One topic regarding Saturn’s rings that I found extremely interesting was the concept of its Shepherd Moons and how they contribute to the uniformity of the rings. If my understanding and memory are correct, this phenomenon is governed by conservation of energy. Essentially, the moons are on opposite sides of the ring, where the moon that has the farthest distance from the planet is moving slower than the closer moon. That’s because of a bunch of physics formulae that illustrate an inverse relationship between velocity and energy (and velocity and radius). Long story short, an equation similar to the gravitational force equation, E=GMm/2r as well as setting up a system of total mechanical energy E = K + U yields E = 1/2mv^2 – GMm/r and we treat E to thus equal GMm/2r when you simplify it. Also, setting the force of gravity equal to centripetal force yields v^2=GM/r which lends to the mathematical proofs of the above relationships.
Aaaanyway, physics aside, the really interesting part about this is how it regulates Saturn’s ring shape! How is it so picture perfect? Well, it’s been a while since I took physics, but basically, if a particle from the ring were to drift, in the direction closer to Saturn, as it’s getting closer to the shepherd moon, the moon will give it a tug…This is because the moon is going even faster (remember, smaller radius, greater velocity), and thus adds extra energy to that system. Remembering that E has an inverse relationship with velocity, now that it has greater energy, it is of a greater radius and lower velocity…aka, it moved to a position farther away from the planet. The opposite also works, but it’s the slower moon on the outer radius that imposes a drag force, if memory serves. Physics might be a drag and tests might be hard but the way it works is undeniably cool!