1+ System / 10 Years

Assume that a manned, interstellar ship can travel between stars at an average speed of .01c, one percent of lightspeed. The nearest star system to our own could then be reached in roughly 450 years.

Traveling at .01c, then, results in the inhabitation of one additional system within 500 years of when such operations begin.

Assume that voyages of 10 lightyears are the longest that would be attempted. At approximately the same time as the first ship leaves for the Alpha Centauri system, six others might head out to the other stars within 10LY.

All traveling at .01c, then, results in the inhabitation of seven extra-solar systems within 1000 years of the beginning.

Assume that development of a human civilization in a new system to the point of sending out more colonizing ships would take about the same amount of time that it took for the original ship to arrive. With subsequent ships also traveling at .01c, and an equal amount of time in between arrival in a new system and further launches, the effective speed becomes .005c.

Humanity expanding outward at .005c, then, results in the inhabitation of 80 extra-solar systems within 4000 years.

And about 1200 systems within 10,000 years.

The number of systems reachable is related to the cube of the distance, and so while the beginnings may seem painfully slow (one new system colonized in five centuries), the returns exponentially increase (1200 new systems in 100 centuries). Is 10,000 years a ridiculously long period of time to consider? It is greater than the span of recorded human history, but despite the rise and fall of many different cultures and civilizations over the past 10 millenia, humanity at large has spread, increased, and developed. Some branches may be dead ends, but that won't stop growing shoots from spreading through the stars.

This model does not account for advances in technology, of course, which should certainly occur in thousands of years of expansion. Also left unsaid in the above is a prediction about when such a venture might be undertaken; it seems reasonable that it could occur within a century of humanity establishing its first permanent presence beyond Earth. If mankind does not colonize the rest of its home system, though, it will surely not colonize other systems.

One final thought: almost all star systems are probably targets for colonization, because any group with the ability to traverse interstellar space could surely prosper with the energy and material resources of a star system.