Barnard’s Star and the ‘Wait Equation’

When do you decide to launch a starship? It’s a question based as much on cultural assumptions as technology. Start with the premise that we can ratchet up today’s velocities to 150 kilometers per second, roughly ten times the speed at which New Horizons will cross Pluto’s orbit. If we want to send a probe six light years to Barnard’s Star at that speed, we would be looking at a travel time of 12,000 years. That’s a lot of time, but better than Voyager’s 70,000-year plus travel time to the Centauri stars (if either Voyager were pointed in their direction).

Clearly, 12,000 years is too many, especially in an age that regards maximum mission time as the lifetime of a researcher working on the project. Besides, if we did launch that kind of mission, it would inevitably be passed enroute by a faster spacecraft. And that’s the conundrum: does there ever come a time when you do launch, or are you always waiting for better propulsion systems and faster travel times?

As Andrew Kennedy discovers in a paper we have just been discussing, there is indeed an optimum time, though one with a twist. Kennedy works with a doubling equation to describe how growth affects velocity of travel. From the paper:

If technology growth is likely to double every 100 years the speed at which this journey could be made, then…it would seem that a voyager need only wait 690 years or so to make the journey in 100 years or less (i.e. at a speed of 6/100 the speed of light). In other words, the star could be reached in well under a thousand years from now simply by waiting. Total time to destination is 690 years of wait + 100 years of travel = 790 years.

Barring unexpected breakthroughs, then, we get to Barnard’s star in roughly 800 years. Or should we wait even longer to launch as better technologies continue to emerge? Now it gets interesting: assuming continuous growth without such breakthroughs, there also comes a time when although growth continues to produce higher speeds, the waiting time for that growth is too long to make up the velocity difference.

After that minimum, the ship that leaves later arrives later. No getting to Barnard’s Star only to be greeted by those who launched a century after you did and got there first. Here’s Kennedy again, on a launch strategy for future mission directors:

If the civilisation has the capability to make several launches, then they could make use of the spread of arrival times to encourage individuals to leave on the basis that others would either be there first to welcome them or be following close behind bringing with them the future technologies.

And again:

…the wait calculation is crucial. Either side of the minimum, voyagers will arrive later than those who set off at the minimum. At the minimum wait time, growth will not catch the voyagers up during their journey. They will arrive to an unsettled destination, expecting others to follow, but not knowing if the vanguard of civilisation will appear on their horizon before much time has passed. If they leave before or after the minimum and find their destination still unsettled when they arrive, they will know that growth has slowed or stopped and that they will be alone for some time.

This is a rich paper that weaves economic growth patterns with the pace of technology over time and takes a sober look at how our culture might adapt to the possibilities of long-term missions. I wrote in a 2004 entry about van Vogt’s classic “Far Centaurus” story (Astounding, Jan. 1944) as an example of travelers being caught by faster technologies, but there are a number of related scenarios that science fiction writers could mine by pondering the equations in this paper. I was also interested to learn in an e-mail from Kennedy that he has a second paper on the subject in the works. We’ll look at it here when it appears.