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https://books.google.com/books?id=RVlEAAAAQBAJ&pg=PA46&lpg=PA46&dq=saturn%27s+rings+rational+numbers+unstable&source=bl&ots=ncGbmhn0J7&sig=ACfU3U1CEkSSdTaHNP8184GNWU_1UqcHbQ&hl=en&sa=X&ved=2ahUKEwiRlZTE8obgAhVBS60KHQ9sCiwQ6AEwAHoECAcQAQ#v=onepage&q=saturns%20rings%20rational%20numbers%20unstable&f=false

Gaps in the Saturn Rings A spectacular example of the instability of rational KAM-tori are the gaps in the rings of the planet Saturn.

The time a particle orbiting in Cassini's gap (between the A-ring and the B-ring, r=118,000km) would need around Saturn is exactly half the time the "shepherd-moon" Mimas needs to orbit Saturn. The quotient of the revolving frequencies is 2:1. Any particle orbiting in Cassini's gap is therefore unstable against the perturbation caused by Mimas and it is consequently thrown out of its orbit.

Here are some other references I ran across while looking:

http://citeseerx.ist.psu.edu/viewdoc/download?doi=10.1.1.456.4816&rep=rep1&type=pdf

http://www.talkorigins.org/indexcc/CE/CE240.html

https://books.google.com/books?id=ULfVoJE3TjIC&pg=PA240&lpg=PA240&dq=rational+numbers+cause+destabilizing+resonances&source=bl&ots=S1YrZ9g-o0&sig=ACfU3U2YqiHkmZaUU3ybRYycxi6uxZp4XA&hl=en&sa=X&ved=2ahUKEwiQr4uk8YbgAhUGQ60KHfOGDk4Q6AEwEnoECAkQAQ#v=onepage&q=rational%20numbers%20cause%20destabilizing%20resonances&f=false

http://www.ptep-online.com/2005/PP-01-08.PDF

https://www.interscalar.com/wp-content/uploads/2018/11/GSCompendiumV2.0.pdf

And this article would be great to submit to the site, if someone wants to send it over to /l/space:

https://news.nationalgeographic.com/news/2010/03/100318-saturn-rings-unstable-scitech-oxygen-atmosphere/



2 points by rain1 671 days ago

Not just understanding more about how that structure came about but that Saturn's rings are new!

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