> Okay. So, going with these figures, that gives us a volume of space approximately equal to 33.51 cubic light years (91.95 if the distance should be 2.8 light years instead of 2) in the shape of a sphere, centred around the Earth, through which a medium-sized star would have to pass in order to have any effect on us at all. That seems to be a tremendously large amount of space to me; is the average galaxy spread out thinly enough that it becomes unlikely for any star to pass through that volume of space?

The thing is, that's a MAXIMUM range of space. A star could be well within that range of space and still not have a perceptible impact. I don't know what the threshold is, but I would think it's a LOT closer to home.

All I can say for sure, though, is that in my intro to astronomy class, I remember the lecture about colliding galaxies, and I'm pretty sure the risk of an impact to any particular solar system being extremely small. The risk of meteors throwing the planet's orbit off-kilter is greater.