This video shows how two planets in an orbit around a "sun" (or singularity) placed in the origin interact if they have approximately the same mass and same initial y-positions, but different (though close) initial x-positions. Keep in mind that since these are assumed to be point particles (a few pixels in size), they don't collide because they intersect each other's orbits in "just the right places". If the objects were big, they probably would collide. I apologize that the quality is a bit blurry (this was recorded with the built-in Windows 10 recorder), but the orbit is described by the dimensionless x- and y-axes.
