Originally Posted by Jragon
So we have
Luna->Earth->Sol->Solar System's CM->?...->Galaxy CM->Local Group CM->...
How many non-trivial "?" are in there? Is there any formal hierarchy like "group of solar systems"->"cluster of solar system groups"->"group of clusters" etc in between? The terms themselves I made up, but I hope they kind of illustrate what I'm getting at.
None. The Sun orbits the center of mass of the Galaxy. Note however that it's not a simple elliptical orbit, but then you can't appoximate the Galaxy as a point mass, which is a prerequisite for an elliptical orbit.. The Sun kind of bobs up and down "above" and "below" the plane of the galactic disk. If you plotted the path with respect to that plane, it would look like a sine wave with a period of (I think) about 80 million years. Much less than the orbital period, anyway. You can think of this bobbing motion as something vaguely like an orbit about the galactic disk.
While there are star clusters, the Sun is not in one. In general, star clusters are either extremely old (globular clusters, which pre-date the galactic disk) or very young (open or galactic clusters). In general, stars form in clusters, but those evaporate as interactions between the various members eject stars. The Sun left its natal cluster a very long time ago.
Globular clusters evaporate too, but they started with many more stars than open clusters do, so they haven't completely evaporated yet. The stars that are left are orbiting very close to each other compared to stars in the galactic disk. And sometimes they do collide. When they do they form blue stragglers
Sorry for any confusion I caused. I suppose I should have said "almost certainly won't collide" or something like that.