How long to populate a galaxy?

[Shinova]

Assume an advanced spacefaring civilization with FTL on par with Star Wars speeds and similar real-time galactic communications and such. How long would it take for them to colonize a galaxy, assuming that every 1 out of say thousand planets is habitable without extreme terraforming?


Second situation, assume the above except that say ten such civilizations start in their own parts of the galaxy, spread out on their own, meet up, ally into one super-civilization, and keep spreading out some more from there. How long do they take to populate the galaxy?


By populate assume at least a hundred thousand people for lightly-inhabited colonies, and at least ten billion for populated worlds, and hundreds of billions for super-populated major population centers.

[Zor]

It depends on how fast said sapient beings breed. If they give birth to litters of four to six, its an entirely diferent thing than if they give birth to a single child at human rates.

Zor

[Shinova]

Assume human reporoduction rates. And this is a little stretching it, but assume they breed much like our world does: rich people breed slower, poorer and frontier people breed more, and such.

[generator_g1]

But won't poorer and frontier people also get the short end on medical facilities and other necessities. They might breed more but many might not reach breeding age....

[Walsh]

So many variables. I would just use our global birthrate and your population limit to estimate the time taken.

Find the equation for compound interest and alter the variables as necessary.

You need to invent an initial population number when colonisation begins, as well as the number of planets. Define how many planets are lightly, moderately, and densely populated, work out how many people this equals, and then plug this figure into the equation. From there you should be able to manipulate the equation to figure out the time taken.

[Winston Blake]

I don't think the second situation is any different from the first, except for 10 times the initial values.

This is harder than I thought it would be. If the number of colony starships was constant, then the number of planets colonised would be increasing linearly. However the number of ships should increase exponentially, since each colony civilisation that reaches maturity should be able to produce its own ships.

I'm not sure about this, but I figure that the number of planets colonised for an exponentially increasing number of ships should be of the form:

P(t) = P_0 * At * B(1 + r)^t

where
P_0 = initial number of colonised planets
A = rate at which a mature civilisation produces starships
B = initial number of starships
r = growth rate for the number of colonised planets with just one starship operating. Doubling time can be found from the growth rate.

Number of stars in the Milky Way is 100 billion. For 1-in-1000 being habitable, that's 100 million planets to colonise. So what we want is the time t for P(t) = 100 million, which you'd have to solve numerically since I think P(t) is transcendental.

I'm not confident enough to try an example until somebody more proficient than me can confirm or correct this model.

[Aeolus]

Historically humans colonising virgin territory double their population roughly every 20 years. Considering that that was when we had very high infant mortality, we could probably do alot better if we wanted to.

[Lord Zentei]

Depends on how fast they can construct the supporting infrastructure.

[kinnison]

Doubling time for humans, with 19th century medicine, expanding into virgin territory was about 20 years. I don't think humans can do much better than that unless they try very hard indeed; if less of your kids die you have less kids.

The problem may well be building the infrastructure and the ships to do the colonising. This is entirely technology-bound; with advanced (mid 21st century perhaps?) machine tools and mining technology it's a lot harder than if you have working nanotech. Bacteria, rather more complex than nanoassemblers and probably less intelligent, have a potential doubling time of 20 minutes.

In the latter scenario, the problem may well be in keeping down the growth rate and not turning the entire galaxy into grey goo.

[Winston Blake]

P(t) = P_0 * At * B(1 + r)^t

Er, by the way, this is wrong. It means that if you start with some planets (P_0), and don't produce any ships (A=0), then all your planets cease to exist (P_0 * 0 = 0), which is just stupid.

I'm going to do this a bit more carefully. Let N(t) be the number of ships.

For a constant number of planets p:
P(t) = p ......................(1)
N(t) = pAt + B

For a constant number of ships n:
P(t) = nrt + P_0 .........(2)
N(t) = n

So you would think:
P(t) = N(t)rt + P_0
N(t) = P(t)At + B

.: P(t) = [P(t)At + B]rt + P_0

Which simplifies to:
P(t) = (Brt + P_0) / (1 - Art^2)

So now,
r=0 -> P(t) = P_0
A=0 -> P(t) = Brt + P_0

Those make a lot more sense, fitting (1) and (2). I was expecting the growth formula to have an exponential term, but hyperbolic growth is fine too. Or at least it would be, if it actually gave me hyperbolic growth. Plotting it in Excel gives me a crap curve. Any ideas?

[ThatGuyFromThatPlace]

take an STL probe and shoot it from your intial starting position to the other side of the Galaxy. I'd be surprised if some one wasn't there to catch it when it got there

[Solauren]

Are we also considering cloning technology and manditory minimum familiy size in this?

i.e - someone is killed or dies before having children reach maturity, a clone of them is grown to replace them in the gene pool

i.e - I don't care how much money you have, you're to have a minimum of 4 children with each mate, and adoption doesn't count.