Mathematics can be incredibly beautiful, and in new research on planetary rings, it proves its grandeur once again.

An international team of researchers has found that the distribution of debris sizes in Saturn’s rings is not unique to the gas giant, but likely universal to all planets, and follows a law of inverse cubes. And the scientists also think that they have solved the mystery of why this happens, and in particular why there is a sharp drop in the abundance of ice and dust debris in the rings as it grows in size. The research is published in the journal Proceedings of the National Academy of Sciences (PNAS).

Creating a mathematical model of ring debris distribution, the scientists found that particles two meters (6.6 feet) in size were eight times less abundant than those one meter (3.3 feet) in size. Three-meter-sized (10 feet) particles were 27 times less abundant, and so on. 

“This holds true up to the size of about 10 meters [33 feet], then follows an abrupt drop in the abundance of particles,” said Professor Brilliantov from the University of Leicester, which was part of the team, in a statement. But until now, the reason for this drop had remained a mystery.

Now the scientists think that they have the answer. They found that over time in the rings, smaller particles will “stick” together at low speeds and form larger particles. But the larger a particle gets, the greater the chance of a high-speed collision that could destroy it, rather than stick to it, with a probability of about 1 in 10,000. 

“Think of it as a big soup of billiard balls,” Jürgen Schmidt from the University of Oulu in Finland, also part of the study, told IFLScience.

“It is this sticking that creates the whole size distribution,” he continued. “It goes on for larger and larger clusters, then at some point, there are more violent collisions, and it breaks the clusters into small pieces, and they go through the whole process and climb that ladder again.” He said that the process typically took just a few weeks.

Schmidt said that evidence for this model was supported by data from the Cassini and Voyager spacecraft. And while observational evidence doesn’t exist for other bodies, the team was fairly confident that other planets and asteroids with rings, even those outside the Solar System, would follow this elegant mathematical law.