I swear, sometimes it's hard to believe that any of you people actually
cook.

Of course ketchup works. Not all that easily, but it works.

When you cook a lot with copper pans, one thing you quickly learn is
that any tomato-based liquid that drips or runs onto the outside of the
pan will remove the patina instantly.

The only time I ever remove the patina completely from a copper pan is
if I've accidentally gotten tomato sauce over the lip. Then you have to
clean the entire pan, or live with a streaky, dirty-looking dark finish
permanently. Even this matters only if you hang your pans on display.

If I have to clean the outside of one of my copper pans, I use Red Bear.
It works in seconds, using just a sponge.

-- Larry