AC10
Saturn’s ring waves: from orbits to starlight
Ice moves through the patterns in Saturn rings. Follow local moon-forced trajectories, derive their missing starlight, and replay a frozen Cassini occultation before reading about self-gravity and age.
L1
How a small moon writes a stripe in Saturn’s rings
Follow moving ice through a moon’s disturbance, distinguish a wave from its particles, and see how Cassini measured the stripes with starlight.
L2
Derive the motion of a small patch of a planetary ring
Derive Kepler shear and Hill motion, solve the free epicycle, and follow how moon kicks and inelastic collisions change a local ring patch.
L3
From a ring’s moving particles to its missing starlight
Derive an occultation from particle columns and photon noise, then learn which extra assumptions let a global density-wave spacing constrain mass.
L3
Replay a real Cassini ring occultation, including its failed fits
Reconstruct optical depth from frozen UVIS counts and geometry, measure local ring-structure scales, and test counting noise, resolution and model failure.
L4
Read from self-gravity wakes to the uncertain age of Saturn’s rings
Follow pinned papers from collective particle structures to transport and pollution ages, separating observations, simulations and unmeasured assumptions.
Sources and calculation scope
- Rein & Tremaine, Symplectic integrators in the shearing sheet, arXiv v2
19April2011 revision; Sections2–3, Hill equations and exact epicycle splitting; Section4 and Figures1–4, free/perturbed trajectory tests. We implement a planar exact-free-motion/symmetric-kick method with an explicitly softened prescribed moon, not their full many-body calculation.
- NASA NSSDCA Saturn Fact Sheet
Updated18March2025, consulted28October2026. Bulk GM and radius establish the physical scale; the Lab adopts the fixed gravitational parameter and reference radius displayed in the course as teaching inputs, not an ephemeris fit or updated gravity solution. The source lists a rounded GM.
- Cassini UVIS alpha Arae2008-261 egress, original PDS3 product label
Product creation27November2020; CO-SR-UVIS-HSP-2/4-OCC-V3.0. Read all12column definitions, elevation54.4degrees,110–190nm band,121-byte records, background-unsubtracted mean counts, star/background models, samples-per-bin, sensitivity threshold and NOTE_FLAG definitions. Exact archived label and1001source rows are preserved for offline replay.
- NASA PDS Cassini UVIS archive README, version3.0
Volume README, dataset citation and organization; version3.0 authors Colwell/Jerousek/Becker/Esposito,2020. Preserved original bytes and hashes. The general UVIS landing page still describes an older v2 release; this course freezes the actual v3 label/README.
- Colwell et al., Cassini UVIS stellar occultation observations of Saturn’s rings
AJ140,1569–1578,2010. Observing geometry, reduction and occultation table including alpha Arae Rev85/2008-261. Consulted primary indexed article text and original PDS product definitions; the tutorial repeats the archived binned-count conversion, not the paper’s full unbinned calibration or global wave analysis.
- Goldreich & Tremaine, The excitation and evolution of density waves
Published ApJ222,850–858,15June1978; full author-archive PDF read, SectionII equations4–17 (especially9,11–15): thin self-gravitating sheet, tightly wound dispersion, resonances and wave winding. Course gives its own Kepler-limit expansion; finite pressure, oblateness and nonlinear waves remain separate limits.
- Salo & Mondino-Llermanos, Photometric modelling of self-gravity wakes and overstable oscillations
Published3March2025, A&A695,A37. Selected original indexed sections4.2/Figure5 (weak-gravity asymmetry and correlation checks), Figure4 (photometric regimes),8.3/AppendixB (transport contributions), and hybrid-model limitations. Primary full-text HTML was available through indexed excerpts; the whole29-page numerical study was not reproduced.
- Kempf et al., Micrometeoroid infall onto Saturn’s rings constrains their age
Published12May2023, Science Advances9,eadf8537; original full-text archive: Results, Figure1, incoming-flux selection and exposure-age conversion. Distinguish measured instrument signatures, inferred external flux and a pollution time conditioned on focusing/retention/initial composition.
- Ricerchi & Crida, Saturn’s rings age I., arXiv v1
4March2026, accepted for Icarus according to arXiv metadata; pin v1. Sections2(planar focusing),3(composition evolution, equations10–14),4.1–4.3(retention, vaporization, cleaning), Figures7–8. Original selected sections read; no billion-year transport or impact-physics reproduction is claimed.