I was doing mirror polish from early morning today. I decided to start from from 320 grit sand paper to remove those deep scratches. As you can see sides of that flat surface are more polished because it isn't flat.
Here you can still see some original scratches. They are not very deep now.
And here you have a picture after 800 grit paper which unfotunately ran out as well. I have to say that fools rush in where angels fear to tread and now I run out of the sanding paper and I can only use polishing mops. I knew what will happen now but you will see yourself.
Here you can see something I was worried about. If you don't spend enough time on low grits then you will not be able to fix it later on. You can see very nice mirror finish here but with lot of scratches from sanding paper.