Alpha Centauri, a.k.a. Alpha Centauri AB, is currently classified (as of 2012, at any rate) as a binary star, approximately 4.37 light years from Earth, with its 2 stars designated as A (the larger) and B (the smaller). Proxima Centauri, a.k.a. Alpha Centauri C, is .2 light years from Alpha Centauri AB. At 1/7th the size, its sun is much smaller than ours and not visible to the naked eye, but its distance from Earth is 'just' 4.24 light years, making it the closest star to ours. It was discovered in 1915. An Earth-mass planet had been detected in orbit around Alpha Centauri B, but, It's not in the habitable zone, instead orbiting very close to the host star. Its surface temperature is estimated to be 1200 °C (about 2200 °F or 1500 K) - far too hot for liquid water, and also above the melting temperatures of many silicate magmas.
This episode takes place in October 1997.
For this episode, John Williams (as Johnny Williams) wrote a good deal of incidental music, much of which would be re-used throughout the course of the series. Especially notable is the music that accompanies the zero-gravity scene. Williams dubbed it "The Weightlessness Waltz" and it would be used again many times for fanciful sequences.
In the original unaired pilot, Alpha Centauri was mistakenly identified as a planet in another galaxy. However, it is a star (actually a trinary star system) rather than a planet, and is in our own galaxy. This was corrected for this broadcast.
Before the role of Dr. Smith was offered to Jonathan Harris, it had been offered to Roger C. Carmel (who'd later appear in Star Trek (1966) as Harry Mudd).