So I'm writing a sci-fi space opera that takes place at a pretty realistic scale meaning even pretty small interstellar nations have millions of systems and the biggest ones have billions of systems under their control.

Although, most of these systems are pretty sparsely populated. In most systems, the population rarely goes over around 10 million so you could think of them as being like villages. There are quite a few systems with populations around 1 billion and you could think of these as towns and a few systems, probably less than a 1,000 even in a large empire, are like cities and have populations around 10 billion or more.

So, with that in mind, how big would a nations' navy need to be to fight nations of similar size? Technologically most nations are very advanced given that the story is set 1,600 years from now. The average ship could blow up a planet by itself but that's a war crime and kinda pointless so nobody does it. Fighters are used pretty heavily as well. Resources and manpower aren't an issue given how many systems even small nations have. It's not meant to be particularly realistic either.

Forgive me if I'm being an idiot but it seems like they'd need tens of thousands if not hundreds of thousands of ships. The Galactic Empire in Star Wars had 25,000 Star Destroyers and god knows how many smaller ships and only had a million planets or so so when you're talking a billion systems, not even just planets, it just seems to get pretty ridiculous. At the scale my story is at it seems like it'd be pretty common to have army sized fleets with thousands of ships in them.

But then again there are the little rural systems. I'm really not sure how they would factor into things. Would nobody bother with them in a war or would they all have to be conquered as well?

Please let me know if there's anything I need to add to my question because this is the first time I've asked a question on this site so I've probably made a few dumb mistakes.

EDIT: Sorry, I should have mentioned that the setting has access to FTL in the form of warp drives. Most ships with a warp drive can travel around 50 light-years per day and it's extremely safe. They also have instantaneous FTL communications

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    $\begingroup$ Do you have FTL travel? If not, controlling a lightyears-spanning empire is pretty much a non-starter. Entire systems will have seceded hundreds of years before news even reaches the capital - there's no way to keep contemporaneous control over such distant locales. $\endgroup$ Feb 17 '21 at 16:01
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    $\begingroup$ You will need instantaneous communications to maintain an economy spanning multiple hundreds of light years. Being paid tens of years after the transaction just can not sustain any form of economic activity. Otherwise, fraud would be your biggest enemy, not physical fighting. But it begs the question be asked, 'What would the point of military aggression be?" With that much expansion room in each 'empire'. it would not be for economic reasons. Pirates would be the biggest problem, methinks, and that is a policing issue, not a military concern. $\endgroup$ Feb 17 '21 at 16:51
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    $\begingroup$ There is really insufficient info to answer this. The question has to be answered the same way in the real world: what does space combat and interstellar war look like and what does the space navy need to do win a war against it's opponents? The fleet can't be big enough to defend every planet, so what is its strategy? For example, you navy might just be 95% space fortresses around important planets, numerous small patrol ships for handling emergencies and delivering mail for undefended worlds, and only a small handful of large fleets to attack enemy strongpoints. $\endgroup$ Feb 17 '21 at 17:06
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    $\begingroup$ "Fighters are used pretty heavily as well" doesn't gel very well with "technologically advanced", but it goes very nicely with the "we wanted to created WW1 in spaaaace" aesthetic that star wars went with. Given the implied heavy reliance on magic and "rule of cool", why not just pull a number out of thin air that fits how you want your setting to feel, or better yet just not mention numbers at all? $\endgroup$ Feb 17 '21 at 18:08
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    $\begingroup$ Continue Starfish Prime comment - pull a big number to be cool, u have a million system - then there is at least one patrol ship, so u need million of those and probably a fleet perr system - just to raise train and guard alarm first response police recon, etc - so a 100-1000 ships bare minimum. And u can draw them in a fight if u need, so u already start with a billion ships, but it more like ordinary border control police duties and reserve so main forces are at least on par with that maybe a few times bigger more war-focused. So a billion is the start number for the small fraction. $\endgroup$
    – MolbOrg
    Feb 17 '21 at 18:20

I'm going to assume that you have FTL. As pointed out in the comments, there's no such thing as an interstellar empire of any significant size without it. To avoid giving myself migranes, I'll assume that you've come up with some method of avoiding time travel problems that doesn't do anything too weird to anything I say.

A lot, however, depends on how fast that FTL is (again, ignoring how little sense that makes), and whether you have FTL communications as well as FTL travel: if you can get from anywhere in the empire to anywhere else in the empire essentially instantly and have FTL communications, then you need one fleet (be that one absurd ship or a bunch of less powerful ones) sufficiently powerful to defeat any plausible threat, which you have cruise around doing "look how cool our ships are" missions around the empire (either together or separately), then when you're attacked, just jump them to wherever the threat is, fight the battle, and go back to your business.

This of course has the issue of potentially causing arms races (after all, if you have a fleet that can defeat any plausible threat, then anybody to whom you are a plausible threat necessarily doesn't have any such fleet, because they can't defeat your fleet), which you can either (a) jump into with merry disregard for how bad an idea arms races are, or (b) apply diplomatic means, such as mutually agreeing with your neighbours to limit the growth of your military capacity (and then inevitably proceeding to work loopholes into the treaties (cough Standard Displacement cough)/apply creative interpretations to the limits (looking at you, 1920s America)/straight up lying about your military development (glares at a Japanese "light" carrier). Either way, plenty of fodder for interesting stuff to happen.

In this scenario, though, there's essentially no point having a reserve force that isn't kept at full active readiness - the enemy will inevitably find out where they're hidden, and with ships this fast, they'll be annihilated before they're out of the docks. You might also want to make sure your active fleet isn't just one massive ship even if that would be optimal (unless you are personally commanding it), because in situations where the people in charge of a state and the people in charge of its military are not the same people, that situation tends to correct itself rather dramatically.

On the other hand, if it takes months to get to the furthest-flung corners of your empire, you need separate fleets in any area of the perimeter where a threat could plausibly come from, plus some fleets hanging around nearby any systems in the interior that might need reminding of their loyalties. You probably also want a powerful reserve force kept somewhere central-ish (or, depending on size, several such scattered around the place), so that (a) if an initial fight goes badly, you get a second go at it without losing too much of the empire first, and (b) if some admiral out on the frontier starts thinking that they would make either a great independent warlord or could do your job better than you, you can correct them, rather than having to hope that some other admirals coming in from the perimeter can get to you in time to stop said uppitty admiral starting a full-scale civil war by killing you. For the latter purpose, this home fleet should ideally be two fleets, both kept within striking distance of the capital, under commanders who dislike each other.

In this case, the number of ships required is less a function of how many systems there are than how far apart they are (in terms of travel time) and how good you are at spotting enemy fleets coming: If the gap between where you'd expect to see an enemy attack coming and the attack hitting a system, you better have something capable of dealing with that attack within $X$ days travel of that system (where "detection" includes any delays involved in communicating that detection to the fleet). Assuming reasonable foreign policy, you can probably get away with not having significant military presences on most of your borders (Canada does not invest much effort into defending its US border these days), instead relying on (a) not being attacked there, and (b) if you do get attacked, just letting the attackers take some border systems while one of other fleets heads over there to fix the issue). In heavily contested areas, you might need every system having a significant force, if it's not being treated as sacrificial in the case of war (which I don't expect the population would be overly happy about).

If your empire is roughly a sphere of travel-time radius $R$ (this is the one that gives you the most stuff per travel time, and travel time is going to be the upper limit on how big your empire is), then you have a border of area $4\pi R^2$. A circle of travel-time radius $T$ covers an area of $\pi T^2$ of that border (actually, slightly more, because of the curvature, but that's a rounding error). How much overlap you get is hard (in the sense of being an open problem even for fairly small numbers of overlapping circles), but let's get an upper bound and say it's about 25% overlap (there's a known solution with 26% overlap for 132 circles, and I'm guessing we'll be well beyond that - overlap goes up as the number of circles does). With that, the effective area coverage is more like $\dfrac{3\pi T^2}{4}$ (again, slightly higher, but whatever, it's not like they'll be perfectly arranged), so you need about $\dfrac{16R^2}{3T^2}$. If, say, your empire is a year in radius (that seems like a lot to me) and you want to be able to get to anywhere around the border in a week (that seems like not a lot to me, we have $\dfrac{R}{T} \approx 50$, so you need about $50^2 \times 16/3 \approx 13,000$ border protection fleets). You probably don't need to defend anything like all of your border that heavily, though, so treat that as a loose upper bound.

If you want to cover the interior similarly (though presumably at much lower densities), then the volume of your empire is $\frac{4}{3}\pi R^3$, and each fleet covers a sphere of volume $\frac{4}{3}\pi T^3$. An upper bound on the optimal packing density for such spheres (on any size of sphere) is $\dfrac{5\sqrt{5}\pi}{24} \approx 1.46$ (so with about 46% overlap, though I expect the actual answer is lower), meaning that you'll need about $\frac{1.85R^3}{T^3}$ interior defence fleets, which, for the empire above, with a 1 month response time, is about 3,200 fleets.

Some other comments on your question:

The average ship could blow up a planet by itself but that's a war crime and kinda pointless so nobody does it.

  1. Something being a war crime has never stopped any military from doing it when it's to their advantage. Anybody willing to declare a war between such large polities is already willing to allow for vast numbers of deaths to get what they want, so blowing up a few planets is a rounding error, if not something they can justify (at least internally) as actively saving lives.
  2. Destroying your enemy's economic base is the exact opposite of "pointless". It's how you win wars. If you don't have enough time for a long, messy ground campaign to get control of a population, and you don't have the precision to just knock out all of their ability to get off the planet any time soon, leaving them behind you is leaving behind a potential threat.

Your setup (or at least, people in some empire believing that this is how the world is set up) isn't implausible because of this, but it is unstable: the moment some large-ish polity has someone ambitious and not particularly bound by conventional morality come to power, it's going to be smashed to pieces by a blitzkrieg on an almost unimaginable scale.

Forgive me if I'm being an idiot but it seems like they'd need tens of thousands if not hundreds of thousands of ships. The Galactic Empire in Star Wars had 25,000 Star Destroyers and god knows how many smaller ships and only had a million planets or so so when you're talking a billion systems, not even just planets, it just seems to get pretty ridiculous. At the scale my story is at it seems like it'd be pretty common to have army sized fleets with thousands of ships in them.

The reasons for splitting your ships up are:

  1. Building ships too big hits some annoying physics problems due to gravity and water/air resistance. This isn't an issue in space.
  2. Allowing you to rearrange your fleets in smaller units. This doesn't really scale much with size of empire beyond a certain point: there's only so much rearrangement that's practical and useful.
  3. Redundancy: if you're operating at that scale, smaller ships just aren't relevant to your large battles (what are they going to do, scratch the paintwork on the real ships?), so don't really need to be part of your war fleets. You might still have them for other purposes (anti-piracy duty if your setting is ridiculous enough to have space piracy be a thing, peacekeeping operations against oppositions that don't have access to real navies, etc.), but for the battle fleets, they'd be better as one massive ship. You can also partially replace this by just having internal redundancy on your bigger ships.

On the other hand, bigger ships are generally more efficient, pound-for-pound (armour weight scales with the square of size, whereas internal volume for putting stuff in scales with the cube).

So overall, I'd expect battle fleets to consist of small numbers of big ships, rather than lots of small ships (we've already done this somewhat: there were 60 ships of the line involved in Trafalgar, whereas many of the major naval battles of the Second World War were exchanges between (low) single-digit numbers of ships).

The exception to this is if offensive firepower has vastly outstripped defensive technology, to the point that relatively compact and cheap to build/run weapons systems can easily destroy anything that you can build, in which case you'll have a whole lot of small ships (and some battles somewhere between horrific and hilarious, as everybody tries to stay far enough apart that you can't take them all out with one shot, while taking shots at ridiculous ranges at any enemy ships that seem to be a bit close together (and if you're defending, you'd better hope you caught the enemy in interstellar space, or they'll trash your system, just with the shots that miss). In that case, though, I'd expect an explanation of exactly why weapons systems got so unnecessarily ridiculous (something like a step-change in firepower on a similar scale to the first nuclear weapons, where you can go from "not enough firepower to kill that ship" to "hilarious overkill for anything" in one jump).

So overall, your answer depends (by many orders of magnitude) on:

  1. How spread out your empire is.
  2. How much you trust your neighbours.
  3. How fast your ships are.
  4. How fast your communications are.
  5. How much firepower you've got compared to your ability to defend yourself from that firepower.
  6. How big/expensive that firepower is.
  7. What missions you want to use your ships for (PR, internal peacekeeping, border defence, commerce raiding, and invasions all call for very different fleet makeups).
  8. How much you care about your less-valuable systems.
  9. How much you trust your admirals.
  10. How your potential enemy fleets are organised (if they're using big ships with armour your little ships can't shoot through, you better have big ships with big guns. If they're using swarms of little ships that your big guns can't track, you better have something that can track them).
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    $\begingroup$ I would argue that in the first situation of near instant FTL, that the size of your army matters a whole lot less. If you break up your army then your enemy could try and find out where the ships are, FTL in, bomb them to hell and when done (or they fail) they FTL to an unknown location in deep space before returning to another secret location for repairs and resupply. And that is assuming you cant FTL the ordnance straight into the target. All attacks would be short and then move to unknown locations. Bases would similarly require secrecy to prevent destruction. $\endgroup$
    – Demigan
    Feb 17 '21 at 18:52
  • $\begingroup$ for u strategy big huge ships are overkilling and somewhat useless - as the first strike, is just about stealth and suppressing almost not existing local defense and destroying the economic base, and move to the next target. wipe everything from the planet's surface with such puny populations of 10kk a few 100MT nukes is probably an overkill already and it takes no time, u appear, launch, 10 minutes to control the result, and u move on. So to prevent that u have to have fleets in each system, so as it u human reserve for noobs and old fleetsmen. $\endgroup$
    – MolbOrg
    Feb 17 '21 at 19:03
  • $\begingroup$ And your revenge with a big ship roaming over my million planets will take thousands of years, so u empire will belong to the dust of history. But there are good points as well, nice answer. and yeah missiles are such an overpowered weapon it 10-100 times less expensive than targets it destroys, some small ship kamikaze style is such a missile(or can be) no problem retrofit it with automatic targeting and all that usual stuff. $\endgroup$
    – MolbOrg
    Feb 17 '21 at 19:03
  • $\begingroup$ @MolbOrg Yeah, that's what I was hinting at with the "unstable due to blitzkrieg" bit. $\endgroup$ Feb 17 '21 at 19:04
  • $\begingroup$ Yeah, did forget about that bit, as it even does not look like blitzkrieg but just a sensible strategy to putting a nail in the head to all the places which can't defend themself and have any economic meaning, as military they are 0. with the layout like yours it asking for 3 layers as bare minimum - border system control fleet just close zerg rush strategy, police work, system monitoring, rescue missions, human reserve; regional fleet - those 1-week ones, u talked about and few strategical fleets which u talked as well. on top of that blackops, recon, logistics, dedicated planetary defense. $\endgroup$
    – MolbOrg
    Feb 17 '21 at 19:18

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