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I call this thing the Orrery of Sarpedon. Sarpedon is a Saturn-like ringed gas giant in the center of the concentric circles. The concentric circles are the orbits of Sarpedon's moons, with the partial arc showing the closest approach of a rogue moon in a particularly eccentric orbit.
Let's say that Sarpedon is in the habitable zone of its star so we can posit a science-fantasy/planetary romance style D&D campaign set on moon E, the next-to-outermost of the regular circles. That orbit corresponds vaguely to Titan's orbit around Saturn.
In lieu of keeping strict time records and tracking orbits at the beginning of each session you can roll d4, d6, d8, d12, d16, d24 and d100 to place the moons in position around Sarpedon. If two or more moons are placed in orbit segments that line up, like say a4 and b6, then you have a Conjunction of those two moons. This allows for all sorts of astrologically based magical effects, like the moons in the Dragonlance books. If the Conjunction is with moon E, the campaign homeworld, then the other moon(s) involved loom extra large in the sky and it's called a Close Approach. Moon G becomes involved in these celestial shenanigans only when the d100 roll comes up between 37 and 68. The rest of the time that moon is just a distant point of light.
If you feel like doing the extra work, you can advance each moon on a daily basis as time passes during the session. Personally, I'm liable to forget to do so and would probably just reroll whenever I remembered that time had passed.
I've been thinking about this concept for a long time. I finally made a draft of the chart in the wake of the recent death of Moebius, who would be one of the inspirational artists for a campaign set on Sarpedon E.