While everyone quotes Alpha Centauri as being the closest star to Earth, I am sure that I remember reading that the Centauri system is a group of three stars, with Alpha Centauri A, Alpha Centauri B, and Proxima Centauri orbiting the two. Wouldn’t this make it so that sometimes, one of the two Alphas are the closest to the Earth, while half of the time, Proxima is?
Proxima is nearly three tenths of a light year closer than the binary pair A, and B. While the theoretical facts you propose are true, for the period of human history during which all observations have been made thus far, Proxima has been closer. It will remain closer for centuries to come. Since Proxima is not generally visible to the naked eye, it is only a curiosity to anyone not particularly interested in astronomy, or science fiction.
Tris
Actually, I quote the sun as being the closest star to earth.
Also, Proxima Centauri is the closest star (outside the sun) to the earth. From what I can tell, nobody really knows whether Proxima orbits around the Alphas or not. If it does, the orbit is at least 1/2 million years long. So, until somebody better versed comes in to answer, I really don’t know.
And in a timespan like that, you’d expect other stars to pass closer, anyway. I’m not sure offhand, but Barnard’s Star (currently the next-closest after the three alpha Cen stars) might have been closer than that: It’s really whizzing through our neighborhood.
It’s nice to know I wasn’t the only person to have this question. (I asked it so long ago it appears to have been turned into hamster fodder, but I phrased it almost exactly the same way)
If the Celestia free planetarium software, which lets you position yourself at any known star in its database, is accurate, Proxima is so faint that you wouldn’t be able to see it with the naked eye even if you were on a planet orbiting one of the Alphas.
Here’s an old thread about Proxima Centauri. In it, I cite an even earlier thread wherein I discuss a star known as Gliese 710. Unfortunately, that old thread doesn’t seem to be around any more (probably lost in the Winter of our Missed Content).
Anyway, Gliese 710 is headed almost strait towards us and will have a closest approach in around a million years or so (it’s 63 ly away, so it’ll take a while). Most sources say it will be within 1.1 light years in less than 1.4 million years. I seem to recall one study that claimed to have allowed for the galactic orbits of the stars (Gliese 710 and the sun) and which figured the star will come within about half a light year.
In the meantime, other stars will come and go as the nearest. Barnard’s Star, for example, will approach within 3.8 ly in 11,800 CE (or AD if you insist).
Well, I admit to not checking on the magnitude lists. Dimmer than I thought.
Tris
Lemme guess, it’s a yellow giant? 
Minor hijack:
“His pattern indicates two-dimensional thinking.” —Spock
I’m not saying anything about this star system specifically, but rather making a more general inquiry. Is there any reason to think that the orbital plane of neighboring star systems should match that of our own? Isn’t it as likely that the plane of this other system should tend toward perpendicularity, instead of being parallel? In other words, from our point of view, the stars wouldn’t be passing in front of and behind one another as the system turns, like gears mounted on the same flat surface, but rather would look to us something like a pinwheel. In that situation, the stars would be more or less constantly equidistant. Of course, if the plane doesn’t have to match, then a perfectly perpendicular arrangement would be just as unlikely as one that is perfectly parallel; far more likely is some sort of skewed arrangement, which, obviously, means that one or another star would indeed be closer at any given time. I’m just wondering: do we know enough about how galaxies form and hang together to make any predictions about this?
This question comes to mind because I recall in the various articles about planet hunters that the location method varies by relative alignment. When the system is viewed edge on, the planet (if large enough relative to the star) will tug the star very slightly back and forth, causing a linear wobble, and perhaps occlude the star’s light. When the system is viewed “top down” (or “bottom up”), the star will trace out a small circular wobble.
Does any of this variation hold for a proximate galactic neighbor?
Let me rephrase that, using properly technical jargon: Barnard’s Star is really zooming through our neighborhood (and yes, “zoom” in this context is, in fact, a technical term).
Cervaise, there’s no reason that a star system couldn’t be orbiting face-on to us, or nearly so. But we know for sure that Proxima isn’t doing so, since if it were, it couldn’t be significantly closer to us than are the other two stars. And a nearly face-on orbit would be much harder to detect, and a planet in such an orbit would probably not be detectable to us at all.