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August 10, 2015

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Planetary rings follow “beautiful” law wherever they are

Aug. 10, 2015
Courtesy of 
and World Science staff

The par­t­i­cles mak­ing up rings around plan­ets fol­low a “beau­ti­ful” law of size dis­tri­bu­tion that is the same for eve­ry ringed plan­et, ac­cord­ing to the re­search­ers be­hind a new stu­dy. 

The in­ves­ti­ga­tors say they have has solved an age-old sci­en­tif­ic rid­dle. Pub­lished in the jour­nal Pro­ceed­ings of the Na­t­ional Acad­e­my of Sci­ences, the study al­so sug­gests Sat­urn’s rings are bas­ic­ally in a steady state that does­n’t de­pend on their his­to­ry.

A simulated image of Saturn's rings (Credit: NASA)


“Sat­urn’s rings are rel­a­tively well stud­ied and it is known that they con­sist of ice par­t­i­cles rang­ing in size from cen­time­ters to about ten me­ters” or yards, said Ni­ko­lai Bril­liantov from the math­e­mat­ics de­part­ment at the Un­ivers­ity of Leices­ter, U.K., one of the au­thors. 

The par­t­i­cles are probably “re­mains of some cat­a­stroph­ic event in a far past, and it is not sur­pris­ing that there ex­ists de­bris of all sizes,” he added. “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.’”

What this means is that, for ex­am­ple, com­pared to one-meter par­t­i­cles, two-meter par­t­i­cles are one-eighth as com­mon. Three-meter par­t­i­cles, one-twenty-se­venth as com­mon. 

“This holds true up to the size of about 10 me­ters, then fol­lows an ab­rupt drop in the abun­dance of par­t­i­cles,” he went on. “The rea­son for this dras­tic drop, as well as the na­ture of the amaz­ing in­verse-cubes law, has re­mained a rid­dle un­til now.

Artist's con­cept of Sat­urn's ring par­t­i­cles seen close up. The plan­et Sat­urn is seen in the back­ground (yel­low and brown). The par­t­i­cles (blue) are made most­ly of ice, but are not uni­form. They clump to­geth­er to form elon­gat­ed, curved ag­gre­gates, con­tin­u­al­lly form­ing and dis­pers­ing. The space be­tween the clumps is most­ly emp­ty. The larg­est in­di­vid­u­al par­t­i­cles shown are a few me­ters (yards) across. (Cred­it: NA­SA)


“We have fi­nally re­solved the rid­dle,” he added. “In par­tic­u­lar, our study shows that the ob­served dis­tri­bu­tion is not pe­cu­liar for Sat­urn’s rings, but has a uni­ver­sal char­ac­ter”—all plan­etary rings are ex­pect­ed to fol­low it.

Most of the plan­ets in the So­lar Sys­tem have satel­lites or­bit­ing them. Some of them, such as Sat­urn, Ju­pi­ter, Ura­nus and Nep­tune, al­so have rings—a col­lec­tion of still small­er, orbit­ing bod­ies of dif­fer­ent sizes. 

Plan­e­tary rings are al­so ex­pected to ex­ist be­yond the So­lar Sys­tem. More­o­ver, large as­ter­oids such as Chariklo and Chi­ron, though far smaller than plan­ets, al­so sport rings.

“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,” Bril­liantov said. “Such sys­tems ex­ist in na­ture and in­dus­try” and fol­low the in­verse-cubes law as well, he added.


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The particles making up rings around planets follow a “beautiful” law of size distribution that is similar for every ringed planet, according to the researchers behind a new study. The investigators say they have has solved an age-old scientific riddle with the study. Published in the journal Proceedings of the National Academy of Sciences, it also suggests Saturn’s rings are basically in a steady state that doesn’t depend on their history. “Saturn’s rings are relatively well studied and it is known that they consist of ice particles ranging in size from centimeters to about ten meters,” said Nikolai Brilliantov from the mathematics department at the University of Leicester, U.K., one of the authors. The particles are probably “remains of some catastrophic event in a far past, and it is not surprising that there exists debris of all sizes,” he added. “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.’” What this means is that, for example, compared to one-meter particles, two-meter particles are one-eighth as common. Three-meter particles, one-twenty-seventh as common. “This holds true up to the size of about 10 meters, then follows an abrupt drop in the abundance of particles,” he went on. “The reason for this drastic drop, as well as the nature of the amazing inverse-cubes law, has remained a riddle until now. “We have finally resolved the riddle,” he added. “In particular, our study shows that the observed distribution is not peculiar for Saturn’s rings, but has a universal character”—all planetary rings consisting of particles, will follow it. Most of the planets in the Solar System have satellites orbiting them. Some of them, such as Saturn, Jupiter, Uranus and Neptune, also have rings—a collection of still smaller bodies of different sizes that also orbit a planet. Planetary rings are also expected to exist beyond the Solar System. Moreover, large asteroids such as Chariklo and Chiron, though far smaller than planets, also sport rings. “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,” Brilliantov said. “Such systems exist in nature and industry” and follow the inverse-cubes law as well, he added.