I didn’t realize something until I used this simulation: with three bodies you can eject one body in one direction and the barycentre of the remaining two in another. This means that compared to the original frame of reference you have an orbiting pair that moves.
It’s one of those things that seems so obvious and yet actually seeing it is a really important step in understanding.
There are animations of how the solar system as a whole moves through space. (The solar system isn’t stationary within our galaxy.) The planets therein are forming spirals around the trajectory of the sun in a similar fashion.