Planetary rings resolve maths mystery
24 Aug 2015 by hjqbcptqcm.d hjqbcptqcm.d
Scientists have discovered that planetary rings such as those orbiting Saturn have a universally similar particle size distribution.
By using mathematical models, an international team of scientists led by the University of Leicester not only found that planetary rings have similar particle size distribution but also resolved a mathematical particle size law.
“We have finally resolved the riddle of particle size distribution. In particular, our study shows that the observed distribution is not peculiar for Saturn's rings, but has a universal character. In other words, it is generic for all planetary rings which have particles to have a similar nature,” said Professor Nikolai Brilliantov from the University of Leicester's Department of Mathematics.
Published in the journal Proceedings of the National Academy of Sciences, the team studied Saturn’s rings and discovered that the abundance of 2 metre-size particles is eight times smaller than the abundance of 1 metre-size particles, the abundance of 3 metre-size particles is 27 times smaller and so on. They discovered the same pattern up to the size of about 10 metres, followed by an abrupt drop in the abundance of particles.
These findings resolved the mathematical relationship between the particle size distributions known as the inverse cube law.
“What is surprising is that the relative abundance of particles of different sizes follows, with a high accuracy, a beautiful mathematical law of inverse cubes. The reason for this drastic drop, as well as the nature of the amazing inverse cubes law, has remained a riddle until now,” said Professor Brilliantov.
The team also found their findings could be applied to other systems such as the Uranian rings, the recently discovered rings of Chariklo and Chiron, and possibly rings around extrasolar objects.
Professor Brilliantov added: “The rather general mathematical model elaborated in the study with the focus on Saturn's rings may be successfully applied to other systems, where particles merge, colliding with slow velocities and break into small pieces colliding with large impact speeds.”
“Such systems exist in nature and industry and will exhibit a beautiful law of inverse cubes and drop in large particle abundance in their particle size distribution.”
