I should point out that I am thinking of the needs to define what is the galaxy for the purposes of political or navigational maps, defining matters like sovereignty over whatever resources might be in an area, or providing for the safe and efficient carrying of things between points.
Yes, but a starfaring power would learn to define those things based on parameters that make sense in space, rather than clinging to ancient planetbound conceits about how to define borders. It would be unreasonable not to adapt to new circumstances.
And, yes, I'm ignoring dark matter. My supposition is that the Federation would be primarily interested in planets --- stuff you could live on, or at least harvest useful resources from --- and the stars which support life on them. If dark matter has some application besides making the starship Voyager's day more difficult, perhaps they'd want to include regions of useful dark matter within the political or navigational boundary.
The point is that the galaxy includes its halo, which contains plenty of stars and globular clusters, even aside from the dark matter. It's not just the disk and the bulge. So whatever you'd define as an "edge" for the entire galaxy would have to be well beyond the edge of the disk, and that doesn't fit the episode, because it would be prohibitively far for the
Enterprise to reach (let alone the
Valiant) and because they would've already had to pass through a great deal of mostly empty space to get there.
A star orbiting the galaxy can be expected to take something like a half-billion years to make the journey. A status of 'inside' or 'outside' the defined bounds of the galaxy that has to be updated approximately once every 250 million years is a problem akin to the need to redraw state boundaries --- which are often tied to latitude or longitude --- to reflect continental drift. (Yes, I'm aware this is potentially multiplied by the number of stars drifting across that boundary. It's still going to be a minor problem. If there were an annoying number of stars crossing the radial 'line' every year they'd set the line farther out.)
Actually it wouldn't be a minor problem if you were concerned with reaching a specific star. The orbital velocity of disk stars ranges from about 50 to 200 kilometers per second, meaning that they change position by maybe about 10-40 astronomical units per year. In space, you can't afford to aim just kinda sorta for where something is; you have to target it precisely, or you'll end up wasting fuel to correct your course -- fuel you probably can't afford to waste if you've traveled all the way to the edge of the galaxy. So you can't afford to get by with old maps.
And the dynamical-systems-based definition you want to use offers obvious problems for political or navigational maps of the galaxy. I'm sure you've thought of at least three problematic but plausible cases.
Why does it offer problems? We're talking about civilizations capable of interstellar travel. For them, a map wouldn't be a bunch of lines drawn on parchment. It would be a computer model, and there's no reason it couldn't be programmed to be dynamic and adaptive. Indeed, it would have to be. Any interstellar civilization would've had to start out as an interplanetary civilization, and since the relative positions of planets, moons, and asteroids within a star system change on a daily basis, the kind of fixed, unchanging maps we use on Earth would be laughably obsolete the moment a civilization started settling its own star system. Any navigational aid used in space must be dynamic and able to change over time. Even the earliest orbital capsules had such instruments. The
"Globus" instruments used by the Soviet and Russian space programs were based on a physical globe of the Earth, but one that constantly rotated within the instrument to plot the capsule's ever-changing position. Change over time was an integral component of the "map." Good grief, even today we use computerized, regularly updated GPS maps more than we use static, unchanging paper maps.
So any spacefaring civilization would've gotten used to 4-dimensional navigational reference tools -- i.e. ones that plot positions in 3 dimensions and changes of position over time -- long before it ever achieved interstellar flight. It would've gotten used to thinking of navigation in terms of converging with a given vector rather than reaching a given point. That's the only way you can navigate in space, because there's no such thing as standing still in space. So naturally any starfaring civilization's galaxy map would be based on orbital vectors and parameters rather than fixed coordinates.
And territorial boundaries would thus have to be defined in the same way. They wouldn't be static borders in empty space, except perhaps as a very rough and unofficial approximation. I tend to think that political boundaries would be defined based on the star systems held by a given power. The territory belonging to a star or planet would probably be defined as its
Hill sphere, the region in which its gravitational influence over satellites dominates over the gravitational influence of other bodies. I trust the political analogy is self-evident. The territory of an interstellar power would probably encompass the Hill spheres of all the stars and rogue planets it governs or occupies, plus the established and patrolled travel routes between those systems. It would be more a bunch of individual dots connected by thin branches than a big contiguous blob. And of course their positions relative to one another would be shifting by an astronomically small but navigationally significant degree every year, so the computer maps would have every object's orbital parameters built in and would always give their current positions.
In this formulation, the "territory" of the Milky Way galaxy might include everything within its Hill sphere. But from what I can tell, that's a radius on the order of a million light-years, maybe a third of the way to the Andromeda galaxy.
Are you setting the update in the same time period?
