Almost periodic Hill's equation and the rings of Saturn

Details Almost periodic Hill's equation and the rings of Saturn Almost periodic Hill's equation and the rings of Saturn

Apr 1981

adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1981phrvl..46.1166a&link_type=abstract

Physical Review Letters, vol. 46, Apr. 27, 1981, p. 1166-1168.

Physics

23

Hill Method, Orbit Perturbation, Periodic Functions, Saturn Rings, Grooves, Lebesgue Theorem, Mimas, Set Theory, Spectrum Analysis, Saturn, Rings, Perturbations, Orbits, Spectrum, Grooves, Gaps, Structure, Resonance, Theoretical Studies, Models, Cassini Division, Particles, Satellites, Mimas

Scientific paper

Incommensurate perturbations of classical orbits lead to an almost periodic Hill's operator whose spectrum, it is argued, is a Cantor set, but one with large Lebesgue measure. Applied to the rings of Saturn, this implies that the complex groove structure in the rings approximates a Cantor set. The possible relevance of the sun in producing 'side gaps' which magnify the apparent gap size is also emphasized

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