Think about what your galaxy spanning civilisation needs
Contrary to popular belief, stars and galaxy arms are independent.
That is, that spiral arms are constantly changing density variations that the stars move through - the stars are actually orbiting the centre of the galaxy at a separate rate the arms do. This is still a mystery as to why for astrophysicists, but there are some theories out there as to the reasons to be confirmed by more observations.
This animation demonstrates that stars and arms do not orbit the centre of the galaxy together:Image may be NSFW.
Clik here to view.
This means your coordinate system should not be able to reference arms, for instance to get to a certain star, as to track a star over a period or even to find out where that star had been, would not be possible. A star would obviously change arm over millions of years, but even over a 1000 years this would cause a complex problem referencing between arms and for a galaxy spanning civilisation this will still make plotting of stars difficult.
Instead I would recommend a simpler Polar Coordinate system measured around the perpendicular axis to the galactic plane, with the 'North' direction a fixed normalised direction to a nearby galaxy. Although this too changes, the time-span for shifting of this direction would be billions of years, not millions as per the arms, so would be far more useful to a galactic spanning civilisation. If not for navigation, perhaps culturally or scientifically.
Plotting the position of the star historically in relation to this would then need a time-index and a computation model of a galaxy.
So your coordinate system would be:This Galaxy, Nearby Galaxy, Polar Angle from Normalised angle, Distance from Centre, Time Index (if referencing a star, not needed otherwise) to be safe measured from the Big Bang. This way you can then plot a course to or from this point at any time.
So it may look like this:
- Coordinate of Sirius Star = Milky Way, Andromeda, 31.252º, 16832LY, 13.451Y
Or you can omit the first 2 coordinates for 'common parlance':
- Coordinate of Sirius Star in the Milky Way = 31.252º, 16832LY, 13.451Y
And you could leave out the time index if you wanted a fixed point at the precise moment of coordinate generation:
- Coordinate to the current position of Sirius Star in the Milky Way = 31.252º, 16832LY
