So you're travelling to Alpha Centauri at 10% the speed of light and the two stars are shining out of your viewscreen. Congratulations, you avoided life support failure, the crew going crazy, or the ship's computer going crazy and killing the crew in their hibernation pods. Now how do you stop? I put this blog post up because I was inspired by the Icarus Project's post on the same subject, and I've been giving this a great deal of thought over the years.
The bad news is that it's going to take all the energy you put into getting up to your velocity into slowing down. You could use your rocket engines (assuming they still work) to slow down, but that means your initial fuel load goes up exponentially and the spacecraft at launch would have been the size of a mountain. (Launching this is going to make the Apollo project look like the Bobsy Twins and their kindly uncle building ships in their back yard*). The alternative is to simply cut your initial velocity in half and use the other half of your delta V (total velocity capacity) to brake at the other end. But it means getting there slowly, and slow means that taxpayers and politicians are less likely to fund such a venture (and the mission is already going to take decades).
Obviously, you would ditch as much of your unneeded payload as possible (but, light years from anywhere, every scrap of material is valuable). Radiation shielding, habitats, soil, empty fuel tanks, all jettisoned except for landers, science payload and your colony equipment. Oh, and colonists, all crammed into a tiny habitat, or camping out in the landers. The high-efficiency motor itself used to get up to this speed is likely to be massive; if one could drop it overboard if there was some other way to break, one probably would. Still, perhaps a fuel reserve could be used to slow the spacecraft a little bit before saying goodbye to the motor. A 10 or 20% reduction in velocity might make all the difference - this must be weighed up against the risk of the motor not working after all these years in vacuum and hard radiation, and already thousands of hours of operation.
The good news is that there are ways to slow down, albeit each with their own limitations. The most viable way to slow down would be with a Magsail. This uses the interstellar medium, which although is a huge vacuum, actually has one or two ions per cubic centimetre. Travelling at such high velocities, this actually translates into a very, very thin mass flow. Running a current through a huge superconducting loop hundreds of kilometres in diameter would tug on these stray ions with a magnetic field, transferring the ship's momentum to the them and slowing the ship down. A very elegant solution which works better when decelerating from higher velocities. Perhaps it would be better to hang onto the engine and only fire it when the ship's velocity got down to ~0.001c, or in the region of a few hundred kilometres per second.
The second no-fuel alternative is to use a solar sail. A BIG solar sail. But to slow down from 0.1c, even a mere 50 tonne payload would require a sail 1000km in diameter, and using an efficient inflated sail made of beryllium diving right in. Making the sail out of super-high strength, high temperature carbon nanotube technology doesn't help that much. Where it does get better though is that when the slower clip you can come in at, the less of a problem it is. The diameter appears to scale with the incoming velocity; so at 0.01c the sail diameter is only 94km. And of course, the sail mass is proportional to the inverse square of the diameter, so a 94km sail only weighs 1% of what a 1000km sail would be. Interested readers should consult Pat Galea's article on this. Alpha Centauri, however, does offer the chance to use two suns to slow down - albeit not in line with one another, making it a lot more difficult to brake at one and then brake at the other. A gravitational slingshot might help, though - calculated to shave off velocity instead of boosting it.
Aerobraking is how planetary landers shed all their nasty orbital velocity, but could we do that to shave off a few percent off of our incoming velocity? Planetary atmospheric deceleration is basically impossible for even a tiny fraction of lightspeed; the probe would almost surely incinerate. At very high velocities, radiative flux heating rather than conductive heating dominates. The radiative flux from plasma sheath surrounding the probe would also incinerate the sidewalls. Also, since this is a huge spacecraft, aerobraking is problematic even for regular atmospheric entry, due to surface area to volume constraints. Heatshields are heavy. Aerobraking also requires a spacecraft to be moving at a speed that is still slow enough to allow the planet's gravity to pull it close in an arc, getting more braking effect. Decelerating from even ~0.001c would create something like a Tunguska explosion on the surface of the planet. Even then, a survivable deceleration spike (say a couple of hundred G's if everybody's vitrified) would only be for a few seconds and shave off a few dozen kps, because, travelling in a straight line at even low sublight means you only dip into the atmosphere for a very short distance. Space shuttles and capsules can afford to decelerate slowly because they travel thousands of kilometres because they are travelling slow enough that they are curving around the planet as they do so. At such high speeds, a planet's gravity wouldn't curve the spacecraft's trajectory at all.
So aerobraking is a no-go. Our spacecraft would disappear in a Tunguska like explosion. So what now? We've got all this mass sitting at (basically) zero velocity for us to slow down, but we're going too fast and planet atmospheres are too small. I considered trying to punch out a "corridor" of atmosphere with projectiles, but I think that would dissipate too fast. Plus, it would be rather catastrophic for the planet's environment, doing some rather drastic remodeling. Not what you want if you want to study it, especially if there's the possibility of life.
This is a somewhat insane proposal that involves using your environment and whatever you have lying about to your advantage. The idea is precisely that your spacecraft is a flying bomb; a snotty tissue tossed out the window at a passing planet would obliterate a city when travelling at even these "low" sublight speeds.
Towards the end of main engine deceleration, the spacecraft dispenses a number of small, independent solar sails. This zip on towards the target star while the main craft continues to large behind. Having no payload, they can decelerate to lower velocities by braking at the star. The main craft then arrives in the system, ditches its main engine and deploys its own solar sail. It brakes hard at the target star, bleeding off a large chunk of its remaining velocity and carries on past the star, heading towards the now near-stationary sails. The next phase is tricky and smacks of insanity. As it approaches each sail, a small railgun on board fires a pellet at each mini-sail in front, blowing it up. The explosion is like a small nuclear detonation, and the main craft's sail catches the debris, slowing it down almost like a parachute. Alternatively, the sails decelerate completely (if the closing velocity is slow enough) because they are so light, and then shoot back out towards the main craft at the same speed, getting a huge energy boost from the sun. If depending on thousands of mini-sails is too problematic, then one big sail could be released and then dole out its energy in the form of small pellets of ice, which the main craft could then ram into. The disadvantage is that not all of the available mass would be used up in the ramming. The mini-sails' total mass would be totally used up in the ramming explosions, whereas the mass of a larger sail wouldn't be used at all - it would just carry on out back towards Sol.
A brief understanding of this concept is that the energy for deceleration is only available at the target star for a short time, which gets even shorter the faster the probe is moving and thus requires much bigger sails. Using mini sails captures this energy and the main craft gathers it up in chunks (by basically ramming into them).
*I have no idea who these characters are, I only know Jerry Pournelle mentioned them. i.e. Something from before my time. I assume it's like the Hardy Brothers (which I also never read).