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Time and Space in the Motion Picture

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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?
Let's not forget that the official explanation for Stardates in the TOS writer's guide was based on a mathematical formula that "varies depending on location in the galaxy, velocity of travel, and other factors" - so in the case of TMP I think one could argue that every time the warp drive was engaged then the following Stardates were no longer synchronized with the previous, so there's no way to determine the number of hours passed.

EDIT: fixed typo
 
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I think there would have to be regions where (for whatever reason, natural or artificial) it was possible to travel much greater multiples of C than normal. In Arena for instance, they cover a phenomenal distance in pursuit, in seemingly only a few hours!
 
Better, it was Warp One! Kirk ordered that speed a lot in season 1.

They were heading back to "where they were supposed to be", whatever that means. Cestus III perhaps? Maybe it was just a short distance away...
 
In my post # 12 in this thread I calculated the distance from Earth that various events in Star Trek: The Motion Picture would happen at if the Enterprise traveled at a various speeds in the movie.

For example:

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.

So which star systems might be the one that V'Ger fought the Klingon ships near in the first scene?

If the Enterprise in Star Trek: The Motion Picture traveled at warp factor seven on the TNG scale V'Ger might have fought the Klingons at a distance of 6.2438984 to 10.531393 light years from Earth while within a sphere of space claimed by the Klingons around Barnard's Star - 5.978 plus or minus 0.002 light years or 5.976 to 5.980 light years from Earth, or Ross 154 - Distance: 9.60 plus or minus 0.05 light years or 9.55 to 9.65 light years from Earth.

The candidate stars and the reasons for selection are below.

List of Star Systems:

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).

2) Barnard's Star.

Distance: 5.978 plus or minus 0.002 light years from Earth, or 5.976 to 5.980 light years.

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.

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.

5) Wolf 359.
Distance: 7.86 plus or minus 0.03 light years from Earth, or 7.83 to 7.89 light years

6) Lalande 21185

Distance: 8.31 plus or minus 0.01 light years, or 8.30 to 8.32 light years.

7) Sirius

Distance: 8.60 plus or minus 0.04 light years or 8.56 to 8.64 light years.

8) Luyten 726-8

Distance: 8.73 plus or minus 0.06 light years, or 8.67 to 8.79 light years.

9) Ross 154

Distance: 9.60 plus or minus 0.05 light years or 9.55 to 9.65 light years.

10) Ross 248

Distance: 10.30 plus or minus 0.02 light years or 10.28 to 10.32 light years.

11) Epsilon Eridani

Distance: 10.475 plus or minus 0.003 light years, or 10.472 to 10.478 light years.

12) Lacaille 9352

Distance: 10.68 plus or minus 0.02 light years or 10.66 to 10.70 light years.

13) Ross 128

Distance: 11.03 plus or minus 0.02 light years, or 11.01 to 11.05 light years.

14) WISE 1506+ 7027

Distance: 11.1 plus or minus 2.3 light years or 8.8 to 13.4 light years

15 EZ Aquarii

Distance: 11.1 plus or minus 0.1 light years, or 11.0 to 11.2 light years.

16) Procyon

Distance: 11.46 plus or minus 0.05 light years, or 11.41 to 11.51 light years.

17) 61 Cygni

Distance: 11.41 plus or minus 0.02 light years, or 11.39 to 11.43 light years.

So all 17 stars systems are more or less in the right distance for V'Ger to fight the Klingons near while 6.2438984 to 10.531393 light years from Earth.

Ecliptic latitude:

When the Enterprise leaves Earth to try to intercept V'Ger it zooms past Jupiter, so the direction that V'Ger comes from should be more or less on the ecliptic plane that the planets in our solar system orbit in. How far from the ecliptic plane and the direction that V'Ger comes from could the klingon ruled star be?

According to this interpretation the Federation should claim a sphere with a radius of 2.8795512 to 3.3474784 light years around our solar system, and presumably the Klingons would claim a sphere with the same radius around each star they rule. At a distance of 12 light years a radius of 2.8795512 light years covers 13.775 degrees of arc. Any star with an ecliptic latitude of less than plus or minus 13.775 degrees is a candidate for V"ger to pass through Klingon space around it on the vary to Earth.

They include:

Wolf 359
Ecliptic coordinates
Longitude 163.37705221
Latitude 0.22988975

Ross 128
Ecliptic coordinates
Longitude 176.86787284
Latitude -0.48045797

Ross 154
Ecliptic coordinates
Longitude 281.37975992
Latitude -0.88764382


EZ Aquarii
Ecliptic coordinates
Longitude 335.46167152
Latitude -6.23470318

At a distance of 5 light years a radius of 3.3474784 light years covers 38.471 degrees of arc. Any star with a ecliptic latitude of less than plus or minus 38.471 degrees might be a candidate, depending on the star's precise distance.

These lesser candidates include:

Procyon
Ecliptic coordinates
Longitude 115.78550204
Latitude -16.01989508

Ross 248
Ecliptic coordinates
Longitude 109.99090527
Latitude -16.93970830

Luyten 276-8
Ecliptic coordinates
Longitude 16.40352624
Latitude -26.18178630

Lacaille 9352
Ecliptic coordinates
Longitude 332.68430632
Latitude -27.51179505

Epsilon Eridani
Ecliptic coordinates
Longitude 48.16776585
Latitude -27.71576387

Barnard's Star
Ecliptic coordinates
Longitude 270.07913943
Latitude 28.13150268

Lalande 21185
Ecliptic coordinates
Longitude 171.75509783
Latitude 35.84152917

Galactic Longitude:

V'Ger is also speculated to have been on the far side of the galaxy, probably because of the direction that V'Ger came from. Assuming that V'ger might have passed by a Klingon ruled star that is within 60 degrees of galactic longitude zero, that Klingon ruled star must have a galactic longitude less than 60 or more than 300.

Stars within the correct galactic longitude range include:

Lacaille 9352

Galactic coordinates:
Longitude 5.10084457
Latitude -65.95703046

Ross 154

Galactic coordinates:
Longitude 11.30714980
Latitude -10.28446002

Ross 248

Galactic coordinates:
Longitude 17.49416953
Latitude 41.44265142

WISE 0855-0714.

Galactic coordinates:
Longitude 333.98582184
Latitude -5.53787476

Barnard's Star.

Galactic coordinates:
Longitude 31.29356328
Latitude 13.51255438

Alpha Centauri A, B, and C.

Galactic coordinates:
Longitude 316.07432269
Latitude -1.06580303

15 EZ Aquarii

Galactic coordinates:
Longitude 47.07120601
Latitude -56.97976513

Galactic latitude:

The direction that V;Ger comes from should also have a galactic latitude close to zero. If v'Ger comes from above or below the galactic plane it might be interpreted as coming from outside the galaxy instead of from the far side of the galaxy. Stars with galactic latitudes of less than plus or minus 13.775 degrees include:

Alpha Centauri A, B, and C.

Galactic coordinates:
Longitude 316.07432269
Latitude -1.06580303

Luhman 16 or WISE 1049-5319.

Galactic coordinates:
Longitude 285.59031100
Latitude 5.19686525

WISE 0855-0714.

Galactic coordinates:
Longitude 333.98582184
Latitude -5.53787476

61 Cygni

Galactic coordinates:
Longitude 82.31971192
Latitude -5.81797579

Sirius

Galactic coordinates:
Longitude 227.51693537
Latitude -8.43316571

Ross 154

Galactic coordinates:
Longitude 11.30714980
Latitude -10.28446002

Procyon

Galactic coordinates:
Longitude 213.70249473
Latitude 13.01923606

Barnard's Star.

Galactic coordinates:
Longitude 31.29356328
Latitude 13.51255438

Stars with galactic latitudes of less than plus or minus 38.471 degrees might be candidates, depending on their precise distances, but there aren't any in the group.

Conclusion:

The star that fits all three conditions is Ross 154,

However, at a distance of 5.980 light years or less from, Earth, the distance of Barnard's Star, a degree of arc would be 0.096342 light years. A sphere of Klingon space 2.8795512 to 3.3474784 light years in radius around Barnard's star would have a radius of 29.888 to 34.745 degrees of arc. Since Barnard's Star has a ecliptic latitude of 28.13150268 and a galactic latitude of 13.51255438 V'ger could pass within Klingon space around Barnard's Star from a direction with ecliptic and galactic latitudes near zero.

If the Enterprise in Star Trek: The Motion Picture traveled at warp factor seven on the TNG scale V'Ger might have fought the Klingons at a distance of 6.2438984 to 10.531393 light years from Earth while within a sphere of space claimed by the Klingons around Barnard's Star - 5.978 plus or minus 0.002 light years or 5.976 to 5.980 light years from Earth, or Ross 154 - Distance: 9.60 plus or minus 0.05 light years or 9.55 to 9.65 light years from Earth.
 
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Better, it was Warp One! Kirk ordered that speed a lot in season 1.

They were heading back to "where they were supposed to be", whatever that means. Cestus III perhaps? Maybe it was just a short distance away...

My assumption is that Warp 1 or even 2, is a preliminary speed, to "warm up the engines" and probably for safety reasons, especially if they are relatively near a star system or other gravity well. We probably shouldn't assume that the Enterprise was coasting at light speed for more than a few hours at most.
 
In my post # 12 in this thread I calculated the distance from Earth that various events in Star Trek: The Motion Picture would happen at if the Enterprise traveled at a various speeds in the movie.

For example:

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.

So which star systems might be the one that V'Ger fought the Klingon ships near in the first scene?

If the Enterprise in Star Trek: The Motion Picture traveled at warp factor seven on the TNG scale V'Ger might have fought the Klingons at a distance of 6.2438984 to 10.531393 light years from Earth while within a sphere of space claimed by the Klingons around Barnard's Star - 5.978 plus or minus 0.002 light years or 5.976 to 5.980 light years from Earth, or Ross 154 - Distance: 9.60 plus or minus 0.05 light years or 9.55 to 9.65 light years from Earth.

The candidate stars and the reasons for selection are below.

List of Star Systems:

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).

2) Barnard's Star.

Distance: 5.978 plus or minus 0.002 light years from Earth, or 5.976 to 5.980 light years.

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.

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.

5) Wolf 359.
Distance: 7.86 plus or minus 0.03 light years from Earth, or 7.83 to 7.89 light years

6) Lalande 21185

Distance: 8.31 plus or minus 0.01 light years, or 8.30 to 8.32 light years.

7) Sirius

Distance: 8.60 plus or minus 0.04 light years or 8.56 to 8.64 light years.

8) Luyten 726-8

Distance: 8.73 plus or minus 0.06 light years, or 8.67 to 8.79 light years.

9) Ross 154

Distance: 9.60 plus or minus 0.05 light years or 9.55 to 9.65 light years.

10) Ross 248

Distance: 10.30 plus or minus 0.02 light years or 10.28 to 10.32 light years.

11) Epsilon Eridani

Distance: 10.475 plus or minus 0.003 light years, or 10.472 to 10.478 light years.

12) Lacaille 9352

Distance: 10.68 plus or minus 0.02 light years or 10.66 to 10.70 light years.

13) Ross 128

Distance: 11.03 plus or minus 0.02 light years, or 11.01 to 11.05 light years.

14) WISE 1506+ 7027

Distance: 11.1 plus or minus 2.3 light years or 8.8 to 13.4 light years

15 EZ Aquarii

Distance: 11.1 plus or minus 0.1 light years, or 11.0 to 11.2 light years.

16) Procyon

Distance: 11.46 plus or minus 0.05 light years, or 11.41 to 11.51 light years.

17) 61 Cygni

Distance: 11.41 plus or minus 0.02 light years, or 11.39 to 11.43 light years.

So all 17 stars systems are more or less in the right distance for V'Ger to fight the Klingons near while 6.2438984 to 10.531393 light years from Earth.

Ecliptic latitude:

When the Enterprise leaves Earth to try to intercept V'Ger it zooms past Jupiter, so the direction that V'Ger comes from should be more or less on the ecliptic plane that the planets in our solar system orbit in. How far from the ecliptic plane and the direction that V'Ger comes from could the klingon ruled star be?

According to this interpretation the Federation should claim a sphere with a radius of 2.8795512 to 3.3474784 light years around our solar system, and presumably the Klingons would claim a sphere with the same radius around each star they rule. At a distance of 12 light years a radius of 2.8795512 light years covers 13.775 degrees of arc. Any star with an ecliptic latitude of less than plus or minus 13.775 degrees is a candidate for V"ger to pass through Klingon space around it on the vary to Earth.

They include:

Wolf 359
Ecliptic coordinates
Longitude 163.37705221
Latitude 0.22988975

Ross 128
Ecliptic coordinates
Longitude 176.86787284
Latitude -0.48045797

Ross 154
Ecliptic coordinates
Longitude 281.37975992
Latitude -0.88764382


EZ Aquarii
Ecliptic coordinates
Longitude 335.46167152
Latitude -6.23470318

At a distance of 5 light years a radius of 3.3474784 light years covers 38.471 degrees of arc. Any star with a ecliptic latitude of less than plus or minus 38.471 degrees might be a candidate, depending on the star's precise distance.

These lesser candidates include:

Procyon
Ecliptic coordinates
Longitude 115.78550204
Latitude -16.01989508

Ross 248
Ecliptic coordinates
Longitude 109.99090527
Latitude -16.93970830

Luyten 276-8
Ecliptic coordinates
Longitude 16.40352624
Latitude -26.18178630

Lacaille 9352
Ecliptic coordinates
Longitude 332.68430632
Latitude -27.51179505

Epsilon Eridani
Ecliptic coordinates
Longitude 48.16776585
Latitude -27.71576387

Barnard's Star
Ecliptic coordinates
Longitude 270.07913943
Latitude 28.13150268

Lalande 21185
Ecliptic coordinates
Longitude 171.75509783
Latitude 35.84152917

Galactic Longitude:

V'Ger is also speculated to have been on the far side of the galaxy, probably because of the direction that V'Ger came from. Assuming that V'ger might have passed by a Klingon ruled star that is within 60 degrees of galactic longitude zero, that Klingon ruled star must have a galactic longitude less than 60 or more than 300.

Stars within the correct galactic longitude range include:

Lacaille 9352

Galactic coordinates:
Longitude 5.10084457
Latitude -65.95703046

Ross 154

Galactic coordinates:
Longitude 11.30714980
Latitude -10.28446002

Ross 248

Galactic coordinates:
Longitude 17.49416953
Latitude 41.44265142

WISE 0855-0714.

Galactic coordinates:
Longitude 333.98582184
Latitude -5.53787476

Barnard's Star.

Galactic coordinates:
Longitude 31.29356328
Latitude 13.51255438

Alpha Centauri A, B, and C.

Galactic coordinates:
Longitude 316.07432269
Latitude -1.06580303

15 EZ Aquarii

Galactic coordinates:
Longitude 47.07120601
Latitude -56.97976513

Galactic latitude:

The direction that V;Ger comes from should also have a galactic latitude close to zero. If v'Ger comes from above or below the galactic plane it might be interpreted as coming from outside the galaxy instead of from the far side of the galaxy. Stars with galactic latitudes of less than plus or minus 13.775 degrees include:

Alpha Centauri A, B, and C.

Galactic coordinates:
Longitude 316.07432269
Latitude -1.06580303

Luhman 16 or WISE 1049-5319.

Galactic coordinates:
Longitude 285.59031100
Latitude 5.19686525

WISE 0855-0714.

Galactic coordinates:
Longitude 333.98582184
Latitude -5.53787476

61 Cygni

Galactic coordinates:
Longitude 82.31971192
Latitude -5.81797579

Sirius

Galactic coordinates:
Longitude 227.51693537
Latitude -8.43316571

Ross 154

Galactic coordinates:
Longitude 11.30714980
Latitude -10.28446002

Procyon

Galactic coordinates:
Longitude 213.70249473
Latitude 13.01923606

Barnard's Star.

Galactic coordinates:
Longitude 31.29356328
Latitude 13.51255438

Stars with galactic latitudes of less than plus or minus 38.471 degrees might be candidates, depending on their precise distances, but there aren't any in the group.

Conclusion:

The star that fits all three conditions is Ross 154,

However, at a distance of 5.980 light years or less from, Earth, the distance of Barnard's Star, a degree of arc would be 0.096342 light years. A sphere of Klingon space 2.8795512 to 3.3474784 light years in radius around Barnard's star would have a radius of 29.888 to 34.745 degrees of arc. Since Barnard's Star has a ecliptic latitude of 28.13150268 and a galactic latitude of 13.51255438 V'ger could pass within Klingon space around Barnard's Star from a direction with ecliptic and galactic latitudes near zero.

If the Enterprise in Star Trek: The Motion Picture traveled at warp factor seven on the TNG scale V'Ger might have fought the Klingons at a distance of 6.2438984 to 10.531393 light years from Earth while within a sphere of space claimed by the Klingons around Barnard's Star - 5.978 plus or minus 0.002 light years or 5.976 to 5.980 light years from Earth, or Ross 154 - Distance: 9.60 plus or minus 0.05 light years or 9.55 to 9.65 light years from Earth.

It may hurt my head and make me ask why, but a part of me also loves this and wants to see it on a map. My internal McCoy has the day off but faxed in a suggestion for analgesics.
 
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