For the jam, I mocked up a danglezone.  Toby used an orrery model to motivate early Apparatus, so I made a dangly orrery, with sun, earth, moon, mars, comet, and giant space fish.  (I had run out of astronomical objects and started thinking about a dangly aquarium instead.)

The objects are suspended from magnetic hooks that can be moved using "robots" (dragging handles) on top of the ceiling.  Each suspension point can be raised or lowered with a "winch" (pulling on the string).

I was imagining a three-dimensional physical Apparatus, where one could bring in objects by hand and define mathematical relationships between them, and then as you move an object by hand, the other objects move automatically.  It's an Apparatus you can stand inside with other people and manipulate with your hands.

Like most dangly things, it doesn't photograph well.

Here's a video of the earth and a comet going around the sun.