Trip to Alpha Centauri!

Alpha Centauri is the closest G-type star system at a distance of 4.365 light years from our solar system. It is thus the closest star system capable of supporting life as we know it, assuming there is a planet like Earth in orbit around one of the three stars in this star system.

In the Fall of 2006, I decided to investigate whether a human voyage to the alpha centauri star system was physically possible and if it was, when it might actually occur. Furthermore, if it was possible to build a spacecraft which was capable of making the trip, I wanted to know whether I could build one. It wouldn't be easy, I knew, but I wanted to know if it would be possible, assuming, for instance, that some enlightened nation's ruler gave me enough time and resources for the job. This investigation was prodded by my reading, late that summer, of Alastair Reynold's marvelous science fiction story Revelation Space. I was fascinated by Reynolds' description of a far-flung, near-earth, space-faring human civilization which used near-light speed spaceships to travel between different colonized worlds. Fantastically, none of what he described seemed to violate any of the laws of physics.⁽¹⁾

Beyond the somewhat whimsical notion of actually constructing a suitable spacecraft to get to alpha centauri, and return, or constructing a robot craft to make the voyage, I knew that the importance of this investigation would be marked by the fact that alpha centauri is one of the closest star systems. If my calculations were to show that it is indeed impossible to get to this star system, then they would also show that it is impossible to get to all other star systems as well. Our species would then be faced with the sobering fact that we would be doomed to living on this planet, or at least among the planets, moons and asteroids of this solar system, forever. In other words, there would be no going where 'no man had gone before', and there would be no voyages of the Starship Enterprise. Doomed is perhaps too strong a word. As I show later, there might be a silver lining to this finding if indeed that was the conclusion I reached by examining the physics of the situation from first principles. But we would certainly have no choice in the matter. If a careful examination of the math and physics showed that interstellar space travel was indeed impossible, according to all the known physical laws, then we would be able to continue to gaze upon the heavens and the many wonderous worlds to be found there, but we would never be able to visit them in person.

It has always been extremely controversial to discuss whether or not human beings will one day colonize the stars. Ask around, and you will find people have strong, visceral opinions about it. Just like they do about whether or not there are other intelligent species besides humans amongst the stars. But mostly these opinions are the result of pride and prejudice and not precise, scientific knowledge. I wanted a definitive word on the subject and I knew I would have to do the calculations myself in order to get it. Most physicists have said it is impossible. But I wanted to know for sure whether or not they were right. My experience with the cold fusion debacle showed me, indeed amply demonstrated, that even the most lauded scientists sometimes make grievous mistakes.

The starting point for my investigation, the bedrock axiom, so to speak, is that the so-called Standard Model of contemporary physics is correct and that there are no unknown forces in the Universe that are relevant to the investigation. The four well-known, well-characterized forces are: gravity, electromagnetism, the nuclear strong force, and the nuclear weak force. Only those things that don't break any of the laws of physics of the Standard Model as we know it would be considered. (On the other hand, as far as technology goes, I would not exclude anything that is technologically possible, even if it seemed exceedingly improbable.)

Why? The reason for this is the comprehensiveness and rigour with which mankind has plumbed the secrets of Nature. While the Higgs Boson has not yet been positively identified, it seems likely that it will be soon after the Large Hadron Collider gets back up and running in the Summer of 2009. When that is done, the next new physics we will find will be so far up the energy scale that the results obtainable at that point will be applicable to cosmological phenomena, but not to such mundane matters as piloting spaceships around from star to star in a perfectly average, ordinary galaxy like the Milky Way (on spatial scales of a few light years). Thus the question answered in this way would hold good for the next thousand years or so. Not bad!

Furthermore, it seemed to me that there might be some urgency attached to this question as far as the survival of the human species went. If such voyages were proven not to be possible, then it seemed to me that we would be forced into cleaning up our act at home, and bettering the earth, knowing that this was the only home we would ever have. The sooner we knew that, the better. On the other hand, given the pressures of an exponentially increasing population and rapidly dwindling planetary resources, if such voyages were indeed proven to be possible, then it might be high time to get started in building a ship and perfecting the technology needed to get there in order to maximize our chances of survival as a species.

But such heady thoughts and ramifications were far from my mind as I returned to Williamstown from my farm in Smyrna one fine fall day and dropped in on my friend, Professor David Park at his office in the Schow Science Center at Williams College to tell him about a story I had read late that summer.

Pierce's Paper

When I told David of Reynold's vision of a far-flung interstellar civilization, we began to discuss whether or not interstellar travel was even possible. David remembered that a fellow named J. R. Pierce, an early radio engineer, had done the calculations and had convinced everybody (or almost everybody) in mainstream science back then that physical travel between star systems was a physical impossibility and that because of that we had to be forever content with sending and receiving messages to or from the inhabitants of other star systems by radio only.

This caused me to seek out Pierce's work to check it for accuracy. I was somewhat crestfallen that the beautiful vision Reynolds had crafted in his epic science fiction masterpiece could be destroyed so easily. So I went to the internet and looked up Pierce, and got the title of his 1959 paper. Luckily, Williams College had it in its "compact journal storage area" in the basement of Schow Library where the huge shelves of bound journals glide open to reveal themselves in perfect mechanical solitude.

Reading through his paper, I could see that Pierce had set out for himself a fairly ambitious task: to see once and for all whether travel to distant star systems was ever going to be physically possible for human beings.

To do so, he went right for the jugular: he didn't bother piddling around with rockets whose propulsive mechanisms lay in chemical power, or in fission or fusion power. He went right to a rocket engine founded on matter-anti-matter conversion right away, and supposed that the ejected reaction mass was not matter at all but rather photons.

Because the speed of the "ejected" mass-energy travels at the ultimate achievable velocity, a photon rocket powered by matter-anti-matter conversion is the most efficient propulsive mechanism of all propulsive mechanisms that are possible in the Universe, to our civilization or to any other alien one as well.

Pierce's equations give the mass left over after accelerations to any arbitrary fraction of the speed of light.  For instance, using Pierce's equations, one can find that if one wants to accelerate to 99.5% of the speed of light, the mass left over will be .05% of the initial weight of the rocket, meaning payload plus fuel.

Note that to slow down and visit the target stellar system, one would also have to decelerate, which would involve the burning of an equal amount of fuel. This obviously doesn't leave you much weight left over for payload.  As Pierce states:

    "Now we remember that to make time pass only a tenth as fast on the ship as on earth, we must attain 99.5 per cent of the speed of light;         that is, v/c must be 0.995. If we use a photon rocket to attain this speed, what fraction of the initial mass or matter will we have left?

    The answer turns out to be a fraction a=0.05.

    This sounds extreme, but think of the trip out and back! We start out with a mass m. After getting up to 99.5 per cent of the speed of light     we have left of the ship only a rest mass of 0.05*m. After stopping at the far end, we have only a mass 0.05 * 0.05 * m, or 0.0025 m. After     starting back and stopping at earth, we are left with only a fraction 0.00000625 of our original mass, which sounds rather impractical."

                  J.R Pierce, Relativity and Space Travel, Proceedings of the IRE, June 1959


As I read the paper, I saw that Pierce was completely correct, as far as he had carried his calculations. But I also saw that he had made a rather basic mistake. Pierce's mistake lay in assuming that one absolutely had to travel at such a large fraction of the speed of light (say 99.5% of the speed of light) rather than at some lower speed where the mass left over would be much more substantial. Traveling at a smaller fraction of the speed of light (say 3%) allows one to travel rather fast, after all (much faster than a speeding bullet, for instance), and to conduct the accelerations and de-accelerations necessary for a return journey in a much more feasible manner.

 For instance, if one were willing to travel at 8% of the speed of light, one could still travel around the near-Galactic environment pretty quickly (after all, .08*c is pretty fast!!!), but still have plenty of fuel left over for maneuvres and a return trip. But because Pierce had limited himself to only considering extreme speeds near 99.5% of light, he had mistakenly concluded that actual physical travel to distant star systems was an impossibility.

Pierce's viewpoint quickly became the viewpoint of establishment physics. After Pierce's calculations appeared, they were championed by others, including the Nobel-prize winning physicist Edward Purcell (among others). In a somewhat uncritical and perhaps self-serving fashion, all those agreeing with Pierce seemed to have an interest in increased funding for radio astronomy and radio science at the expense (perhaps) of physical space flight. As a result, the engineering needed for planning an actual interstellar space voyage has languished for 50 years, and the only people willing to talk about it in any sort of detail have been science fiction writers.

The purpose of the following calculations on this website are to show that a trip to another stellar system might be possible someday, and might even be possible within the next 50- 100 years.

The most practical choice for an initial first journey is to the alpha centauri system. Alpha centauri is a yellow G-type sun which is alot like our good old Sun. It is also the closest yellow G-type star, so that if one of the criteria for our voyage is to see whether there are other "people" out there like us, or whether or not there is another planet out there for us to colonize, it ranks high on the list.