterprise episode "Home" And over sixteen light years from Earth in the Enterprise episode "Daedalus". Thus it is 16.0 to 17.0 light years from Earth. If Scott's four days were between 3.0 and 5.0, the speed would be between 1,168.8 and 2,069.75 times the speed of light. If the Enterprise traveled in that speed range to reach V'Ger, the speed of V'Ger would be 842.0387 to 1,733.4156 times the speed of light. 4) Distance the Enterprise intercepts V'Ger If the Enterprise intercepts V'Ger more than a day from Earth (24 to 48 hours): V'Ger is 0.6765435 to 1.5729637 light years from Earth if the Enterprise travels at TOS warp factor seven. V'Ger is 1.2941804 to 3.0089694 light years from Earth if the Enterprise travels at TOS warp factor seven. V'Ger is 2.3053763 to 9.4916659 light years from Earth if the Enterprise travels at the speed of the hypothetical trip to Vulcan. 5) Distance V'Ger Crosses the Federation Frontier near Epsilon IX station: 1) If the official TOS warp scale is used, 1.5053092 to 1.749922 light years from Earth. 2) If the official TNG warp scale is used, 2.8795512 to 3.3474784 light years from Earth. 3) if warp factor seven was the speed of the discussed trip from Earth to Vulcan, 5.129462 to 10.559478 light years from Earth. So V'ger crosses the Federation border near Epsilon IX 53.4 hours before reaching Earth, at a distance of: 1) If the official TOS warp scale is used, 1.5053092 to 1.749922 light years from Earth. 2) If the official TNG warp scale is used, 2.8795512 to 3.3474784 light years from Earth. 3) if warp factor seven was the speed of the discussed trip from Earth to Vulcan, 5.129462 to 10.559478 light years from Earth. 6) V'Ger crossing the Federation Border in relation to other times On stardate 7410.2 Kirk told Sonak and Scott that the Enterprise would launch in 12 hours, and also told Sonak to report aboard in 1 hour. Sonak's accident as anhour after that or 11 hours before launch. The recreation deck scene when V'Ger crossed the Federation border near Epsilon IX was after the transporter accident. The pre launch countdown was scheduled to begin 40 minutes (0.666 hours) later. Thus V'Ger crossed[/i] the Federation border 11.000 to 0.666 hours before launch. The first attempt to go to warp on stardate 7412.6 was 1.8 hours after launch, and thus V'Ger crossed the Federation border 12.8 to 2.466 hours before the first attempt to go to warp. So the first attempt to go to warp should have been when V'Ger was 40.6 to 50.934 hours from Earth. But it was less than 48.000 hours from Earth. 7) When Spock reached the Enterprise The Enterprise V'Ger when V'Ger was over 24.000 hours from Earth. Since the Enterprise traveled 1.1940298 to 1.3880597 times the speed of V'Ger, it would travel that distance in over 17.290322 to 20.1 hours. But less than 20.1 hours since that was the travel earlier hen V;Ger as more distant. Thus the Enterprise should have gone into warp the second time when V'Ger was at least 41.290322 to 45.000 hours from Earth, but no more than 45.000 hours. Spock worked on rebalancing the engines for less than three hours, or about 2.5 to 3.0 hours. So Spock should have boarded at least 43.790322 to 47.5 hours before V'Ger reached Earth. Therefore: Spock boarded the Enterprise 43.790322 to 48.000 hours before V'Ger reached Earth. 8) When Spock left Vulcan Spock was on Vulcan when he sensed V'Ger and took a trip to Earth: If Spock made the trip at the same speeds as Scott's proposed trip from Earth to Vulcan, the trip would take 3.0 to 5.0 days (72.0 to 120 hours). If Spock ended the trip 43.790322 to 48.000 hours before V'Ger reached Earth, Spock began the trip 115.79032 to 168 hours (4.8245966 to 7 days) before V'Ger reached Earth. 9) V'Ger's distance from Earth when Spock left Vulcan 1) If the official TOS warp scale is used, 3.2640492 to 5.505373 light years. 2) If the official TNG warp scale is used, 6.2438984 to 10.531393 light years. 3) 3) if warp factor seven was the speed of the discussed trip from Earth to Vulcan, 11.12251 to 33.220832 light years. 9) The Total Distance of V'Ger's Voyage Nobody can tell the total distance V'Ger traveled, but there are clues. Spoiler KIRK: V-G-E-R ...V-O-Y-A-G-E-R ...Voyager! ...Voyager VI? The machine civilization rebuilt it and eventually V'Ger headed for Earth. So by assuming various possible speeds for V'Ger it is simple to calculate the distance V'Ger traveled if it fell into a black hole 300 to 400 years earlier and emerged immediately and was immediately rebuilt and immediately headed for Earth. But if those time intervals were not "immediately" but took years, decades or centuries, then V'Ger could have traveled a much shorter distance. And of course if the black hole sent V'Ger into the past or future as well as a great distance in space, V'Ger might have been travelling unknown distances for unknown periods of time.
Hello everyone, I'd[SIZE=4] just like to ask MAGolding [/SIZE]if he's the same person who wrote some similar articles for Trek magazine, quite a while ago. They were some of the highlights of the Best of Trek books for me, and it's nice to see this quite amazing level of mathematical analysis once again. Timon
In my previous post I deduced that V'Ger probably traveled an immense distance on its journey while the events during the movie only happened a short distance from Earth - a short distance in cosmic terms, of course. So let's try to calculate where the nearest star system ruled by the Klingons would be if V'Ger fought the klingons about the time Spock started his trip to Earth. As said above, if the Enterprise traveled at warp 7 on the TOS warp scale: V'Ger would be 1.5053092 to 1.749922 light years from Earth when it crossed the Federation border near station Epsilon IX. V'Ger would be 3.2640492 to 5.505373 light years from Earth when Spock started his journey from Vulcan to Earth - which may have been the same time V'Ger fought the Klingons. The Federation border would be less than half the distance to where V'Ger fought the Klingons inside Klingon space. So either there is a Federation-Klingon border closer to Earth than to the nearest Klingon star, or else there is some unclaimed space between the Federation and Klingon Borders. So what are the candidate stars for the closest Klingon star system. 1) Alpha Centauri A, B, and C, 4.365 plus or minus 0.007 light years from Earth, or 4.358 to 4.372 (A & B) or 4.2421 light years (C). The distance is right. But there is no evidence that Alpha Centauri was ever ruled by the Klingons. Alpha Centauri is the first Earth colony in canon. And just a few years before STTMP Kirk says that Alpha Centauri is a beautiful place, and thus presumably Klingon free. 2) Barnard's Star. 5.978 plus or minus 0.002 light years from Earth, or 5.976 to 5.980 light years. The distance is not too bad and Barnard's star has never been mentioned by name in any Star Trek canon. There is nothing to contradict Bernard's Star. 3) Luhman 16 or WISE 1049-5319. 6.516 plus or minus 0.001 light years away, or 6.515 to 6.517 light years. The distance is not so close and the system is two brown dwarf sub stars. Not likely to have habitable planets but Klingons could establish bases on lifeless asteroids, moons, or planets in that system. It was discovered in 2013 and was not known when STTMP was made. 4) WISE 0855-0714. About 7.27 plus or minus 0.13 light years from Earth, or 7.14 to 7.40 light years. Even father away and even less of a star system. It is described as a (sub) brown dwarf or a rogue planet. But the Klingons could possibly have bases on objects orbiting it. It was discovered in 2013 and was not known when STTMP was made. 5) Wolf 359. 7.86 plus or minus 0.03 light years from Earth, or 7.83 to 7.89 light years. A proper star with planets, but even farther away from Earth. So examine the coordinates of those star systems in the usual equatorial coordinate system. 1) Alpha Centauri. 14h 39m 36.494s Declination -60 50 02.3737 2) Barnard's Star. 17h 57m 48.5s Declination +04 41 36.2072 3) Luhman 16. 10h 49m 18.723s Declination -53 19 09.86 4) WISE 0855-0714. 08h 55m 10.83s Declination -07 14 42.5 5) Wolf 359. 10h 56m 28.99s Declination + 07 00 52.0 When the Enterprise leaves Earth and zooms off into outer space it passes l close to Jupiter and its big moons before going into warp. Thus it is logical to assume that V'Ger is coming from a direction that happens to be in the direction of the ecliptic plane of the solar system, the plane that Earth and the other planets orbit in. Converting Equatorial coordinates to ecliptic coordinates at an astronomy conversion site we get the following ecliptic coordinates for the star systems. In order of closeness to the ecliptic plane they are: 1) Wolf 359. 163.37705221 0.22988975 0.22988975 degrees difference. At a distance of 7.83 to 7.89 light years 1 degree of arc is 0.136 to 0.137 light years. If the Klingons claim space in a radius of 1.5053092 to 1.749922 light years around Wolf 359, that would be 10.987 to 12.860 degrees. 2) WISE 0855-0714. 139.22695198 -23.61224374 23.61224374 degrees difference. At a distance of 7.14 to 7.40 light years 1 degree of arc is 0.124 to 0.129 light years. If the Klingons claim space in a radius of 1.5053092 to 1.749922 light years around WISE 0855-0714, that would be 11.669 to 13.565 degrees. 3) Barnard's Star. 270.07913943 28.13150268 28.13150268 degrees difference. At a distance of 5.976 to 5.980 light years 1 degree of arc is 0.104 light years. If the Klingons claim space in a radius of 1.5053092 to 1.749922 light years around Barnard's Star, that would be 14.474 to 16.826 degrees. 4) Alpha Centauri. 240.17825927 -42.59466934 42.59466934 degrees difference. At a distance of 4.358 to 4.372 light years 1 degree of arc is 0.076 light years. If the Klingons claim space in a radius of 1.5053092 to 1.749922 light years around Alpha Centauri, that would be 19.806 to 23.025 degrees. 5) Luhman 16. 195.71074197 -53.89500925 53.89500925 degrees difference. At a distance of 6.515 to 6.517 light years 1 degree of arc is 0.113 light years. If the Klingons claim space in a radius of 1.5053092 to 1.749922 light years around Luhman 16, that would be 13.321 to 15.486 degrees. And when they discover that V'Ger was Voyager VI Kirk says: Kirk might believe that V'Ger came from the far side of the galaxy if it was coming from the direction of the galactic center. The coordinates of the galactic center in the equatorial coordinate system are 17h 45m 40.04s, -29 degrees 00 minutes 28.1 seconds. Translating them into ecliptic coordinates they are: 267.55041319 -5.60769325 And into galactic coordinates they are: 0.29113749 -0.64870542 https://ned.ipac.caltech.edu/forms/calculator.html In the ecliptic coordinates for the galactic center the -5.60769325 degrees is the angle between the galactic center and the ecliptic plane of the solar system. So if V'Ger was coming from the direction on the ecliptic plan that was closest to the direction to the galactic center, it would be coming from about 267.55041319 0.0000 in ecliptic coordinates. That is 17h52m21.97774s -23d26m03.1076s in equatorial coordinates and 5.49603809 1.53616461 in galactic coordinates. In galactic coordinates the stars in their order of closeness to the galactic center in galactic longitude are: 1) WISE 0855-0714. 333.98582184 -5.53787476 26.015 degrees difference. 2) Barnard's Star. 31.29356328 13.51255438 31.293 degrees difference. 3) Alpha Centauri. 316.07432269 -1.06580303 43.926 degrees difference. 4) Luhman 16. 285.59031100 5.19686525 74.410 degrees difference. 5) Wolf 359. 245.17490170 56.43838889 114.82 degrees difference. And in their order of closeness to the galactic plane: 1) Alpha Centauri. 316.07432269 -1.06580303 1.06580303 degrees difference. At a distance of 4.358 to 4.372 light years 1 degree of arc is 0.076 light years. If the Klingons claim space in a radius of 1.5053092 to 1.749922 light years around Alpha Centauri, that would be 19.806 to 23.025 degrees. 2) Luhman 16. 285.59031100 5.19686525 5.19686525 degrees difference. At a distance of 6.515 to 6.517 light years 1 degree of arc is 0.113 light years. If the Klingons claim space in a radius of 1.5053092 to 1.749922 light years around Luhman 16, that would be 13.321 to 15.486 degrees. 3) WISE 0855-0714. 333.98582184 -5.53787476 5.53787476 degrees difference. At a distance of 7.14 to 7.40 light years 1 degree of arc is 0.124 to 0.129 light years. If the Klingons claim space in a radius of 1.5053092 to 1.749922 light years around WISE 0855-0714, that would be 11.669 to 13.565 degrees. 4) Barnard's Star. 31.29356328 13.51255438 13.51255438 degrees difference. At a distance of 5.976 to 5.980 light years 1 degree of arc is 0.104 light years. If the Klingons claim space in a radius of 1.5053092 to 1.749922 light years around Barnard's Star, that would be 14.474 to 16.826 degrees. 5) Wolf 359. 245.17490170 56.43838889 56.43838889 degrees difference. At a distance of 7.83 to 7.89 light years 1 degree of arc is 0.136 to 0.137 light years. If the Klingons claim space in a radius of 1.5053092 to 1.749922 light years around Wolf 359, that would be 10.987 to 12.860 degrees. So in closeness to the ecliptic plane only Wolf 359 qualifies. V'Ger could travel in the ecliptic plane and pass close by Wolf 359. In closeness in galactic longitude to the galactic center WISE 0855-0714, Barnard's Star, and Alpha Centauri qualify. V'Ger could travel from the far side of the galaxy close to the galactic center and pass close by them. But Luhman 16 and Wolf 359 are disqualified, being in directions away from the far side of the galaxy. In closeness to the galactic plane Alpha Centauri, Luhman 16, WISE 0855-0714, and Barnard's Star qualify. V'Ger could travel from the far side of the galaxy along the galactic plane and pass close by them. But Wolf 359 is too far from the galactic plane. Thus it seems there is no star system among the five closest to Earth that fits all the qualifications necessary. Either one of the qualifications is not really necessary or the star that V'Ger fought the Klingons near is not among the five known star systems closest to Earth. Next I will discuss more distant stars that V'Ger might have passed by and fought the Klingons near if the Enterprise was traveling at higher speeds than TOS warp factor seven and so V'Ger was also traveling faster. Note: This discussion was rewritten on January 19 to 20, 2017 and the conclusions changed. Yes I am the same person.
!) I was serious about the decimal places. You don't get anything in your computations out of them, and it comes off as the mathematical equivalent of using big words to distract from content. No mathematician or engineer does that in practice unless it's actually necessary for the computations involved. As someone with a post-grad degree in math, it almost pains me to see that. Seriously, there's no reason in any of this work that you need to write out 7 decimal places. 2) If you're talking about in-universe, why does it matter that certain stars weren't discovered at the time they wrote TMP? The writers never considered things to this much detail anyway. And even if they had, who cares what the writers considered if something other than their intentions works better? Writer intention isn't in the text, so you can just ignore it. Unless you're saying that the only stars that exist in the Trek universe are those that were known at the time the series was created. But you're using a distance measurement for Alpha Centauri that was only measured in 2012, rather than the 1970-measured value of 4.39 ± 0.04 ly, and I'm assuming your other distance figures and stellar coordinates aren't the best known in 1979 but the best known today; there's no reason to be historically accurate with one and not the other. Which, by the way, comes back around to 1): This is an example of why those chains of decimal places are bad. Because the distance to Alpha Centauri isn't 4.3650 ly. The 2012 figure measured was 4.365 ± 0.007 ly. That is, it could be anywhere between 4.358 and 4.372 ly. Which is why people usually just say "4.3". Because that's as accurate as we can guarantee is true. We can guarantee that it's close to 4.3. I mean, we can even be pretty confident it's close to 4.36, saying that and using that in computation would be fine. But we can't guarantee that it's close to 4.3650. You even added an extra decimal place for no reason there, that's literally lying about the level of accuracy you have. If you're going to use a figure without the error range rather than using the bounds of the error range throughout the computation (which honestly is usually a good idea because keeping track of compounding error that way is horrible even for something professional, let along a hobby thing like this), you need to reduce the number of decimal points you use to account for the removal of the error range. I can't believe something on TrekBBS got me ranting about sigfigs. I'm really having TA grading flashbacks here.
Well, it is possible that being informed that I have rewritten my post # 17 above in part because of your criticisms might possibly mollify you. You will note that when rewriting it I changed my conclusions somewhat.
In Post # 16 of this thread I wrote: So now I am discussing more distant stars that might have been part of the Klingon empire near where V'Ger fought the Klingon ships. In post # 12 of this thread I wrote: 2) If the Enterprise in Star Trek: The Motion Picture traveled at warp factor seven on the TNG scale: V'Ger would be 1.2941804 to 3.0089694 light years from Earth when the Enterprise reached it. V'Ger would be 2.8795512 to 3.3474784 light years from Earth when it crossed the Federation border near station Epsilon IX. V'Ger would be 6.2438984 to 10.531393 light years from Earth when Spock started his journey from Vulcan to Earth - which may have been the same time V'Ger fought the Klingons. V'Ger could travel 141,809.82 to 219,805.22 light years in the 300 to 400 years that were the maximum length of its trip back to Earth from the Machine Planet if V'ger was rebuilt and sent immediately after been launched from Earth more than 300 years before. The important distances for this discussion are: 1) The Federation border being 2.8795512 to 3.3474784 light years from Earth. If all space realms claim a sphere with a radius in that range around each star they rule. Note that if the Federation rules both Sol and Alpha Centauri the spheres of Federation space around them would overlap a bit. 2) Spock starting his journey from Vulcan to Earth when V'Ger would be 6.2438984 to 10.531393 light years from Earth, which may be when and where V'Ger fought the Klingons. Note that V'Ger could have been closer to Earth than the star ruled by the Klingons or farther away from Earth than the star system ruled by the Klingons. These are the candidate star systems, starting with the five listed in post # 16. 1) Alpha Centauri A, B, and C. Distance: 4.365 plus or minus 0.007 light years from Earth, or 4.358 to 4.372 (A & B) or 4.2421 light years (C). Equatorial coordinates: Right Ascension 14h 39m 36.494s Declination -60 50 02.3737 Ecliptic coordinates: Longitude 240.17825927 Latitude -42.59466934 Galactic coordinates: Longitude 316.07432269 Latitude -1.06580303 2) Barnard's Star. Distance: 5.978 plus or minus 0.002 light years from Earth, or 5.976 to 5.980 light years. Equatorial coordinates: Right Ascension 17h 57m 48.5s Declination +04 41 36.2072 Ecliptic coordinates: Longitude 270.07913943 Latitude 28.13150268 Galactic coordinates: Longitude 31.29356328 Latitude 13.51255438 3) Luhman 16 or WISE 1049-5319. Distance: 6.516 plus or minus 0.001 light years away, or 6.515 to 6.517 light years. Equatorial coordinates: Right Ascension 10h 49m 18.723s Declination -53 19 09.86 Ecliptic coordinates: Longitude 195.71074197 Latitude -53.89500925 Galactic coordinates: Longitude 285.59031100 Latitude 5.19686525 4) WISE 0855-0714. Distance: About 7.27 plus or minus 0.13 light years from Earth, or 7.14 to 7.40 light years. Equatorial coordinates: Right Ascension 08h 55m 10.83s Declination -07 14 42.5 Ecliptic coordinates: Longitude 139.22695198 Latitude -23.61224374 Galactic coordinates: Longitude 333.98582184 Latitude -5.53787476 5) Wolf 359. Distance: 7.86 plus or minus 0.03 light years from Earth, or 7.83 to 7.89 light years Equatorial coordinates: Right Ascension 10h 56m 28.99s Declination + 07 00 52.0 Ecliptic coordinates Longitude 163.37705221 Latitude 0.22988975 Galactic coordinates: Longitude 245.17490170 Latitude 56.43838889 And more stars that are farther away from the solar system: 6) Lalande 21185 Distance: 8.31 plus or minus 0.01 light years, or 8.30 to 8.32 light years. Equatorial coordinates: Right Ascension 11 93 20 Declination +35 58 12 Ecliptic coordinates Longitude 171.75509783 Latitude 35.84152917 Galactic coordinates: Longitude 143.24492347 Latitude 80.80721075 7) Sirius Distance: 8.60 plus or minus 0.04 light years or 8.56 to 8.64 light years. Equatorial coordinates: Right Ascension 06 45 08.9173 Declination -16 42 58.0171 Ecliptic coordinates Longitude 104.77974428 Latitude -39.60534546 Galactic coordinates: Longitude 227.51693537 Latitude -8.43316571 8) Luyten 726-8 Distance: 8.73 plus or minus 0.06 light years, or 8.67 to 8.79 light years. Equatorial coordinates: Right Ascension 01 39 01.54 Declination -17 57 01.8 Ecliptic coordinates Longitude 16.40352624 Latitude -26.18178630 Galactic coordinates: Longitude 176.25775779 Latitude -75.10306565 9) Ross 154 Distance: 9.60 plus or minus 0.05 light years or 9.55 to 9.65 light years. Equatorial coordinates: Right Ascension 18 49 49.3625 Declination -23 50 10.4291 Ecliptic coordinates Longitude 281.37975992 Latitude -0.88764382 Galactic coordinates: Longitude 11.30714980 Latitude -10.28446002 10) Ross 248 Distance: 10.30 plus or minus 0.02 light years or 10.28 to 10.32 light years. Equatorial coordinates: Right Ascension 23 41 54.99 Declination + 44 10 40.8 Ecliptic coordinates Longitude 109.99090527 Latitude -16.93970830 Galactic coordinates: Longitude 17.49416953 Latitude 41.44265142 11) Epsilon Eridani Distance: 10.475 plus or minus 0.003 light years, or 10.472 to 10.478 light years. Equatorial coordinates: Right Ascension 03 32 55.84496 Declination -9 27 29.7312 Ecliptic coordinates Longitude 48.16776585 Latitude -27.71576387 Galactic coordinates: Longitude 195.84460726 Latitude -48.05133568 12) Lacaille 9352 Distance: 10.68 plus or minus 0.02 light years or 10.66 to 10.70 light years. Equatorial coordinates: Right Ascension 23 05 52.03604 Declination -35 51 11.0475 Ecliptic coordinates Longitude 332.68430632 Latitude -27.51179505 Galactic coordinates: Longitude 5.10084457 Latitude -65.95703046 13) Ross 128 Distance: 11.03 plus or minus 0.02 light years, or 11.01 to 11.05 light years. Equatorial coordinates: Right Ascension 11 47 44.3964 Declination + 00 48 16 Ecliptic coordinates Longitude 176.86787284 Latitude -0.48045797 Galactic coordinates: Longitude 270.14720000 Latitude 59.55895693 14) WISE 1506+ 7027 Distance: 11.1 plus or minus 2.3 light years or 8.8 to 13.4 light years Equatorial coordinates: Right Ascension 15 06 49.89 Declination + 70 27 36.23 Ecliptic coordinates Longitude 146.55042102 Latitude 74.04542217 Galactic coordinates: Longitude 108.27058956 Latitude 42.60525328 15 EZ Aquarii Distance: 11.1 plus or minus 0.1 light years, or 11.0 to 11.2 light years. Equatorial coordinates: Right Ascension 22 38 33.73 Declination -15 17 57.3 Ecliptic coordinates Longitude 335.46167152 Latitude -6.23470318 Galactic coordinates: Longitude 47.07120601 Latitude -56.97976513 16) Procyon Distance: 11.46 plus or minus 0.05 light years, or 11.41 to 11.51 light years. Equatorial coordinates: Right Ascension 07 39 18.1 Declination + 05 13 29 Ecliptic coordinates Longitude 115.78550204 Latitude -16.01989508 Galactic coordinates: Longitude 213.70249473 Latitude 13.01923606 17) 61 Cygni Distance: 11.41 plus or minus 0.02 light years, or 11.39 to 11.43 light years. Equatorial coordinates: Right Ascension 21 06 53.9434 Declination + 38 44 57.898 Ecliptic coordinates Longitude 336.95686137 Latitude 51.89907974 Galactic coordinates: Longitude 82.31971192 Latitude -5.81797579 So what do these figures mean? Saving incomplete post.