As space exploration continues, the job for these guys just gets harder and harder. Some of the latest moon counts include...
Jupiter - 69
Saturn - 53
Uranus - 27
Neptune - 14
Of course, many of these are very minor moons so wouldn't be modeled in an orrery.
I've never seen one with the outer gas giants (Uranus and Neptune) modeled. Note also that the near 90 degree tilt of Uranus' spin axis is correctly shown. Its spin axis lies almost in the ecliptic plane and thus its moons orbit in and out of the plane.
Fascinating work. Given their skills, they should try to build a model of the Antikythera mechanism.

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