Adobe After Effects is the software.
Essentially the concept is using the motion tracking feature, which attempts to discern objects via contrast between pixels. You get it to latch to the disc, and from there it generates a set of keyframes that you can then "build" the effect (i.e. their blue light trail) from.
The beauty is in the details, and I have to say Michael did a pretty sweet job with theirs. A couple of years ago I was playing around with one myself, mine looked more like sonar pings, it wasn't as elegant. It's a massive pain in the ass against bright skies, because the tracker feature often loses the disc and you have to manually correct the keyframes.