Algodoo

Watch closely as these objects orbit. They are locked in resonance orbits. This means they orbit the parent at specific intervals.
the vulcanian object, the closest to its parent, sets the beat for the rest. It is first to complete an orbit, and after each orbit it completes, each object completes its first. The objects will only all align every 680 vulcanian orbits, or 13600 seconds, which is every 3 hours, 46 minutes, and 40 seconds, almost exactly.
The period of each object is its number times 20.
the second object orbits in 2 vulcanian orbits, the third orbits in 3, the fourth 4, and so on.

something interesting for you:
the 8th and 7th only coincide with the spring at the same time every 56 vulcanian orbits, which is every 18 minutes and 42.8 seconds.
All this was calculated by me with the help of my fx-115ES PLUS cala, and i may have misdone some of it. if i have, and it bothers you, let me know.

Thanks for clicking this scene. I'm gonna pretend it's a big help though i don't get much from it.