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Is there a mathematical relationship here or am I looking for relations when there are none?
When I was taking classical mechanics, we dealt a lot with pendulums, and orbiting bodies problems. For some reason, my intuition is begging that there these two cases are somehow mathematically related.

Given that the strings magically "go through each other" at every rotation, can't this be related to the case in which the two orbiting masses orbit a third body, say a star, located at the center of the axis of rotation?
Again, What relevant equations are needed here to establish a relationship between these two cases? Going even further: This is getting pretty hand wavy, but I was thinking that perhaps this could be a new way of looking at the 3-body problem or multi-body problem using the string and ball model? Not the answer you're looking for?Browse other questions tagged gravity classical-mechanics mathematical-physics orbital-motion unified-theories or ask your own question.

What is the relationship between scale model size and playback rate that looks normal scale in video?
It seems that the as the string twists and the balls get closer and closer to each other, its awfully similar to the case when two bodies in space orbit each other until they collide too!

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