I can be a little awkward polishing the hubcap on the car, and it can be a little awkward holding it with one hand and polishing with the other.
So put it on a hub.
Ahh, Steve, if you left them on the car, and did a shoe shine style rag buff on them (over and under), wouldn't that be easy? That's what I do on mine, of course they're not brass, they're nickel. But polishing is work no matter how you do it, might as well take the easiest way. And somehow, removing them, then polishing them and then having to put them back on, just seems to me to be more work than necessary.
Put it on jack stands start it up and let the engine do the work then switch the front caps to the back.
If you have a lathe, turn down a piece of wood so you can slide the cap on it tight enough so it does not spin and polish away.
Get an old hub chuck in a lathe or rig something for a drill press.
It looks like someone shined that hub cap with a wire wheel!
"awkward polishing the hubcap on the car"
Not quite the proper thing to do nowadays but all you need is 4 rags and 4 kids to run alongside yer car while you putter down the driveway a few times!
Get the wife to do it!!!!!!!!!!!!! Makes it much easier for me.
Steve, I use the wood dowel in the lathe approach (see Mikes comments). If set up that way, one can use finer and finer paper grits to get rid of the scratches and pits, then finish with polishing compound to a mirror finish.
I hope no one asks what kind of polish is the best to use on that cap.
Like that'll ever happen in this house Tom!! LOL