What fascinated me was the irregularity in speed and distant to the Airliner

The whole thing might have been some sort of illusion, but I thought I'd just mention it. 
I was sitting outside that day.  It was a very clear starry night (which is very usual in our part of the world) when my attention was drawn to a passenger aircraft flying over (I would like to point out that I like watching them fly past,night or day, beause I have a huge interest for Aviation).  We have an International airport in the city, so I guessed Commercial Airlines used it as a waypoint, thus frequently passing overhead. 
Anyway, on this occasion, a strange thing happened.  As I stared at the aircraft's strobes flashing away, an object like a star (but without the twinkle) suddenly appeared at some distance behind the aircraft.  This object then suddenly sped up towards the airplane at incredible speed and stopped right behind it, then it started moving from side to side, as if studying the airplane.  It would move back abruptly, then suddenly flash forward, but never overtook the aircraft. 
What fascinated me was the irregularity in speed and distance to the airliner.  There was no pattern that would suggest some sort of light reflection or something like that.  
Anyway, after trailing the Aircraft for about 20-25 seconds, it changed direction completely to the right, traveled some distance,(to scale with the aircraft, I would say about 10-15 lengths of the wingspan) then simply vanished. 
I continued to stare at the airplane until it vanished, thinking it might uccur again but nothing happened. (Sorry about the date. I'm not even sure of the year and month; it was just a wild guess.)
Witness indicates that the date of the incident is approximate.  PD