Mike Williams  <mike@econym.demon.co.uk> wrote:

Let's suppose that there's a civilisation whose numbers double every 50
years, and they have a technology that's capable of sending out 10
spaceships carrying two people each to the 10 nearest stars, with enough
technology to get a colony started.

I just want to point something out here...

The assumption you made there about a colonization source
is a fairly common one, but does not match well with what
we know of possible methods for interstellar travel.

In fact, the largest single cost of interstellar travel
the most efficient way we know how (laser pumped lightsails)
is going to be the power generation and laser transmission
infrastructure.

And once built, that should have a very long effective
capital lifetime, and assuming say that you accellerate
each lightsail craft for 10 years on its merry way,
then you will probably be launching one new mission
every decade forever.  Until upgrading the laser array
becomes cheaper, and then you're launching one every
two years, and then every year, and then once a month...

Once accellerated, the limits for range of transit are
basically craft onboard independent lifetime and velocity.
Going from a craft barely able to cross to Alpha Centauri
at 0.1C to one able to cross 20 LY at 0.1 C is not all
that hard... very little added mass, though a lot of
better and more thorough and redundant engineering.
And out to 100 LY at 0.1 C...

Especially given that, as time goes on, available energy
will probably be growing exponentially, so the velocity
we can send colony ships out at will be increasing quite
significantly, along with their effective range.

And, most importantly, the source world will keep sending
them out, because the infrastructure isn't much good
for anything else.

Given any reasonable set of assumptions for evolving
technology levels, a single source planet will probably
directly colonize a large fraction of a galaxy.  Some of
the factors related to how far you ultimately could
directly launch colony missions are unclear... but thousands
of light years may well be possible.  The colonies looking
to send out their own probes in a second generation will be
playing catch-up to direct explorations from the homeworld,
in most cases.  The detailed math assumptions of how fast
the homeworld ramps up its launch energy capability,
how fast the colonies grow and generate their own infrastructure,
etc. are all subject to wide ranges of possible conditions.
But the odds are high that it just takes one successful
world with one successful launch system...


-george william herbert
gherbert@retro.com