far away. . . .
....There was this small spec of light, at distance - mute, and indifferent from other star clusters around, but a few light-years approach, it starts to glow, glowing in the radio spectrum, that tiny region of the galaxy harbored about 14 thousand stars each with a couple or more inhabited planets and virtually infinite resource at it's reach.
This foreign territory, besides heavily polluted with radio broadcasting, is also filled with the wonders of a Kardashev II society, Dyson Swarms, mining stations on orphan planets, enormous arrays of instruments working as giant telescopes or beacons around planet-less stars, and maybe even planetary crusts completely ripped apart in order to extract it's natural resources...
Still, such a territory would only expand about 100 light-years from the founder-species home planet.
The keeping of large territories requires serious politics behind the holding of a centuries long government - see, the Roman Empire - and mainly if this government is focused on the expanse of space without expecting any return in their lifetimes - which is a very altruistic thing to do by a certain side - a thing I'm very inclined to think is that such societies are susceptible to be short lived, as they will be never able to maintain absolute control over the thousands of planets under their 'own', unless their establish some sort of undermining tactics.
I call the way I solve that on my fictions, "Minimum Populus" regime, ie, if a planet's estimated resources could sustain a 10 billion population - say, Earth as example - keep that planet's population bellow 2 billion, and keep a large chunk of the exceeding population working outside the planet, in stations or mining colonies on the border of that star system, or even make your space military out of the exceeding population.
By doing that you secure a couple important things:
1. The planet's resources will last longer.
The Earth has rate at which soil, fish, and air can recover over time, as the population and resource demand grow, at some point that demand will overcome the recovery rate, and the society and ecosystem will collapse.
2. With longer lasting resources and a relatively small population demand, everyone can live pretty well on their own.
If such a planet can make, say food for 10 billion people a year without much problem, and considering such a space faring society would have the mechanical and biological means to harvest and seed large quantities of food with a very small personnel (I suggest the heavy use of machinery to do most of the work), they may as well produce without any heavy effort more than enough so they can live with tens of times the minimum required for their survival - by that I mean, clothes, ice cream, and fancy houses, if the colony purpose is to sustain itself. If otherwise, the colony could be used as food source, then they could heavily rely on AI to aid them in harvesting as much food they need to export without heavily wearing out the soil.
3. Divide et impera.
2 billion people population may seem like a lot, but 2 billion people spread across an entire world is not. 100 New York sized cities and about +400 cities and settlements with <2 million inhabitants could be a model for distribution. And remember, every colony will start from zero once they arrive, so to undermine any resistance from the start, is a really good idea to pave the way for settlers with several colonies hundreds of kilometers apart and - for more than I hate including them - politicians, or whatever influencers you can stuff your ship with, that one guy that will from time to time remember the crew that they work for X-corporation or Y-country, or Z-empire. The same thing for your settling lots, and over time you will get a favorable part of population that besides having a decent sense of identity towards that planet (ex; Martian, Terran, Venusian, etc...), they do all recognize themselves as citizens of your Z-empire, summed up to the relative abundance of resource like food, literature and other fancy stuff, they will all hail the great Z-empire.
Sure it will take about a long time until the planet reach it's 2 billion mark, at a Terran rate of +1,1%/yr, it would take about 1459 years to reach 2 billion, if your starting colonist pool is 1000 people. Of course that value reduces a lot as you (Z-empire) will continue to send settlers to work the land for some more decades / centuries to come.
This will also limit the force of any - even after all that mind work - rebel insurgence that may arise, as they will more probably be already a small part of the small population of the planet.
As big example, the ISIS effective were about 80k at it's peak in 2014, about 0,16% of all the 48 million people that inhabit both Syria and Iraq. Despite the reason as why they come together, that is about a thousandth of population. So at most, we, the Z-empire, will be dealing with a 3,2 million man army.
A relatively average port country like Ukraine could get over these numbers with a full scale mobilization, It could be easily outnumbered and outmaneuvered since you probably control a dozen neighboring star systems for support.
And that's on the late days of the population ceiling we established previously, it would be very inside the handling capacity for quite a long time - and be repelled via a number of other ways we will discuss later.
4. Fortress Worlds.
A big concept we can observe in the Halo series are what can be called Fortress Worlds, planets like Reach, which purpose is to serve as a military stronghold among the stars, very useful if a certain system can accommodate more than one habitable planet - it's main task is besides establishing a rigid order under the command of said Z-empire within the local star system, is to act as a guardian of the surrounding sector, being within days or a jump away from any surrounding star systems with insurrectionists or foreign alien attackers. Fortress worlds are responsible for the intense development of spacecraft, weapons and military training fields the size of entire countries, besides a large civil population of course so they can work in all of that stuff - a concept rather interesting that besides rather contradictory aspect of "putting all your eggs on the same basket", you are actually pulling the enemy's attention away from important worlds, like those which produce food, or raw materials or even your core worlds - still within the series, the alien alliance Covenant initially thinks planet Reach is the homeworld of mankind due to the heavy military, dense population and humanity sending most of their efforts on the protection of Reach.
Now, even though you may have lost an entire planet like this to the aliens or insurgents, that is one out of tens, and a few million deaths upon billions that could have gone if we weren't using the Minimum Populus.
Apart from what will you do, or not do, one thing is granted, you don't have a paper to say to the aliens "I own this system", you will need to get there first.
Assuming that the early states that would unify and become the Z-empire had already classified and catalogued hundreds and thousands of planets and stars, among them - the ones able to sustain life as they know it as an immediate matter, the only big effort they'll need to perform is to get there within a reasonable amount of time. By this time, they would have already tried some planetary travel designs. At 0,15c. a travel from Earth to Mars can take as much as 1 hour and 22 minutes, at 0,5c it is about 25 minutes, which is already about some serious technology and probably the opening to relativistic mass destruction weapons that could wipe entire fleets or countries - posing a great threat this society have to overcome in order to become interstellar - unless this technology is discovered after they go interstellar.
TIME TO BUILD AN EMPIRE
We need to start thinking about how will we start spreading throughout the galaxy before packing up seeds and frozen embryos.
Let's start by what I initially called Island Hopping, Chain Island Hopping, and Core Reaching/Grab.
Note that in each and every one of these scenarios, in that case, going towards 5 stars, there are the same number of travels (arrows), be they short or long.
ISLAND HOPPING
In this scenario, our empire launches a mission to a good planet, waits for it to develop, and then that first colony sends a mission to the next, and this happens over and over with each planet launching one mission after critical mass.
Of course space is not a neat little line like that which is drawn there, but lets consider that:
The civilization has mapped its surroundings to an appreciable extent, and thus knows what planets to colonize and in such order they never retreat, that is, built a stellar route from the core world up the farthest star system, going through every system in between, in 3D space this route should look like a mess of lines, but we can open and stretch that to look like a neat line.
One neat thing about this model is that the last trip is no harder or longer than the first trip, given that travel speed doesn't increase with time in that simplistic scenario.
That happens if your target systems are nearly evenly spread throughout the dominion you plan to establish, like on average 10ly from the nearest habitable system, so at 0,1c it shouldn't take your civilization more than a century per travel doing it that way, system by system.
That is the geometric principle of our first two methods of spread, shorten and standardize the travel time between stars.
Let S be space between stars on average, we calculate that by taking the volume of our spherical dominion around the home planet and dividing that by the number of stars we intend to reach n*. That operation will give us the volume around each star, we cube root it to find the linear distance in between them.
For example 5 systems at an average of 10ly from each other at 0,1c is 50ly/0,1c = 500 years spent traveling in total.
We are not only going to just travel stick a flag then go away, that's not how it works, in the spread model we are doing, this colony we just established will take some time to develop. Let's say about 200-300 years (based on the New World colonies).
So call that variable P for period, in that example P is around 2,5 centuries. It is one of the limiting factors for time to build an empire, even if we could instantly to other stars, each of those systems would still take P time to develop. In that case, we can conclude that for non-zero travel time, the empire-building time is:
FROM PREVIOUS POSTS:
There are ~13.860 stars within 100 light years, from which only ~512 are sun-like stars, from which 38 have confirmed planets. [link]
For
as well, we may consider some extra ~947 K-type stars per 100Ly radii,
for sake of more liberal results later, which 21 (2,21%) have planets
around, 947 would be ~6,83% of all stars. Assuming the same of life
percentage goes for them.
As for the other percentage it's mainly composed of red dwarfs and a minuscule part of giant stars.
From nearly 14.000 stars, about 1474 (10%) of them are suitable for life as far we're concerned about energy needs. And from those, about 59 may certainly have at least one planet, 60 if you may wish to include yourself. And as you could probably guess, unless your territory take galactic proportions, the only danger to you is your own species.
BUT, going for a semi realistic scenario, because we wanna see Star Wars and Star Trek like demographics - say life is inevitable and it's just a matter of at which stage it is in a given place, by then we may include a few thousand red dwarfs.
Assuming we have about 100 systems suitable for life (certainly not Earth-like, but still, life), then that is anything between 100 and up to maybe +1000 worlds (for multiplanetary systems), for an average of maybe 500 planets within reach. Statistics for 50ly around Earth show that around 11 worlds might be suitable or at least rocky for establishment, geometrically speaking, a radius of 100ly should contain 8x more candidate worlds if they are randomly scattered, and so our dominion has around 90 suitable planets for settling, that's our n* value.
So per 100ly radius we have 90 planets suitable for settling, that gives us ~36 light-years between any potentially habitable planets (pretty lonely in here).
Plugging in our S value for P = 250 years and v = 0,1 lightspeed, gives us... 54,9 millennia!
Even at those incredible speeds, it would still take us 1830 years to build 3 stable colonies around Sol. And 32,4 million years with near future technology at 0,0001 c.
CHAIN ISLAND HOPPING
Now this model seeks to diminish the time taken to reach the total number of planets by making an extra effort in the launch, with more launches at the start, making smaller chains.
For example if we are splitting the number of targets which currently lie in a single path, in two smaller paths, we can reach them in half the time, or one-third the time if we do 3 launches.
In which case we might just be able to really fraction that time down to 11 thousand years with 0,1 c and down to 6,5 million years at 0,0001 c if we do 5 initial launches.
CORE REACH or GRAB
This model incorporates a more geocentric perspective of the spread, in which case the colonies cannot yet or are prohibited from spreading even though hundreds of years have passed by. In this model the distance between stars is not average or uniform, and so we have to find another way around that problem, this is we have two approaches:
- Invest in 1 colony at a time before doing the next.
- Invest in multiples at a time before the next batch.
CASE 1, the total distance we have to travel is just the sum of the distances from those systems down to our core world, then we can add all the developing time at the end for all the colonies.
For this sort of model, establishing new colonies makes the homeworld reach further and further into space each time, if the for first few systems within 25 ly it took about 500 years, for a system 50 ly away it would have taken 750 years on top of the hundreds of years already spent on shorter trips...
The way the case 2 stacks over time each wave is the following:
And so for this next example, let the distances be 25, 50, 75 and 100 ly, P is still 250yrs and v is constant at 0,1 c.
Assuming we did three launches every time, for 12 colonies we spent a total of 3500 years on them, way more than before and in little exceeding time. So far this seems like the best way to spread across the galaxy.
To occupy the whole set of possibly habitable planets in this 100ly bubble (~90 worlds), we would have to launch 7 in the first wave, 5 in the second wave, 45 in the third wave, and 33 fourth wave (as per volumetric relationship).
WHICH IS MORE EFFICIENT?
Now to test the spread models against each other we can use either a python code or spreadsheets to get a set of numbers to work with. I asked google spreadsheets for 90 distances between 5 and 100 ly.
Let the race start at 0,1 c !
ISLAND HOPPING - 54 900 years
CHAIN ISLAND HOPPING (5 launches) - 11 000 years
CHAIN ISLAND HOPPING (5 launches) - 11 000 years
CORE REACH (1 at a time) - 66 360 years
EXPANSION WAVE (expand 25 ly each time) - 3 500 years | by far the best method so far IF we could execute 45 launches at once of course
FIXED EXPANSION WAVE (for 5 launches each wave) - 20 planets in the first 3500 years, repeat 4,5x to cover 90 systems, 15 750 years total
Even when greatly downgraded the expansion wave model still deliveries great results in shortening the time to build an interstellar empire, down to the human society lifespan, this somewhat implies that even with far far subluminal travel speed our species can still go interstellar within the next one or two millennia.
BUT WE'RE NOT STOPPING YET!
So far we have assumed that the interstellar civilization didn't come up with anything better than 0,1c travel for 3000 years, bit of unrealistic in the sense that technological advancements stack up over time. To account for this, we can determine that our velocity v, is no longer constant, but a function of time!
ISLAND HOPPING
Here, v is a function of in which star along the line we stand, assuming that further down the line our tech has advanced significantly during the period P in between trips.
That function could take any form in reality, but we could assume it to be linearly growing with time, or compounding interest.
Where i is how much it grows between trips in fractions, so 0,1 = 10%.
If for the island hopping model, our ship improves 1% for the time in between (every 250yrs), by the end of the process we will have ships going 24,5% of the speed of light! So if it took 1830 years to make 3 colonies before, now it takes 1812 years. And only 35 731 years instead of 54 900 years for all 90 systems. And dividing it in smaller chains still divides that time by how many chains you have.
CORE REACH
With growing speeds each time, we have to put the 1/v part inside the sum with the corresponding element:
For v with 1% improvement each time, the time goes down from 66 400 years, down to some 30 000 years time scale.
EXPANSION WAVE
If we just apply the 1% improvement we get 3 450 years, which is not very productive at first, but then remember that realistically we would do 4 or 5 waves of expansions to cover all of the 90 systems, that's 20 total steps for k in the compound interest growth of v. Computing for 4,5 waves, we get 14 789 years.
CHAIN ISLAND HOPPING WINS!
Though it takes 35 700 years to island hop between stars, dividing into 5 smaller chains makes building a large 100 ly radius interstellar dominion just as fast as 7-8 thousand years, while it would take you twice that long to send waves to every habitable planet in that space. Of course, being so fast has the downside of still having to deal with ships at 0,12 c after the last planet is settled instead of 0,24 c if you did the whole course in one go, that also assumes that each chain advances equally with no breakthroughs our regressions.
However, expansion waves are great for scouting new planets or civilizations since they can go further into space, or even setting your baseline of nearby core worlds before switching to island hopping.
As said earlier, building a space empire is a task that will outlive dozens of government models and names, and break up every couple centuries even within the same species, see the New World's wars of independence as a recent example of how difficult is to maintain an ultramarine colony.
Even so, that may be a task for a multi-race senate, in case the races you encounter agree with submitting to your power under the promise of proper representation on the command decisions, modern society is just about 100 years old to say the least, and we still have many differences to solve among ourselves, so along with solving our problems we may also have to wait or try to solve alien stuff all over the place.
No wonder that in Star Wars, the galaxy seemingly breaks in war like every 20 years.
Unless the rise of some serious force threat many worlds, some parts of the territory will never be united.
HERE IS A CALCULATOR FOR THE EQUATIONS USED HERE, SO YOU CAN COMPARE RESULTS OF WHAT WORKS BEST FOR A GIVEN PARTICULAR CASE
- M.O. Valent, 04/01/2020
- M.O. Valent, updated 17/08/2022
- M.O. Valent, updated 24/08/2022
