I had an idea, but cannot try it out coz I am at work.... maybe someone else can run with it.
Each planet name is spelled out on the other planets. What if we assume the "dots" are holes, and place each planet one at a time in reverse order over the disc of the planet, rotating the top disc so the letter from the planet name matches the location of the planet symbol.
Um, so, on earth you would have a pile with Mercury then Jupiter, Neptune, Venus, Saturn and Earth on the bottom. Mercury would rotate once counter clockwise, Jupiter twice clockwise.... etc