Since the Sun moves relative to the other stars around it at about 45,000 miles/hr, if you change the frame of reference from the Sun to the surrounding stellar system, you get planetary motion that looks something like this:
I would take this video with a grain of salt though, especially when it says things like “the Sun is like a comet, dragging the planets in its wake”…the planets don’t lag behind the Sun. Better to think of the thing as a conceptual schematic: resembling reality but not really accurate. (via @pieratt)
Update: There’s a new version of the video that addresses some of the concerns raised about the first video:
Update: Phil Plait from Bad Astronomy has posted a pretty thorough takedown of this video.
However, there’s a problem with it: It’s wrong. And not just superficially; it’s deeply wrong, based on a very wrong premise. While there are some useful visualizations in it, I caution people to take it with a galaxy-sized grain of salt.