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Each asteroid would be represented by a grain of sand. All grains being individually connected to the central motor and appropriately complex gearing system by tiny "L" shaped prongs, which never bump into each other, because of the precise engineering.
(simplex version consists of a brick on each
end of a string that you whirl around, while standing in the middle of a field)
||The Comet Orrery presumably uses telescopic prongs?