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Star Trek: The Motion Picture mostly seems to take place in interstellar space, with brief stops at Vulcan, Earth and prolonged sequences aboard the Enterprise.

But where in interstellar space does V'Ger fight the Klingons? Where in interstellar space does the Enterprise intercept V'Ger?

  • The battle with the Klingons is said to be 'within Klingon boundaries' and is then plotted to be on a 'precise heading for Earth' - chakoteya.net/movies/movie1.html - somebody with a map and a ruler may be able to suss it out :) – NKCampbell Jan 30 '17 at 19:43
  • 3
    It happens... IN SPAAAAACE! – Xantec Jan 30 '17 at 20:01
8

The excellent Star Trek: Star Charts gives us the route taken by V'Ger through Klingon space and then into Federation space. The initial conflict with the Klingons seems to have taken place near to Khitomer, just inside the Federation/Klingon border, hence why the Epsilon Monitoring Station was able to detect the event.

V'ger then proceeded toward Earth, passing relatively close to Andoria and Vulcan, before finally encountering the Enterprise somewhere between Vulcan and Earth.

enter image description here

enter image description here

Red Arrow = Initial conflict with Klingons
Dark Green Arrow = Epsilon Stations
Lime Arrow = V'ger stopped by Enterprise.

  • 2
    Everything happens at or near Khitomer in the Star Trek universe, doesn't it? – CBredlow Jan 30 '17 at 21:41
  • 1
    @CBredlow - Most of Voyager doesn't. – Valorum Jan 30 '17 at 21:44
  • A map. I love it! – wogsland Feb 12 '17 at 1:54
-3

Part One of My Answer - MAGolding

Here I give a somewhat different answer than Valorum did.

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:

According to Star Trek: Deep Space Nine Technical Manual, (p. 3) the exact distance between Cardassia and Bajor was 5.25 light years.

https://www.google.com/webhp?sourceid=chrome-instant&ion=1&espv=2&ie=UTF-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:

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.

After the failed attempt to go to warp, Kirk says just minutes later:

KIRK: That object out there is less than two days from Earth.

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:

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.

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:

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.

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.

[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.

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... ..KIRK: Viewer off. ...Pre-launch countdown will commence in forty minutes.

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 was an hour 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 reached 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 when V'Ger was 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 rebalencing 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:

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.

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.

10) The Total Distance of V'Ger's Voyage

Nobody can tell the total distance V'Ger traveled, but there are clues.

KIRK: V-G-E-R ...V-O-Y-A-G-E-R ...Voyager! ...Voyager VI?

DECKER: ...this was launched more than three hundred years ago....disappeared into what they used to call a black hole.

KIRK: It must have emerged sometime on the far side of the Galaxy and fell into the machine's planet's gravitational field.

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.

So having established distance ranges for the various events in Star Trek: The Motion Picture the direction may possibly be deduced.

  • 6
    ....there's a lot of information here, and it's kind of interesting, but I'm not sure if it's an actual answer – NKCampbell Jan 31 '17 at 2:03
  • NKCampbell - from the data given in the movie I have deduced what should be the possible distance ranges for various events in the movie. Thus answers that put events in the movie at much greater distances from Earth are likely to be inaccurate. – M. A. Golding Jan 31 '17 at 18:32
  • 1
    Is all this information really necessary? Is there any way to shorten it to one post? Splitting an answer into three posts makes it difficult to understand what you're trying to say, especially since the three answers will not appear in your intended order due to voting. – Null Mar 9 '17 at 16:01
  • @Null - I've downvoted and voted to delete all three. Although I'm sure there's an answer in here somewhere, I'm blowed if I can find it. – Valorum Apr 30 '17 at 16:56
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    @Null can you delete at least two of these? Attempting a multi-part answer like this is an abuse of the Stack Exchange format, and makes voting on the answer difficult. It costs 3 times as much rep to vote on it, and then the serial-voting script might reverse it anyway. – Molag Bal Apr 30 '17 at 17:06
-3

Part Two of My Answer - MAGolding

In Part One of my answer I showed the probable relative speeds of the Enterprise and V'Ger and deduced the distance from Earth that various events happen if the Enterprise traveled at various speeds.

for example:

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.

There are five stars systems that V'Ger might have been near when it fought the Klingons if that battle was when Spock started his journey from Vulcan to Earth.

Note that in this scenario the Federation border seems to be 1.5053092 to 1.749922 light years from Earth. If the Klingons claim a sphere 1.5053092 to 1.749922 light years in radius around each star system in their Empire, V'Ger could have to pass closer than 1.5053092 to 1.749922 light years from some Klingon claimed star system.

I didn't find any star systems that precisely fit the requirements, but Barnard's Star and WISE 0855-0714 might possibly fit a somewhat relaxed set of requirements.

Candidate 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).

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

Ecliptic Latitude:

When the Enterprise leaves Earth and zooms off into outer space it passes 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 14.112 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.

Galactic Longitude:

And when they discover that V'Ger was Voyager VI Kirk says:

KIRK: It must have emerged sometime on the far side of the Galaxy and fell into the machine's planet's gravitational field 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 plane 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.

Galactic Latitude:

If V'Ger came from a direction above or below the galactic plane they might think that it came from another galaxy instead of from the far side of our galaxy.

And in their order of closeness to the galactic plane and galactic latitude zero:

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 14.112 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.

Conclusion:

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 a distant part of the galaxy along the galactic plane and pass close by them. But Wolf 359 is too far from the galactic plane.

So if the Klingons claim a sphere with a radius of 1.5053092 to 1.749922 light years around each star in their empire, 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.

But maybe the Klingons claim a sphere with a greater radius around each star in their realm than the Federation does.

Or maybe the Federation claims a wider radius than 1.5053092 to 1.749922 light years around each star. Possibly V'Ger crossed the Federation border hours or days before it passed close enough to Epsilon IX to detect and attack it. Thus the Federation border might be farther from Earth than calculated and the Klingon border might be farther from each Klingon star than calculated.

If each realm claims a sphere with a radius of 3 light years around each star, for example, Barnard's Star and WISE 0855-0714 might both be close enough to the ecliptic plane, the galactic center, and the galactic plane to qualify.

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.

-4

Part Three of my Answer - MAGolding

In the first part of my answer I listed the distances from Earth of various events in Star Trek: The Motion Picture 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.

Candidate Stars:

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 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 could the Klingon star passed by V'Ger 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 way 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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