I was somewhat curious about this, how often did the IISS need to update the star charts. I found this paper describing how fast, in general, stars in the local space were moving relative to each other. According to the paper stars have an average radial velocity of 13.1 ± 11.1 km/sec. Radial velocity means either toward or away from the Sol system. Smaller (M, G, K) stars are moving faster than larger (F, A) stars.
To move a star one hex closer or farther away requires covering about 1/2 a parsec. At this velocity it takes (on average) 0.5 parsecs * 3.08e13 km / parsec ÷ 13.1 km / sec ÷ 3.15e7 sec / year = 37,320 years to cross the distance.
Take the 50 closest stars to a given target, this is, on average stellar density, the stars in an area a little larger than a subsector. Given a random distribution, one star should change hex position relative to Sol every 746 years.
The one problem this this analysis is it considers only radial velocity (away or toward Sol). And the stars would have a transverse (side to side) component to their velocity as as well. I think, since the original calculation multiplied the velocity vector by the sine of the angle between the star's vector and the radial vector, we now need to divide the vector by the sine of the angle to return to the full velocity.
Since we have not measured the velocity (and angle) of each star relative to Reference we have to assume the average is 45°. This would give an average velocity of 18.5 km/sec. So 0.5 parsecs * 3.08e13 km /parsec ÷ 18.5 km/sec ÷ 3.15e7 sec/year = 26,426 years per parsec. Or about 528 years per change for the 50 stars in the local space.
To expand this larger area there are two ways to consider this. First would be how often stars move relative to Reference, the center of the Imperium. For 9000 stars this would be one star changing position every 3 years.
But the stars are not moving just relative to Reference, but to each other as well.
1225 pairs of stars in the local space (50 stars), each having a 1 in 26426 chance of changing position per year,for an overall 0.04529 chance of a star changing position every year or about 1 every 22 years. Across the (about) 300 subsectors in the Third Imperium, this ends up with 13.6 stars per year, or a little more than one per month.
This assumes a 1 to 1 mapping between real space and the destinations of jump space. This is strongly implied by the description of jump distances, but not by the astrography of the real stars.
To move a star one hex closer or farther away requires covering about 1/2 a parsec. At this velocity it takes (on average) 0.5 parsecs * 3.08e13 km / parsec ÷ 13.1 km / sec ÷ 3.15e7 sec / year = 37,320 years to cross the distance.
Take the 50 closest stars to a given target, this is, on average stellar density, the stars in an area a little larger than a subsector. Given a random distribution, one star should change hex position relative to Sol every 746 years.
The one problem this this analysis is it considers only radial velocity (away or toward Sol). And the stars would have a transverse (side to side) component to their velocity as as well. I think, since the original calculation multiplied the velocity vector by the sine of the angle between the star's vector and the radial vector, we now need to divide the vector by the sine of the angle to return to the full velocity.
Since we have not measured the velocity (and angle) of each star relative to Reference we have to assume the average is 45°. This would give an average velocity of 18.5 km/sec. So 0.5 parsecs * 3.08e13 km /parsec ÷ 18.5 km/sec ÷ 3.15e7 sec/year = 26,426 years per parsec. Or about 528 years per change for the 50 stars in the local space.
To expand this larger area there are two ways to consider this. First would be how often stars move relative to Reference, the center of the Imperium. For 9000 stars this would be one star changing position every 3 years.
But the stars are not moving just relative to Reference, but to each other as well.
1225 pairs of stars in the local space (50 stars), each having a 1 in 26426 chance of changing position per year,for an overall 0.04529 chance of a star changing position every year or about 1 every 22 years. Across the (about) 300 subsectors in the Third Imperium, this ends up with 13.6 stars per year, or a little more than one per month.
This assumes a 1 to 1 mapping between real space and the destinations of jump space. This is strongly implied by the description of jump distances, but not by the astrography of the real stars.