Even if it was traveling at near light speed, it should take thousands of years before they encounter another planet. And if they were traveling that fast, they would barely see these planets for a fraction of a second before continuing on their journey :-)
But well, great scifi show back then.
still remains the problem of everything needing to be pitch black all the time. i think even without finding any other planets they had a magic light source on the moon.
It's going in a random direction, and probably in a straight line.
Statistically, even at light speed, they would probably only encounter another system every few millions of years or so.
i am assuming the most optimistic outcome that is physically possible, no matter how unrealistic. because if we go by statistics we'd have to scrap most movies that are about an unrealistic (but possible) event.