Is it possible to aim from earth to Alpha Centauri? This question came to mind after hearing about Starshot: Basically you take small spacecraft and accelerate them to 0.2c and make them fly for a few years to Alpha-Centauri at which point it then shoots some pictures back.
They have a lot of things they need to improve to even come remotely close to their goal, but there is one thing that struck me as being potentially unfeasible (there might be others), and that is actually aiming towards Alpha-Centauri or even worse, back to Earth.
There main thing I am unsure about (and which is ultimately the question here) is it possible (in human feasible terms) to actually aim from earth for something like Alpha Centauri? And can something that small (less than a cm) actually aim to earth from 5ly?
The reason why I don't think so is because:


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*Precisely Pinpointing Alpha Centauri is difficult (This gets worse when wanting to point back to Earth)

*It is really far away 


The angular resolution of Alpha Centauri is just 0.007" which is pretty small. I am unable to think of a system where if you aim from earth you could actually get a precision of 1AU at 5ly.
 A: There's a couple things to remember about this problem. First, the spacecraft can easily make course correcting maneuvers en route. Yes, it's difficult (though not at all impossible) to aim for a distant star and hit it without course corrections, but luckily we have that option available. Second, sending an image back is easy. When you transmit a signal, it spreads out. All you have to do is send it in more or less the direction of Sol and it will more than likely hit Earth too. Doesn't even have to be that precise. The signal will need to be amplified like nothing ever before, but if you can do that, then dispersion will likely mean Earth gets it. Heck, even if you shone a laser at Earth from Alpha Centauri, you could easily be off by 6 arcminutes and you'd hit Earth. And that's with a really good laser; low beam divergence.
Recently, NASA has already been able to shoot something off to Mars and hit a $1km^2$ area on its surface. What's the angle on that when aimed from Earth? Or the probe they sent out to Pluto, it got there no problem. It all comes down to timing and math. Our space programs on Earth have already shown they're the best long-distance darts players ever. Getting a spacecraft to another star is certainly feasible, at least aiming-wise.
A: I think you are right that there is a significant technical problem to overcome here and one that is not mentioned on the wikipedia pages you reference.
The current position of Alpha Cen is not known with infinite precision. Alpha Cen is too bright for the current TGAS Gaia DR1 catalogue. The earlier Hipparcos mission established the parallax as $754.8 \pm 4.1$ milli-arcsec. The current velocity of the star is also uncertain. The proper motion is known to 1% and is about 4 arcseconds per year (van Leeuwen 2007).
This translates to an absolute tangential velocity uncertainty of about 0.3 km/s and over a 20 year journey, even with "perfect aim", this translates to a 1 au error with respect to where the star is on arrival.
If the aim is to explore exoplanets (as yet undiscovered around Alpha Cen), then an even more precise "aim" would be required. EDIT: The target may now be Proxima Cen, but the argument is more or less the same.
I think inevitably what will be required is much more accurate astrometry for Alpha Cen (or other targets) and a means of trimming the trajectory. For instance, it is perfectly feasible to alter the thrust vector of a light sail by angling it with respect to the laser beam. The problem is, most of the thrust happens very early in the mission (first few minutes!), so aiming thereafter while its enroute would seem to be a big technical issue and not at all equivalent to accurate navigation within our own solar system.
According to this page the aim may only be to get to within 1 au of the exoplanet, so perhaps this is feasible with a very accurate aim. In addition, if as planned they send lots of these small spacecraft, then I would think they will send them to slightly different aim points to pepper the system and thus mitigate navigation errors.
