Turning on projected orbital lines in an N-body simulation of our solar system and seeing what happens when you toss a star in there is really enlightening... the rings all shift in tandem in a visceral way that really helps me "feel" what happens.
There's a simulation that comes out of the box that simulates the circumstances of the book "Nomad" (I haven't read the book) where a small solar-mass rogue black hole drifts past the solar system at high speed. With orbital path projections turned on you get to watch all the paths shift like wobbling hula hoops as the unseen object drifts past. Most orbits remain stable but very deeply shifted from where they were (earth's aphelion ends up far out where Jupiter was, with its perihelion much closer than before...)
The effects described in the article are obviously less extreme, but the game helps me get a sense of just how perilous our planetary orbits are and how vulnerable to outside influences they can be.