Earth is moving across one of the spiral arms (far from the galactic center) like a yo-yo. Other stars are doing the same thing. Earth will approach these stars many times.
Also, when the Milky Way collides with Andromeda, there is so much emply space that few stars will actually collide, IIRC. The two galaxies will lose their spiral shape.
Cool, thanks!
As they get closer, do they go faster?