First, one must begin at the beginning. For my purposes, the beginning is in figuring Earth's position within the galaxy. Since it is nearly universally agreed that Earth lies on the Alpha/Beta border, I put it there. That takes care of Earth's X-Coordinate (X = 0). As for the Y-Coordinate (Distance from the galactic core), I took it to be -22500. This is for several reasons:1. Originally, I had figured Earth to be at -32500. It was just easy to add 10000 to it.
2. Scientifically, I have read Earth was 23000 ly from the galactic core. At the time, the Beta Quadrant problem had already reared its ugly head, so I decided to be nice and give the writers a 500 ly leeway.
3. As will be revealed below, this provided a very nice equation for Voyager's route home.
Earth's position now established, the figuring of Voyager's original distance came next. Canonically, two different distances have been given for the Ocampa-Earth distance, these being 70000 ly and 75000 ly. For my calculations, I have chosen to use the 70000 ly distance. "Why?" you may ask? Simple. A 75000 ly-radius circle centered on Earth does not intersect the galaxy. Earth would have to be 25000 ly from the galactic core just for the circle to touch the edge of the galaxy, at the intersection of the Delta/Gamma border and the galactic edge. A 70000 ly-radius circle is the only one that works.
Distance established, Voyager's direction came next. I had at my disposal three possible vectors:
1. The vector given in the DS9TM.
2. The vector given in "Message in a Bottle." Janeway rattles off a set of coordinates in attempting to communicate with the Prometheus. Ignoring the strange third coordinate (which I believe was established here at the Forums to be some sort of distance unit), it provided another logical course for the ship. However, this was a roughly calculated vector, as the exact position of the Prometheus was unknown.
3. The vector given in a map that came with a 30th Anniversary Star Trek Magazine I purchased. Although its position of Earth was clearly wrong, it did provide the location of the Delta Quadrant terminus of the Barzan Wormhole, which we know was along Voyager's path.
In comparing all three vectors, Vector #3 happened to be very nearly the average of Vector #1 and Vector #2. Therefore, I used it. This provided a very nice equation of 4.2X - 22500 for Voyager's route.
Now that the route itself had been established, Voyager's speed along that route came next. "Pathfinder" gives Voyager's average speed as Warp 6.2, or about 437.8c. However, this was not its original speed, because of Janeway's avoidance of the Borg after "Scorpion" (+2 years) and the effectiveness of the new astrometrics lab (-5 years) Therefore, Voyager's speed during the different time periods are as follows:
"Caretaker" - "Scorpion, Part 2" : 428.3269963c
"Scorpion, Part 2" - "Year of Hell, Part 1" : 422.2323796c
"Year of Hell, Part 1" and afterwards : 437.8301166c (Warp 6.2)
However, this is Voyager's average speed, factoring in all the stops they make. Voyager's true speed between stops was established in "Caretaker" as being 933.3333333c (70000 ly in 75 years). Taking into account the Borg avoidance and astrometrics lab, this becomes 954.0408278c after "Year of Hell." This larger "no-stop" speed appears to be the speed used in figuring how much time each jump has taken off their trip.
Therefore, Voyager's distance covered at normal warp (as of "The Voyager Conspiracy") is:
(.4283269963)(51003.7 - 48315.6) + (.4222323796)(51212.3 - 51003.7) + (.4378301166)(53329.0 - 51212.3)
This works out to 2166.218481 ly.
The jumps must then be added in:
9500 ly ("The Gift," Kes' last gift, distance specifically given.)
300 ly ("Hope and Fear," slipstream drive, distance specifically given.)
2500 ly ("Night," spatial vortex, distance specifically given.)
9540.408278 ("Timeless," slipstream drive, 10 years at 954.0408278c.)
20000 ly ("Dark Frontier," transwarp drive, distance specifically given.)
200 ly ("Dragon's Teeth," subspace conduits, distance specifically given.)
600 ly ("The Voyager Conspiracy," catapult, 30 sectors at 20 ly/sector.)
So, as of "The Voyager Conspiracy," the ship has travelled 44806.62676 ly, and has 25193.37324 ly left to go.
Finding the intersection of a circle 25193.37324 ly in radius centered on Earth and the aforementioned path Y = 4.2X - 22500, one finds Voyager's position to be:
X = 5835.3024
Y = 2008.2701
This would mean that Voyager's distance from the Beta Quadrant is 2071.563388 ly.
The End.
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"We exist in a boundless time continuum. There is no weekend!"
- Zorak, "Hungry," Space Ghost: Coast to Coast.