The arithmetic of interstellar travel

There’s been a lot of excitement about the discovery of two Earth-like[^1] planets, a mere 1200 light years away. Pretty soon, I guess, we’ll be thinking about sending colonists. So, I thought it might be worthwhile to a little bit of arithmetic on the exercise.

I’m going to assume (generously, I think) that the minimum size for a successful colony is 10 000. The only experience we have is the Apollo program, which transported 12 astronauts to the Moon (a distance of 1 light second) at a cost of $100 billion or so (current values). So, assuming linear scaling (again, very generously, given the need to accelerate to near lightspeed), that’s a cost of around $100 trillion per light-second for 10 000 people. 1200 light-years is around 30 billion light-seconds, so the total cost comes out roughly equal to the value of current world GDP accumulated over the life of the universe.

Even supposing that technological advances made travel possible over such distances possible, why would we bother. By hypothesis, that would require the ability to live in interstellar space for thousands of years. A civilisation with that ability would have no need of planets.

On behalf of my fellow Australians, I’m going to make a counter-offer. For a mere $10 trillion, we can find you an area of land larger than a typical European country, almost certainly more habitable than the new planets, and much closer. We’ll do all the work of supplying water and air, build 10 000 mansions for the inhabitants and guarantee a lifetime supply of food. I’m hoping for a spotters fee of 0.01 per cent.

On a related point, what should we be wishing for here? The fact that no-one has sent a detectable signal in our direction suggests that intelligent life forms similar to humans are very rare. If habitable planets are very rare, then this is unsurprising – interstellar distances preclude both travel and any kind of two-way communication. If on the other hand, the emergence of intelligent life is common, then the evidence suggests that its disappearance, through processes like nuclear war, must also be common.

[^1] Where Earth-like means somewhere between Venus-like and Mars-like.