Final answer:
The varying orbital periods of Saturn's rings provide the strongest proof that they are made of independently orbiting particles, as observed by the Cassini mission.
Step-by-step explanation:
The strongest proof of Saturn's rings being made of independently orbiting particles, rather than a solid sheet of materials, is (e) The rings have different orbital periods. This is indicative of the fact that ring particles are moving independently, as objects in different orbits around a planet will have different periods depending on their distance from the planet.
If the rings were a solid sheet, they would move as a single body with a uniform orbital period. Additional evidence of the particles' independent movement comes from the Cassini mission, which observed waves in the rings caused by embedded moons, as well as low-speed collisions and gravitational interactions between the particles, which behave like waves moving across the ocean.