How would political borders work in space? I'm currently treating interplanetary space as ocean and planets as landmasses. A polity has complete sovereignty over their planet and its gravity well. For large planets, the space occupied by the planet's orbit is also considered an exclusive economic zone. foreign entities may travel freely through this zone, but may not exploit resources found there or set up permanent orbital colonies there.
I suppose I'd have to look at what a polity is capable of defending militarily, since practically you can only keep what you're capable of defending from rivals. A planet's surface and gravity well are easily defensible, but I'm not sure about the entire orbit. Planets move around relative to each other.
The yinrih are also quite fond of building massive spaceborn archologies that are nations unto themselves, though they are much smaller than planets and don't have a significant gravity well.
There are two polities that require special consideration, The Spacer Confederacy and Partisan Territory. Both are collections of these spaceborn archologies occupying resource-rich asteroid belts[^1].
The Spacer Confederacy is a loose collection of independent city-states that somehow hate each other just little enough to form a federal council and police force to protect the common interests of the inner belt. Partisan Territory occupies the Outer Belt and has a totalitarian system of government.
Here's story that explains a bit of how the Spacer Confederacy works. I'm not sure how viable such a system is, but if it doesn't work, I'm hoping it "doesn't work" in a way that allows for more interesting worldbuilding rather than just being stupid.
spoiler
"And you're the interim chief?" asked the federal councilman, his voice echoing throughout the cavernous main axis of the newly constructed colony.
"That's correct." said Graypelt.
"Gentlemen, my dame," the councilman addressed the pair of envoys from the Allied Worlds along with the hearthkeeper floating by their side. "Would you allow Graypelt and I a moment alone?" He moved toward the docking port where a shuttle was stationed, beckoning Graypelt to follow.
Graypelt started as the inside airlock door shut behind him. The federal councilman had floated across the threshold of the airlock separating the colony's hull from his docked shuttle craft.
"Why did you shut--" Graypelt began, but the councilman raised a paw to silence him.
"What did the envoys from the Allied Worlds tell you about the Spacer Confederacy?" he asked.
"The laws are few, but the penalty for transgressing them is severe."
"So far, so good," said the councilman, "and what are those laws?"
Graypelt thought for a moment, then began ticking off items on his claws. "Each colony gets one perch on the federal council. The council is responsible for assigning asteroids for colonies to mine. The council levies a tax of twelve per gross on all revenue earned through the sail of the minerals. Colonies may only mine the body they have been assigned. There's a six year mandatory conscription into the federal police for all eligible males upon reaching the age of majority. Any interaction between colonies within the Confederacy must be mediated by the council."
The councilman tilted his muzzle up in affirmation. "Now let me tell you what those glossy-pelted stooges from the AW won't. We get all sorts of kooks coming here to the Inner Belt looking to set up half baked social experiments or off the wall cults."
"We're not--" Graypelt objected, but the councilman raised his paw again and resumed his lecture.
"Everyone comes here for their own reasons. We have about as many world views, ideologies, belief systems, conceptual frameworks, religions, whatever you want to call them, as there are colonies in the Confederacy. But there's one thing we all value. What do you suppose that is?"
"Uh--" Graypelt began, but the councilman cut him off again.
"Freedom!" he barked. "You want to start a gel head parlor? Go ahead. You want to run a tree-dweller baiting ring? Be my guest. Wanna start making mind candy?" He flicked his left ear back, leaned forward, and whispered, "I'll even give you the name of a supplier."
He slapped the inner hull of the colony with a rear paw. "Whatever you do inside these walls is your own business. But if you so much as stick a whisker outside with whatever nonsense you get up to, then that becomes our problem." he tossed his muzzle back, toward the federal shuttle behind him. "And you do not want the federal police paying you a visit."
"Is that a threat?" Graypelt stammered.
"A warning." The councilman leaned forward, running a claw across a scar on his muzzle.
"I thought this was--" Graypelt once again failed to get a word in edgewise.
"Anarchy? A free for all? A libertarian paradise? Everyone always assumes the Inner Belt is a lawless frontier where they can get away with anything, and you know what? Your roof, your rules, but out there, outside these walls, you're under OUR roof. If you mind your own business, keep your nose prints off of other peoples' windows, you'll be fine. But if you mess around, you will find out.
"Do you think we keep this confederacy together with a bunch of ink on paper?" The councilman made a show of examining the iron-red claws on his left forepaw. "Within a three-day ferry trip from here there are a bunch of Misotheists who would kill every last one of you hearth lickers, pups and all, if they thought they could get away with it. The only reason they won't is that they know exactly what will happen to them if they even try." He pantomimed an explosion with his forepaws.
"You folks wanted freedom, and you've got it, but freedom isn't free."
The councilman pulled the release for the interior airlock door with his tail. He began floating into his shuttle, adopting a cheerful tone for his parting words. "On behalf of the Federal Council, I'd like to welcome you and the citizens of Wayferers' Haven to the Spacer Confederacy."
[^1]: Yes I know the IRL asteroid belt has a tiny amount of total mass, but this is my world, dang it!
I think you need to keep mind how borders are enforced. Each political entity wants all the resources under their control, but since all political entities want the same limited resources, they have to fight for them. Depending on the scarcity of resources and the efficiency of each economy, each entity will reserve a different amount of resources to their military, which will then determine how far out their territory can reach.
A good model for territory (assuming all space is equally valuable and equally as hard to defend) are weighted voronoi graphs. Essentially, the power of a military decreases as you move further from the capital, and the borders are drawn where two opposing militaries have equal power. (i.e. a stable equilibrium point) If one of the militaries manage to push past this equilibrium point, the opposing military will become stronger due to being closer to the capital, and will push the border back to where it was.
Now, reality is significantly more complex than this simple model, especially due to the sparsity of resources in space, so a resource-point based model is going to more accurate than a resource-area based model.
In a resource point model, there are two big aspects you need to consider: surface curvature and caravan routes. If you imagine territory as a 3d object rather than a 2d one, then the surface of that object becomes the borders of the territory. If you imagine a sphere around a planet, that planet can be attacked from six different sides. If instead the planet was located in a sphere centered on the sun, the planet could only be attacked from one side. The difference between these two scenarios is how much the surface of the territory curves.
When you take into account caravan routes, the optimal shape for a territory reaching out to a resource is a shallow cone with the base centered around the capital.
TLDR; the best borders for a political entity is a spiky ball.
That was very helpful thank you.