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Science, Maths & Technology

How long would it take to colonise the galaxy?

Updated Friday 4th November 2011

 With habitable planets so far apart, is it mathematically feasible to believe that humankind could ever spread across the universe?

Our current technology precludes any of us from travelling beyond the Solar System in a human lifetime. However, with our present technology, or at least the technology that might come in the next century or so, we can imagine an amazing prospect.

Imagined vision of a spaceship passing above a distant planet Copyrighted image Icon Copyright: Algol | Dreamstime.com

Consider a ship that leaves the Earth and takes 90 years to traverse the 10 light-years to a nearby star.

The ship departs carrying 1000 people, with equal numbers of male and female volunteers from a variety of key professions (engineers, scientists, crew, teachers, doctors and so on).

Upon arrival at a suitable stellar system - let’s call it Stellar One - it has the resources to create a copy of itself, exploiting as much material as it can from planets, asteroids and comets in the host system.

Ten years after arrival, one hundred years after its departure from Earth, two ships can depart Stellar One, leaving behind a self-sustaining colony if a suitable location is available.

In another 100 years, another two ships will be constructed at each of two new locations about 10 light-years distant from Stellar One.

Doing the maths

Assume that humans embarking on the voyage are 25 years old on departure and live to an age of 75. Further suppose that couples on the ship have an average of four children each, and that their children (and grandchildren, and so on) have offspring after 25 years.

How many generations are alive upon arrival and what are their populations?

The first generation of 500 couples produce 4 × 500 = 2000 children.

After 25 years, these children will produce 4 × 1000 = 4000 grandchildren.

Fifty years into the voyage, the first generation dies out, but 4 × 2000 = 8000 great-grandchildren are born.

In 75 years, the number of additions now doubles to 16,000 great-great-grandchildren, but the second generation have now died out.

This leaves a population of 24,000, composed of two generations: 16,000 humans in their mid-twenties and 8000 humans around the age of fifty.

Covering 10 light-years in 100 years, the human race can start colonizing the opposite side of the Galaxy (which is about 100 000 light-years away) after 1 Megaannum (a million years).

By this time, given sufficient resources, the initial population of 1000 on the first ship to Stellar One will have been doubled 106years/25 years = 40,000 times.

That’s an unimaginably large number, namely 240000.

The number of ships will double every 100 years, and after about 30,000 years there will be as many ships as there are stars in the Galaxy.

In practice, this tells us that it is the availability of resources rather than technology that will limit galactic colonization.

The point of this fantasy is that we could colonize the Galaxy with sub-lightspeed technology on timescales much shorter than that of the billions of years that characterize the evolution of Sun-like stars, or the 4.6 Gigaannums it has taken for our civilization to appear on Earth. (A Gigaannum is one thousand million years).

This remains true even if the above colonization rate is reduced by a couple of orders of magnitude, because say, resources are short, or it really takes 1000 years to cover 10 light-years.

This article is adapted from The Open University course Planetary Science and the Search For Life

Clarification: In the process of bringing this item from book to web, a rogue digit '1' appeared prior to the commas in some numbers. This odd maths has now been corrected. 

 

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