Let's talk about the Birch World introduced in the awesome Gigastructural Engineering mod. You can read more about it here.

*slaps the outer shell* This bad boy can fit so many fucking xenos on it.

Here I'm gonna do some math and try to calculate exactly *how many* xenos (or humans if you want to) can fit here.

According to Wikipedia, the mass of a black hole in the center of our galaxy is approximately 4*10^{6} solar masses or 8*10^{36} kilograms. The Earth's mass is "only" about 6*10^{24} kg so our black hole is about 1.3*10^{12} times heavier than Earth. Let's assume that the Stellaris black hole is a bit smaller and round it down to 1000000000000 Earths.

A birch world is a sphere (many spheres, in fact) surrounding a black hole at such distance where its gravity is roughly equal to Earth's gravity. Since gravity force goes down as a radius squared, to get pulled into this black hole with 1g we need to stay at a safe distance of 10^{6} Earth's radiuses from its center: approximately 6 billion kilometers, well past the Neptune's orbit. Therefore, our sphere will have an area of around 10^{12} Earths.

That's a lot of space but can we fit even more? Yes we can! According to the description, we can build multiple spheres in layers because the gravity will still be livable over a large portion of distances from the black hole. How large? Let's say we want our pops to experience gravity from 0.8g on the outer layer to 1.2g on the inner. To calculate the required radius we need to take a square root of this values and get a range from 0.9 of the "1g" radius to 1.1. Or a "mere" 300 million kilometers of height. Even if we give each layer a comfortable ceiling distance of 300 km (about a quarter less than the International Space Station orbit height) we can still fit **a million layers** here. This gives us the total habitable area of about 10^{18} Earths.(yes, I know that outer layers will be a bit larger and the inner will be smaller but this doesn't affectthe result much)

So if we house people there at a slightly-higher-than-Earth density at about 10 billion people per Earth we will end up with 10^{28} or…

**10000000000000000000000000000 people.**

If we pack them to the ecumenopolis density of 10 *trilllion* people per planet (it's not that dense actually, it's just Paris copypasted to cover the entire Earth, though that can also be kinda grimdark), we will house **10000000000000000000000000000000** people.

How much is this? Let's try to settle our Birch World with a race of rapid breeders that don't have Reddit or Netflix and have nothing better to do than get married and have 4 kids each at an average age of 25. No exceptions. This way, our population will double every 25 years and multiply by slightly more than 1000 every 250 years. For the Earth, this population explosion would've been catastrophic in a matter of decades. Our 10^{31} living spaces birch world ecumenopolis can sustain this rate of growth for *over 2500 years* until they run out of space.

TL;DR? This thing is **HUGE**.

Source: **Original link**

©Post "Birch World population mathematics (Gigastructural Engineering mod)" for game Stellaris.

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