I'm trying to make some roughly close estimates on the resources that a multi-galactic empire of a certain size and level of technology would possess, which is relevant for a detailed background story and perspective view that I want to include in a story I'm writing. Suffice to say, I could use some help and advice as for the matter of designing such an empire for the story. (My 'Cataclysmic Infinium' story was the predecessor to this one.
I think the problem I had before is that I had not yet figured out the entire plot structure and order of events before I tried to write it, and had not thought enough about character development, just throwing a bunch of random characters into the story to fill in where needed, too many characters at once for me to give any one of them any distinction. But that's besides the point - I'll provide what I've figured out so far, and I'd appreciate any suggestions or corrections you all might have. (I won't give much of the plot away, mostly because I don't have much of a plot right now - only ideas.)
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The story takes place starting in the year 31503 CE, and humanity has spread throughout several galaxies besides the Milky Way: Sagittarius, the Large and Small Magellanic Clouds, and partially into the Andromeda Galaxy.
The only thing I've calculated so far is a hypothetical population number by 31503, which I did like this:
Assuming an unchanging rate of population growth between 2010 CE and the year 10000 CE of roughly 2.5% per year, the population would reach 54,052,350,000,000. I calculated this this way: 6,600,000,000 x (1.025 x 7990). This assumes that sometime in the near future, humanity develops at least near or slightly above FTL speed travel capability, and utilizes that ability to expand its population to as many planets as are suitable to colonize in the surrounding galaxy.
Next, I've assumed that following the year 10,000, the population would skyrocket to a 7% per year increase as biological immortality becomes possible, and technology undergoes a revolution that allows a new, much faster form of FTL travel. I've calculated this using the following formula: 54,052,350,000,000 x (1.07 x 21503).
This equals a grand total of 1,243,647,819,793,500,000 - a little bit above 1 quintillion.
First, I want to know if someone can confirm if my math there is roughly close, or if I did it entirely wrong.
Now all I need is someone's 'expert' knowledge on the matter of such an empire's size and resources.
1. How many planets would such a population need? This figure requires accounting for the fact that Earth would be the center of the Empire, and colonies closest to it would be the most densely populated, the farther out you go, the less dense the population gets.
2. What would be the industrial power of such an empire? By this, I mean to ask - what would be a good guess as to how many ships would there likely be of various different levels of size?
Such as:
Fighters/Bombers/Shuttles - up to 20 meters in length,
Corvettes/Frigates/Freighters - from 25 to 250 meters in length.
Cruisers (most common) - 300 to 500 meters in length
Capitals/Dreadnaughts - 600 meters to 3 km in length
Supercapitals/Juggernaughts/Destroyers - between 4 and 35 km in length
Hypercruisers - between 40 and 300 km in length
Monoliths/Titans - between 500 and 2000 km in length (most likely as space space stations)
Behemoth/Colossus - 3000 to 100,000 km in diameter (most likely built as spherical planet ships)
I don't know whether or not the last two orders of magnitude on ship size are even within the constructive ability of the empire I've described though. I would guess that the majority of people in a empire this size would occupy jobs pertaining to mining and mass-construction, service jobs being the minority of the workforce.
Also, I'm wondering about how much agriculture and artificial cloning would be required to feed such a large population as well.
I may come up with more questions, but that's all for now. As I said, I want to give the reader a good perspective on the setting of the story, so if you have any ideas for me to consider (ideas as to how such an empire would compensate for 'time' dilation, how trade and infrastructure would need to be set up at this scale, how would government need to be organized, etc, etc.)
Sorry for any spelling or grammar errors.