Q: How can I minimize the shiny marks on my satin finish oak dining room table, caused by being rubbed with a cloth during cleaning? It looks terrible when the sun shines on it.
A: In my experience you can’t make a satin finish shiny by rubbing it.
It is more likely there is contamination on the finish making it look more dull and the rubbed spots have removed that.
It could be furniture polish, oil soaps. Even some mopping products which contain wax will leave contamination. I would suggest you get a cleaner from your local hardwood dealer, meant to be used on polyurethane finishes.