wondering what are the limits for power projection for worlds and polities of different sizes. How many parsecs away would an individual world, pocket empire, or Imperium-sized entity be able to make its presence known economically and militarily?
Economically, you need to have commercially viable ship designs capable of turning a profit when "making the rounds" away from a home port. The simplest rule of thumb is going to be 12J* for a 12 jumps out/12 jumps back kind of range.
- If you've only got J1, then that's 12 parsecs out and back.
- If you've got J2, then you can manage up to 24 parsecs out and back.
- With J3, you can manage up to 36 parsecs out and back ... although being able to make a profit on J3 gets difficult on passengers and cargo freight alone (but speculative goods trading can become extremely profitable with J3 because of "reach").
Point being that 24-25 jumps per year at a "1 jump per 2 weeks" operational tempo is just about as far as you can go in a single year before needing annual overhaul maintenance. If there's only ONE (singular) place that can be your home port and provide that service, you're kind of "stuck" being tethered to that one location, so how far you can jump in a year (and get back in time for maintenance) pretty much defines the radius of influence for a single world economically (in overly simplified terms).
However, once you have multiple worlds and can start chaining things together, you can start building up links in a much longer chain. You still have a "weakest link" problem when moving passengers and goods along that chain, but so long as different sections can link up together at common points, you can leapfrog your way to larger reach and longer distances of influence. But you need to have those "local centers of economic gravity" to move between to build out your network.
Militarily speaking, it's going to be substantially the same thing ... except you're looking at needing to look at military bases as the logistical support structure. In some ways, however, you may want to think of the military "radius of action/influence" as being reduced relative to the economic radius, simply as a matter of military operations potentially needing more time to complete their mission objectives than a mere "1 week" at the destination. If you're looking at a patrol rotation scenario, you might be looking at 2/3 to 1/2 the radius of action from the nearest military base (so basically up to 6 jumps) rather than the more expansive 12 jumps that a merchant operation would be undertaking. However, military bases can potentially be located more strategically than high tech worlds with type A starports, so the constraints are similar but different.
What's the minimum population size/industry concentration/tech level that a world would need to begin to form an embryonic pocket empire?
Population: 7 minimum (because 6 is Non-industrial), but a more reasonable number would be 8, although 9-A is even better.
Agricultural+Rich worlds would be particularly well suited as the starting point for embryonic pocket empires.
Tech Level: 9 minimum but A makes for a decent starting point (especially if using LBB2 standard drives for starships).
Homeworld had better have Atmosphere: 5, 6 or 8 for the "cradle of civilization" that colonizes outwards.
Being on a J1 main makes it SO MUCH EASIER to start exploration and expansion @ TL=9-A. By TL=B-C you can build up some pretty sizeable reach in terms of spheres of influence, just with J2-3.
societal factors might effect the outcome the most?
Merchant vs military.
Military might can conquer, but it cannot necessarily BIND a conquest into a hegemony.
The enduring way to build an empire that can hold the center against the centrifuge is going to be through economic trade and cultural ties.
I can even offer proof of these assertions that readers of these forums may recognize.