Remove skylight & burned-in dirt with scouring milk
If over time on the skylight the dirt from the sun's rain has burnt down on the glass, then you only get it away with commercially available scouring cream. I have not found a better remedy yet. All previous funds have absolutely nothing brought.
After thoroughly cleaning the disc with scouring milk, it becomes really clear again.
Attention: Scratches did not occur to me. But to be on the safe side, first clean a small spot in the corner of the window and check if the scrubbing liquid does not cause scratches.