There is a simple recipe for shining up a copper bottom pan:
Salt and Vinegar + bit of elbow grease. That's it!
Sprinkle salt on the bottom of the kettle. Add some vinegar to a paper towel or other scrubbing device and start working in a circular motion.
Just plain white vinegar works fine.
This is Himalayan salt, but just any normal granulated salt works.
Keep scrubbing in a circular motion, adding more salt and vinegar as needed.
Was able to remove most of the burnt on food and discoloration before my arm decided it had had enough of a workout for one day.
Just rinse when done and dry with a towel. Easy as pie. :)