Abstract
Planetary rings are the only nearby astrophysical disks and the only disks that have been investigated by spacecraft (especially the Cassini spacecraft orbiting Saturn). Although there are significant differences between rings and other disks, chiefly the large planet/ring mass ratio that greatly enhances the flatness of rings (aspect ratios as small as 10− 7), understanding of disks in general can be enhanced by understanding the dynamical processes observed at close range and in real time in planetary rings.We review the known ring systems of the four giant planets, as well as the prospects for ring systems yet to be discovered. We then review planetary rings by type. The A, B, and C rings of Saturn, plus the Cassini Division, comprise our solar system’s only dense broad disk and host many phenomena of general application to disks including spiral waves, gap formation, self-gravity wakes, viscous overstability and normal modes, impact clouds, and orbital evolution of embedded moons. Dense narrow rings are found both at Uranus (where they comprise the main rings entirely) and at Saturn (where they are embedded in the broad disk) and are the primary natural laboratory for understanding shepherding and self-stability. Narrow dusty rings, likely generated by embedded source bodies, are surprisingly found to sport azimuthally confined arcs at Neptune, Saturn, and Jupiter. Finally, every known ring system includes a substantial component of diffuse dusty rings.Planetary rings have shown themselves to be useful as detectors of planetary processes around them, including the planetary magnetic field and interplanetary impactors as well as the gravity of nearby perturbing moons. Experimental rings science has made great progress in recent decades, especially numerical simulations of self-gravity wakes and other processes but also laboratory investigations of coefficient of restitution and spectroscopic ground truth. The age of self-sustained ring systems is a matter of debate; formation scenarios are most plausible in the context of the early solar system, while signs of youthfulness indicate at least that rings have never been static phenomena.
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Notes
- 1.
The Laplace plane is the plane about which orbits precess. When the vertical motions of objects are damped by mutual collisions, material will settle into a ring centered on the Laplace plane.
- 2.
Throughout this work, we will use the word “dust” to refer to μm-sized particles regardless of their composition.
- 3.
The phase angle is formed by the Sun-object-observer lightpath. Dust-sized particles, having size comparable to the wavelength of visible light, tend to diffract light forward and are brightest at high phase angles. Larger objects tend to reflect light and are brightest at low phase angles.
- 4.
As recently formalized by the IAU, a “division” is defined as a region between two lettered rings that contains a sheet of material, while a “gap” is a clear region within a lettered ring that may or may not contain one or more ringlets (http://planetarynames.wr.usgs.gov/append8.html).
- 5.
Credit: G. H. Jones in JPL podcast, 6 March 2008 (http://www.jpl.nasa.gov/podcast/content.cfm?content=671)
- 6.
Here, we refer to the inclination of the planet’s equatorial plane with respect to the line of sight from Earth.
- 7.
along with the three planets of the HR 8799 system, announced at the same time
- 8.
For brevity, this discussion is limited to inner Lindblad resonances and inner vertical resonances, where the disk is inward of the forcing moon. Nearly all known spiral waves in rings are of this kind, though Tiscareno et al. (2007) detected inwardly propagating spiral density waves excited by outer Lindblad resonances with Pan.
- 9.
The azimuthal parameter m gives the number of spiral arms in the resonant wave pattern, while k + 1 is the “order” of the resonance, with first-order resonances generally being strongest, followed by second-order, etc.
- 10.
The exception is the nodal resonance, labeled − 1:0, in which the mean motion of the ring particles is resonant with the forcing moon’s nodal precession \({\dot{\Omega}}\). This peculiar resonance has a negative pattern speed, and its bending wave propagates outward (Rosen and Lissauer 1988).
- 11.
Moonlet wakes have little in common with self-gravity wakes (3.1.4), despite an unfortunate similarity in terminology.
- 12.
The periodicity of this alignment was recalculated by Chavez (2009), using updated orbital data.
- 13.
For Saturn’s Anthe and Methone arcs, as for Neptune’s Galatea arc, the circumferential ring is too faint to have been detected as yet but likely consists of material recently escaped from the arc-confining mechanism.
- 14.
References
Acuna, M. H., & Ness, N. F. 1976, The main magnetic field of Jupiter. J. Geophys. Res., 81, 2917–2922
Agarwal, M., Tiscareno, M. S., Hedman, M. M., & Burns, J. A. 2008, Dynamics of faint rings associated with Methone, Anthe and Pallene. AAS Div. Planet. Sci. Meet. Abstr., 40, 30.02
Agarwal, M., Tiscareno, M. S., Hedman, M. M., & Burns, J. A. 2009, Dynamics of rings and arcs associated with three small moons of Saturn: Methone, Anthe and Pallene. AAS Div. Dyn. Astron. Meet. Abstr., 40, 3.05
Albers, N., Sremčević, M., Colwell, J. E., & Esposito, L. W. 2012, Saturn’s F ring as seen by Cassini UVIS: kinematics and statistics. Icarus, 217, 367–388
Alexander, A. F. O. 1962, The Planet Saturn: A History of Observation, Theory and Discovery (London: Faber and Faber)
Andrews, J. P. 1930, Theory of collision of spheres of soft metals. Phil. Mag. Ser. 7, 9, 593–610
Barnes, J. W., & Fortney, J. J. 2004, Transit detectability of ring systems around extrasolar giant planets. Astrophys. J., 616, 1193–1203
Beurle, K., Murray, C. D., Williams, G. A., Evans, M. W., Cooper, N. J., & Agnor, C. B. 2010, Direct evidence for gravitational instability and moonlet formation in Saturn’s rings. Astrophys. J. Lett., 718, L176–L180
Borderies, N., & Longaretti, P. Y. 1987, Description and behavior of streamlines in planetary rings. Icarus, 72, 593–603
Borderies-Rappaport, N., & Longaretti, P.-Y. 1994, Test particle motion around an oblate planet. Icarus, 107, 129–141
Borderies, N., Goldreich, P., & Tremaine, S. 1983, The dynamics of elliptical rings. Astron. J., 88, 1560–1568
Borderies, N., Goldreich, P., & Tremaine, S. 1984, Unsolved problems in planetary ring dynamics, in Planetary Rings, ed. R. Greenberg, & A. Brahic (Tucson: University of Arizona Press), 713–734
Bosh, A. S., Olkin, C. B., French, R. G., & Nicholson, P. D. 2002, Saturn’s F ring: kinematics and particle sizes from stellar occultation studies, Icarus, 157, 57–75
Bridges, F. G., Hatzes, A., & Lin, D. N. C. 1984, Structure, stability and evolution of Saturn’s rings. Nature, 309, 333–335
Brown, T. M., Charbonneau, D., Gilliland, R. L., Noyes, R. W., & Burrows, A. 2001, Hubble Space Telescope time-series photometry of the transiting planet of HD 209458. Astrophys. J., 552, 699–709
Burns, J. A., & Cuzzi, J. N. 2006, Our local astrophysical laboratory. Science, 312, 1753–1755
Burns, J. A., Lamy, P. L., & Soter, S. 1979, Radiation forces on small particles in the solar system. Icarus, 40, 1–48
Burns, J. A., Showalter, M. R., & Morfill, G. E. 1984, The ethereal rings of Jupiter and Saturn, in Planetary Rings, ed. R. Greenberg, & A. Brahic (Tucson: University of Arizona Press), 200–272
Burns, J. A., Schaffer, L. E., Greenberg, R. J., & Showalter, M. R. 1985, Lorentz resonances and the structure of the Jovian ring. Nature, 316, 115–119
Burns, J. A., Showalter, M. R., Hamilton, D. P., Nicholson, P. D., de Pater, I., Ockert-Bell, M. E., & Thomas, P. C. 1999, The formation of Jupiter’s faint rings. Science, 284, 1146–1150
Burns, J. A., Hamilton, D. P., & Showalter, M. R. 2001, Dusty rings and circumplanetary dust: observations and simple physics, in Interplanetary Dust, ed. E. Grün, B. Å. S. Gustafson, S. Dermott, & H. Fechtig (Berlin: Springer), 641–725
Burns, J. A., Simonelli, D. P., Showalter, M. R., Hamilton, D. P., Porco, C. D., Throop, H., & Esposito, L. W. 2004, Jupiter’s ring-moon system, in Jupiter: The Planet, Satellites and Magnetosphere, ed. F. Bagenal, T. E. Dowling, & W. B. McKinnon (Cambridge: Cambridge University Press), 241–262
Canup, R. M. 2010, Origin of Saturn’s rings and inner moons by mass removal from a lost Titan-sized satellite. Nature, 468, 943–926
Canup, R. M., & Esposito, L. W. 1995, Accretion in the Roche zone: coexistence of rings and ring moons. Icarus, 113, 331–352
Canup, R. M., & Ward, W. R. 2002, Formation of the Galilean satellites: conditions of accretion. Astron. J., 124, 3404–3423
Canup, R. M., & Ward, W. R. 2006, A common mass scaling for satellite systems of gaseous planets. Nature, 441, 834–839
Chandrasekhar, S. 1969, Ellipsoidal Figures of Equilibrium (New Haven: Yale University Press)
Charnoz, S., Porco, C. C., Déau, E., Brahic, A., Spitale, J. N., Bacques, G., & Baillie, K. 2005, Cassini discovers a kinematic spiral ring around Saturn. Science, 310, 1300–1304
Charnoz, S., Brahic, A., Thomas, P. C., & Porco, C. C. 2007, The equatorial ridges of Pan and Atlas: terminal accretionary ornaments? Science, 318, 1622–1624
Charnoz, S., Dones, L., Esposito, L. W., Estrada, P. R., & Hedman, M. M. 2009a, Origin and evolution of Saturn’s ring system, in Saturn from Cassini-Huygens, ed. M. Dougherty, L. Esposito, & S. M. Krimigis (Dordrecht: Springer), 537–575
Charnoz, S., Morbidelli, A., Dones, L., & Salmon, J. 2009b, Did Saturn’s rings form during the Late Heavy Bombardment? Icarus, 199, 413–428
Charnoz, S., Salmon, J., & Crida, A. 2010, The recent formation of Saturn’s moonlets from viscous spreading of the main rings. Nature, 465, 752–754
Charnoz, S., et al. 2011, Accretion of Saturn’s mid-sized moons during the viscous spreading of young massive rings: solving the paradox of silicate-poor rings versus silicate-rich moons. Icarus, 216, 535–550
Chavez, C. E. 2009, Appearance of Saturn’s F ring azimuthal channels for the anti-alignment configuration between the ring and Prometheus. Icarus, 203, 233–237
Chiang, E. I., & Goldreich, P. 2000, Apse alignment of narrow eccentric planetary rings. Astrophys. J., 540, 1084–1090
Colombo, G., Goldreich, P., & Harris, A. W. 1976, Spiral structure as an explanation for the asymmetric brightness of Saturn’s A ring. Nature, 264, 344–345
Colwell, J. E., Esposito, L. W., & Sremčević, M. 2006, Self-gravity wakes in Saturn’s A ring measured by stellar occultations from Cassini. Geophys. Res. Lett., 33, L07201
Colwell, J. E., Esposito, L. W., Sremčević, M., Stewart, G. R., & McClintock, W. E. 2007, Self-gravity wakes and radial structure of Saturn’s B ring. Icarus, 190, 127–144
Colwell, J. E., et al. 2008, Ejecta from impacts at 0.2–2.3 m/s in low gravity. Icarus, 195, 908–917
Colwell, J. E., Cooney, J. H., Esposito, L. W., & Sremčević, M. 2009a, Density waves in Cassini UVIS stellar occultations. 1. The Cassini division. Icarus, 200, 574–580
Colwell, J. E., Nicholson, P. D., Tiscareno, M. S., Murray, C. D., French, R. G., & Marouf, E. A. 2009b, The structure of Saturn’s rings, in Saturn from Cassini-Huygens, ed. M. Dougherty, L. Esposito, & S. M. Krimigis (Dordrecht: Springer), 375–412
Colwell, J. E., Jerousek, R. G., & Esposito, L. W. 2010, Sharp edges in Saturn’s rings: radial structure and longitudinal variability. AAS Div. Planet. Sci. Meet. Abstr., 42, 50.01
Cooper, J. F., Eraker, J. H., & Simpson, J. A. 1985, The secondary radiation under Saturn’s A-B-C rings produced by cosmic ray interactions. J. Geophys. Res., 90, 3415–3427
Crida, A., Papaloizou, J. C. B., Rein, H., Charnoz, S., & Salmon, J. 2010, Migration of a moonlet in a ring of solid particles: theory and application to Saturn’s propellers. Astron. J., 140, 944–953
Cuzzi, J. N., & Burns, J. A. 1988, Charged particle depletion surrounding Saturn’s F ring: evidence for a moonlet belt? Icarus, 74, 284–324
Cuzzi, J. N., & Scargle, J. D. 1985, Wavy edges suggest moonlet in Encke’s gap. Astrophys. J., 292, 276–290
Cuzzi, J., Clark, R., Filacchione, G., French, R., Johnson, R., Marouf, E., & Spilker, L. 2009, Ring particle composition and size distribution, in Saturn from Cassini-Huygens, ed. M. Dougherty, L. Esposito, & S. M. Krimigis (Dordrecht: Springer), 459–509
Cuzzi, J. N., et al. 2010, An evolving view of Saturn’s dynamic rings. Science, 327, 1470–1475
Daubechies, I. 1992, Ten Lectures on Wavelets (Philadelphia: SIAM)
Dawson, R. I., French, R. G., & Showalter, M. R. 2010, Packed perturbers: short-term interactions among Uranus’ inner moons. AAS Div. Dyn. Astron. Meet. Abstr., 41, 8.07
de Pater, I., Martin, S. C., & Showalter, M. R. 2004, Keck near-infrared observations of Saturn’s E and G rings during Earth’s ring plane crossing in August 1995. Icarus, 172, 446–454
de Pater, I., Gibbard, S. G., Chiang, E., Hammel, H. B., Macintosh, B., Marchis, F., Martin, S. C., Roe, H. G., & Showalter, M. 2005, The dynamic neptunian ring arcs: evidence for a gradual disappearance of Liberté and resonant jump of Courage. Icarus, 174, 263–272
de Pater, I., Hammel, H. B., Gibbard, S. G., & Showalter, M. R. 2006, New dust belts of Uranus: one ring, two ring, red ring, blue ring. Science, 312, 92–94
de Pater, I., Hammel, H. B., Showalter, M. R., & van Dam, M. A. 2007, The dark side of the rings of Uranus. Science, 317, 1888–1890
Denk, T., et al. 2010, Iapetus: unique surface properties and a global color dichotomy from Cassini imaging. Science, 327, 435–439
Dermott, S. F., & Murray, C. D. 1980, Origin of the eccentricity gradient and the apse alignment of the epsilon ring of Uranus. Icarus, 43, 338–349
Dilley, J., & Crawford, D. 1996, Mass dependence of energy loss in collisions of icy spheres: an experimental study. J. Geophys. Res., 101, 9267–9270
Dones, L., & Porco, C. C. 1989, Spiral density wakes in Saturn’s A ring? Bull. Am. Astron. Soc. 21, 929
Dumas, C., Terrile, R. J., Smith, B. A., Schneider, G., & Becklin, E. E. 1999, Stability of Neptune’s ring arcs in question. Nature, 400, 733–735
Duncan, M. J., & Lissauer, J. J. 1997, Orbital stability of the Uranian satellite system. Icarus, 125, 1–12
Durda, D. D., Movshovitz, N., Richardson, D. C., Asphaug, E., Morgan, A., Rawlings, A. R., & Vest, C. 2011, Experimental determination of the coefficient of restitution for meter-scale granite spheres. Icarus, 211, 849–855
Durisen, R. H., Cramer, N. L., Murphy, B. W., Cuzzi, J. N., Mullikin, T. L., & Cederbloom, S. E. 1989, Ballistic transport in planetary ring systems due to particle erosion mechanisms I. Theory, numerical methods, and illustrative examples. Icarus, 80, 136–166
Durisen, R. H., Bode, P. W., Cuzzi, J. N., Cederbloom, S. E., & Murphy, B. W. 1992, Ballistic transport in planetary ring systems due to particle erosion mechanisms II. Theoretical models for Saturn’s A- and B-ring inner edges. Icarus, 100, 364–393
Elliot, J. L., Dunham, E., & Mink, D. 1977, The rings of Uranus. Nature, 267, 328–330
Elliott, J. P., & Esposito, L. W. 2011, Regolith depth growth on an icy body orbiting Saturn and evolution of bidirectional reflectance due to surface composition changes. Icarus, 212, 268–274
Esposito, L. W. 2006, Cassini observations and the history of Saturn’s rings. AGU Fall Meeting Abstracts, P23E-0110
Esposito, L. W. 2010, Composition, structure, dynamics, and evolution of Saturn’s rings. Ann. Rev. Earth Planet. Sci., 38, 383–410
Esposito, L. W., Brahic, A., Burns, J. A., & Marouf, E. A. 1991, Particle properties and processes in Uranus’ rings, in Uranus, ed. J. T. Bergstralh, E. D. Miner, & M. S. Matthews (Tucson: University of Arizona Press), 410–465
Esposito, L. W., Meinke, B. K., Colwell, J. E., Nicholson, P. D., & Hedman, M. M. 2008, Moonlets and clumps in Saturn’s F ring. Icarus, 194, 278–289
Farmer, A. J., & Goldreich, P. 2005, Spoke formation under moving plasma clouds. Icarus, 179, 535–538
Fillius, R. W., McIlwain, C. E., & Mogro-Campero, A. 1975, Radiation belts of Jupiter: a second look. Science 188, 465–467
Foryta, D. W., & Sicardy, B. 1996, The dynamics of the neptunian Adams ring’s arcs. Icarus, 123, 129–167
Franklin, F. A., Cook, A. F., Barrey, R. T. F., Roff, C. A., Hunt, G. E., & de Rueda, H. B. 1987, Voyager observations of the azimuthal brightness variations in Saturn’s rings. Icarus, 69, 280–296
French, R. S., & Showalter, M. R. 2011, Cupid is doomed: an analysis of the stability of the inner Uranian satellites. AAS Div. Dyn. Astron. Meet. Abstr., 42, 6.02
French, R. G., Nicholson, P. D., Porco, C. C., & Marouf, E. A. 1991, Dynamics and structure of the Uranian rings, in Uranus, ed. J. T. Bergstralh, E. D. Miner, & M. S. Matthews, (Tucson: University of Arizona Press), 327–409
French, R. G., et al. 1993, Geometry of the Saturn system from the 3 July 1989 occultation of 28 SGR and Voyager observations. Icarus, 103, 163–214
Gaudi, B. S., Chang, H., & Han, C. 2003, Probing structures of distant extrasolar planets with microlensing. Astrophys. J., 586, 527–539
Giese, B., Denk, T., Neukum, G., Roatsch, T., Helfenstein, P., Thomas, P. C., Turtle, E. P., McEwen, A., & Porco, C. C. 2008, The topography of Iapetus’ leading side. Icarus, 193, 359–371
Goertz, C. K., & Morfill, G. 1983, A model for the formation of spokes in Saturn’s rings. Icarus, 53, 219–229
Goldreich, P., & Tremaine, S. 1978a, The velocity dispersion in Saturn’s rings. Icarus, 34, 227–239
Goldreich, P., & Tremaine, S. 1978b, The formation of the Cassini division in Saturn’s rings. Icarus, 34, 240–253
Goldreich, P., & Tremaine, S. 1979a, Towards a theory for the Uranian rings. Nature, 277, 97–99
Goldreich, P., & Tremaine, S. 1979b, Precession of the epsilon ring of Uranus. Astron. J., 84, 1638–1641
Goldreich, P., & Tremaine, S. 1980, Disk-satellite interactions. Astrophys. J., 241, 425–441
Goldreich, P., & Tremaine, S. 1981, The origin of the eccentricities of the rings of Uranus. Astrophys. J., 243, 1062–1075
Goldreich, P., & Tremaine, S. 1982, The dynamics of planetary rings. Ann. Rev. Astron. Astrophys., 20, 249–283
Goldreich, P., Tremaine, S., & Borderies, N. 1986, Towards a theory for Neptune’s arc rings. Astron. J., 92, 490–494
Goldreich, P., Murray, N., Longaretti, P. Y., & Banfield, D. 1989, Neptune’s story. Science, 245, 500–504
Hahn, J. M. 2007, The secular evolution of a close ring-satellite system: the excitation of spiral bending waves at a nearby gap edge. Astrophys. J., 665, 856–865
Hahn, J. M. 2008, The secular evolution of a close ring-satellite system: the excitation of spiral density waves at a nearby gap edge. Astrophys. J., 680, 1569–1581
Hahn, J. M., Spitale, J. N., & Porco, C. C. 2009, Dynamics of the sharp edges of broad planetary rings. Astrophys. J., 699, 686–710
Halme, V.-P., Salo, H., Sremčević, M., Albers, N., Schmidt, J., Seiss, M., & Spahn, F. 2010, Dynamical and photometric simulations of propeller features in Saturn’s A ring. AAS Div. Planet. Sci. Meet. Abstr., 42, 50.02
Hamilton, D. P. 1996, The asymmetric time-variable rings of Mars. Icarus, 119, 153–172
Hamilton, D. P. 2006, The collisional cascade model for Saturn’s ring spokes. AAS Div. Planet. Sci. Meet. Abstr., 38, 51.04
Hamilton, D. P., & Krüger, H. 2008, The sculpting of Jupiter’s gossamer rings by its shadow. Nature, 453, 72–75
Hänninen, J., & Porco, C. 1997, Collisional simulations of Neptune’s ring arcs. Icarus, 126, 1–27
Hatzes, A. P., Bridges, F. G., & Lin, D. N. C. 1988, Collisional properties of ice spheres at low impact velocities. Mon. Not. Roy. Astron. Soc., 231, 1091–1115
Hatzes, A. P., Bridges, F., Lin, D. N. C., & Sachtjen, S. 1991, Coagulation of particles in Saturn’s rings: measurements of the cohesive force of water frost. Icarus, 89, 113–121
Hedman, M. M., et al. 2005, Morphology, movements and models of ringlets in Saturn’s Encke gap. AAS Div. Planet. Sci. Meet. Abstr., 37, 64.01
Hedman, M. M., Nicholson, P. D., Salo, H., Wallis, B. D., Buratti, B. J., Baines, K. H., Brown, R. H., & Clark, R. N. 2007a, Self-gravity wake structures in Saturn’s A ring revealed by Cassini VIMS. Astron. J., 133, 2624–2629
Hedman, M. M., Burns, J. A., Tiscareno, M. S., & Porco, C. C. 2007b, The heliotropic rings of Saturn. AAS Div. Planet. Sci. Meet. Abstr., 39, 10.09
Hedman, M. M., et al. 2007c, Saturn’s dynamic D ring. Icarus, 188, 89–107
Hedman, M. M., Burns, J. A., Tiscareno, M. S., Porco, C. C., Jones, G. H., Roussos, E., Krupp, N., Paranicas, C., & Kempf, S. 2007d, The source of Saturn’s G ring. Science, 317, 653–656
Hedman, M. M., Nicholson, P. D., Showalter, M. R., Brown, R. H., Buratti, B. J., & Clark, R. N. 2009a, Spectral observations of the Enceladus plume with Cassini-VIMS. Astrophys. J., 693, 1749–1762
Hedman, M. M., Murray, C. D., Cooper, N. J., Tiscareno, M. S., Beurle, K., Evans, M. W., & Burns, J. A. 2009b, Three tenuous rings/arcs for three tiny moons. Icarus, 199, 378–386
Hedman, M. M., Burns, J. A., Tiscareno, M. S., & Porco, C. C. 2009c, Organizing some very tenuous things: resonant structures in Saturn’s faint rings. Icarus, 202, 260–279
Hedman, M. M., Nicholson, P. D., Baines, K. H., Buratti, B. J., Sotin, C., Clark, R. N., Brown, R. H., French, R. G., & Marouf, E. A. 2010a, The architecture of the Cassini division. Astron. J., 139, 228–251
Hedman, M. M., Burt, J. A., Burns, J. A., & Tiscareno, M. S. 2010b, The shape and dynamics of a heliotropic dusty ringlet in the Cassini division. Icarus, 210, 284–297
Hedman, M. M., Cooper, N. J., Murray, C. D., Beurle, K., Evans, M. W., Tiscareno, M. S., & Burns, J. A. 2010c, Aegaeon (Saturn LIII), a G-ring object. Icarus, 207, 433–447
Hedman, M. M., Nicholson, P. D., Filacchione, G., Capaccioni, F., Ciarnello, M., & Clark, R. N. 2011a, Correlations between the spectra and structure of Saturn’s main rings. AAS Div. Planet. Sci. Meet. Abstr., 43, 532
Hedman, M. M., Burns, J. A., & Tiscareno, M. S. 2011b, Of horseshoes and heliotropes: the dynamics of dust in the Encke gap. AAS Div. Dyn. Astron. Meet. Abstr., 42, 8.02
Hedman, M. M., Nicholson, P. D., Showalter, M. R., Brown, R. H., Buratti, B. J., Clark, R. N., Baines, K., & Sotin, C. 2011c, The Christiansen effect in Saturn’s narrow dusty rings and the spectral identification of clumps in the F ring. Icarus, 215, 695–711
Hedman, M. M., Burns, J. A., Evans, M. W., Tiscareno, M. S., & Porco, C. C. 2011d, Saturn’s curiously corrugated C ring. Science, 332, 708–711
Heißelmann, D., Blum, J., Fraser, H. J., & Wolling, K. 2010, Microgravity experiments on the collisional behavior of saturnian ring particles. Icarus, 206, 424–430
Hill, J. R., & Mendis, D. A. 1981, On the braids and spokes in Saturn’s ring system. Moon Planet, 24, 431–436
Horányi, M., Burns, J. A., Hedman, M. M., Jones, G. H., & Kempf, S. 2009, Diffuse rings, in Saturn from Cassini-Huygens, ed. M. Dougherty, L. Esposito, & S. M. Krimigis (Dordrecht: Springer), 511–536
Ip, W.-H. 2006, On a ring origin of the equatorial ridge of Iapetus. Geophys. Res. Lett., 33, L16203
Jacobson, R. A., Campbell, J. K., Taylor, A. H., & Synnott, S. P. 1992, The masses of Uranus and its major satellites from Voyager tracking data and Earth-based Uranian satellite data. Astron. J., 103, 2068–2078
Jacobson, R. A., Spitale, J., Porco, C. C., Beurle, K., Cooper, N. J., Evans, M. W., & Murray, C. D. 2008, Revised orbits of Saturn’s small inner satellites. Astron. J., 135, 261–263
Jones, G. H., et al. 2006, Formation of Saturn’s ring spokes by lightning-induced electron beams. Geophys. Res. Lett., 33, L21202.
Jones, G. H., et al. 2008, The dust halo of Saturn’s largest icy moon, Rhea. Science, 319, 1380–1384
Julian, W. H., & Toomre, A. 1966, Non-axisymmetric responses of differentially rotating disks of stars. Astrophys. J., 146, 810–830
Kalas, P., Graham, J. R., & Clampin, M. 2005, A planetary system as the origin of structure in Fomalhaut’s dust belt. Nature, 435, 1067–1070
Kalas, P., Graham, J. R., Chiang, E., Fitzgerald, M. P., Clampin, M., Kite, E. S., Stapelfeldt, K., Marois, C., & Krist, J. 2008, Optical images of an exosolar planet 25 light-years from Earth. Science, 322, 1345–1348
Kempf, S., Beckmann, U., & Schmidt, J. 2010, How the Enceladus dust plume feeds Saturn’s E ring. Icarus, 206, 446–457
Krivov, A. V., & Hamilton, D. P. 1997, Martian dust belts: waiting for discovery. Icarus, 128, 335–353
Laughlin, G., Korchagin, V., & Adams, F. C. 1997, Spiral mode saturation in self-gravitating disks. Astrophys. J., 477, 410–423
Levison, H. F., Walsh, K. J., Barr, A. C., & Dones, L. 2011, Ridge formation and de-spinning of Iapetus via an impact-generated satellite. Icarus, 214, 773–778
Lewis, M. C., & Stewart, G. R. 2009, Features around embedded moonlets in Saturn’s rings: the role of self-gravity and particle size distributions. Icarus, 199, 387–412
Lin, C. C., & Shu, F. H. 1964, On the spiral structure of disk galaxies. Astrophys. J., 140, 646–655
Lissauer, J. J. 1985, Shepherding model for Neptune’s arc ring. Nature, 318, 544–545
Longaretti, P.-Y., & Borderies, N. 1991, Streamline formalism and ring orbit determination. Icarus, 94, 165–170
Lubow, S. H. 2010, Eccentricity growth rates of tidally distorted discs. Mon. Not. Roy. Astron. Soc., 406, 2777–2786
Mamajek, E. E., Quillen, A. C., Pecaut, M. J., Moolekamp, F., Scott, E. L., Kenworthy, M. A., Collier Cameron, A., & Parley, N. R. 2012, Planetary construction zones in occultation: discovery of an extrasolar ring system transiting a young Sun-like star and future prospects for detecting eclipses by circumsecondary and circumplanetary disks. Astron. J., 143, 72
Matson, D. L., Castillo-Rogez, J. C., Schubert, G., Sotin, C., & McKinnon, W. B. 2009, The thermal evolution and internal structure of Saturn’s mid-sized icy satellites, in Saturn from Cassini-Huygens, ed. M. Dougherty, L. Esposito, & S. M. Krimigis (Dordrecht: Springer), 577–612
McGhee, C. A., French, R. G., Dones, L., Cuzzi, J. N., Salo, H. J., & Danos, R. 2005, HST observations of spokes in Saturn’s B ring. Icarus, 173, 508–521
Meyer, J., & Wisdom, J. 2007, Tidal heating in Enceladus. Icarus, 188, 535–539
Meyer, J., & Wisdom, J. 2008a, Tidal evolution of Mimas, Enceladus, & Dione. Icarus, 193, 213–223
Meyer, J., & Wisdom, J. 2008b, Episodic volcanism on Enceladus: application of the Ojakangas-Stevenson model. Icarus, 198, 178–180
Michikoshi, S., & Kokubo, E. 2011, Formation of a propeller structure by a moonlet in a dense planetary ring. Astrophys. J. Lett., 732, L23.
Millis, R. L., Wasserman, L. H., & Birch, P. V. 1977, Detection of rings around Uranus. Nature, 267, 330–331
Miner, E. D., Wessen, R. R., & Cuzzi, J. N. 2007, Planetary Ring Systems (Chichester: Springer Praxis)
Mitchell, C. J., Horányi, M., Havnes, O., & Porco, C. C. 2006, Saturn’s spokes: lost and found. Science, 311, 1587–1589
Mitchell, C., Porco, C., Dones, L., & Spitale, J. 2012, The behavior of spokes in Saturn’s B ring. Icarus, submitted
Morfill, G. E., & Thomas, H. M. 2005, Spoke formation under moving plasma clouds: The Goertz-Morfill model revisited. Icarus, 179, 539–542
Mosqueira, I., & Estrada, P. R. 2002, Apse alignment of the Uranian rings. Icarus, 158, 545–556
Mosqueira, I., & Estrada, P. R. 2003, Formation of the regular satellites of giant planets in an extended gaseous nebula I: subnebula model and accretion of satellites. Icarus, 163, 198–231
Murray, C. D., & Dermott, S. F. 1999, Solar System Dynamics (Cambridge: Cambridge University Press)
Murray, C. D., & Thompson, R. P. 1990, Orbits of shepherd satellites deduced from the structure of the rings of Uranus. Nature, 348, 499–502
Murray, C. D., & Thompson, R. P. 1991, Erratum: orbits of shepherd satellites deduced from the structure of the rings of Uranus. Nature, 350, 90
Murray, C. D., Chavez, C., Beurle, K., Cooper, N., Evans, M. W., Burns, J. A., & Porco, C. C. 2005, How Prometheus creates structure in Saturn’s F ring. Nature, 437, 1326–1329
Murray, C. D., Beurle, K., Cooper, N. J., Evans, M. W., Williams, G. A., & Charnoz, S. 2008, The determination of the structure of Saturn’s F ring by nearby moonlets. Nature, 453, 739–744
Namouni, F., & Porco, C., 2002, The confinement of Neptune’s ring arcs by the moon Galatea. Nature, 417, 45–47
Nicholson, P. D., & Hedman, M. M. 2010, Self-gravity wake parameters in Saturn’s A and B rings. Icarus, 206, 410–423
Nicholson, P. D., Mosqueira, I., & Matthews, K. 1995, Stellar occultation observations of Neptune’s rings: 1984–1988. Icarus, 113, 295–330
Nicholson, P. D., et al. 2008, A close look at Saturn’s rings with Cassini VIMS. Icarus, 193, 182–212
Ockert-Bell, M. E., Burns, J. A., Daubar, I. J., Thomas, P. C., Veverka, J., Belton, M. J. S., & Klaasen, K. P. 1999, The structure of Jupiter’s ring system as revealed by the Galileo imaging experiment. Icarus, 138, 188–213
Ohta, Y., Taruya, A., & Suto, Y. 2009, Predicting photometric and spectroscopic signatures of rings around transiting extrasolar planets. Astrophys. J., 690, 1–12
Øieroset, M., Brain, D. A., Simpson, E., Mitchell, D. L., Phan, T. D., Halekas, J. S., Lin, R. P., & Acuña, M. H. 2010, Search for Phobos and Deimos gas/dust tori using in situ observations from Mars global surveyor MAG/ER. Icarus, 206, 189–198
Orton, G. S., Baines, K. H., Cruikshank, D., Cuzzi, J. N., Krimigis, S. M., Miller, S., & Lellouch, E. 2009, Review of knowledge prior to the Cassini-Huygens mission and concurrent research, in Saturn from Cassini-Huygens, ed. M. Dougherty, L. Esposito, & S. M. Krimigis (Dordrecht: Springer), 9–54
Owen, T., Danielson, G. E., Cook, A. F., Hansen, C., Hall, V. L., & Duxbury, T. C. 1979, Jupiter’s rings, Nature, 281, 442–446
Pan, M., & Chiang, E. 2010, The propeller and the frog. Astrophys. J. Lett., 722, L178–L182
Papaloizou, J. C. B., Nelson, R. P., Kley, W., Masset, F. S., & Artymowicz, P. 2007, Disk-planet interactions during planet formation, in Protostars and Planets V, ed. B. Reipurth, D. Jewitt, & K. Keil (Tucson: University of Arizona Press), 655–668
Perrine, R. P., Richardson, D. C., & Scheeres, D. J. 2011, A numerical model of cohesion in planetary rings. Icarus, 212, 719–735
Porco, C. C. 1991, An explanation for Neptune’s ring arcs. Science, 253, 995–1001
Porco, C. C., Nicholson, P. D., Cuzzi, J. N., Lissauer, J. J., & Esposito, L. W. 1995, Neptune’s ring system, in Neptune and Triton, ed. D. P. Cruikshank (Tucson: University of Arizona Press), 703–804
Porco, C. C., et al. 2005a, Cassini imaging science: initial results on Phoebe and Iapetus. Science, 307, 1237–1242
Porco, C. C., et al. 2005b, Cassini imaging science: initial results on Saturn’s rings and small satellites. Science, 307, 1226–1236
Porco, C. C., Thomas, P. C., Weiss, J. W., & Richardson, D. C. 2007, Saturn’s small satellites: clues to their origins. Science, 318, 1602–1607
Porco, C. C., Weiss, J. W., Richardson, D. C., Dones, L., Quinn, T., & Throop, H. 2008, Simulations of the dynamical and light-scattering behavior of Saturn’s rings and the derivation of ring particle and disk properties. Astron. J., 136, 2172–2200
Rappaport, N. J., Longaretti, P., French, R. G., Marouf, E. A., & McGhee, C. A. 2009, A procedure to analyze nonlinear density waves in Saturn’s rings using several occultation profiles. Icarus, 199, 154–173
Rein, H., & Papaloizou, J. C. B. 2010, Stochastic orbital migration of small bodies in Saturn’s rings. Astron. Astrophys., 524, A22.
Renner, S., & Sicardy, B. 2006, Use of the geometric elements in numerical simulations. Cel. Mech. Dyn. Astron., 94, 237–248
Richardson, D. C. 1994, Tree code simulations of planetary rings. Mon. Not. Roy. Astron. Soc., 269, 493–511
Richardson, J. E., Melosh, H. J., Lisse, C. M., & Carcich, B. 2007, A ballistics analysis of the Deep Impact ejecta plume: determining Comet Tempel 1’s gravity, mass, & density. Icarus, 190, 357–390
Robbins, S. J., Stewart, G. R., Lewis, M. C., Colwell, J. E., & Sremčević, M. 2010, Estimating the masses of Saturn’s A and B rings from high-optical depth N-body simulations and stellar occultations. Icarus, 206, 431–445
Rosen, P. A., & Lissauer, J. J. 1988, The Titan -1:0 nodal bending wave in Saturn’s ring C. Science, 241, 690–694
Roussos, E., Jones, G. H., Krupp, N., Paranicas, C., Mitchell, D. G., Krimigis, S. M., Woch, J., Lagg, A., & Khurana, K. 2008, Energetic electron signatures of Saturn’s smaller moons: evidence of an arc of material at Methone. Icarus, 193, 455–464
Salmon, J., Charnoz, S., Crida, A., & Brahic, A. 2010, Long-term and large-scale viscous evolution of dense planetary rings. Icarus, 209, 771–785
Salo, H. 1992, Gravitational wakes in Saturn’s rings. Nature, 359, 619–621
Salo, H. 1995, Simulations of dense planetary rings III. self-gravitating identical particles. Icarus, 117, 287–312
Salo, H., & Karjalainen, R. 2003, Photometric modeling of Saturn’s rings I. Monte Carlo method and the effect of nonzero volume filling factor. Icarus, 164, 428–460
Salo, H., Karjalainen, R., & French, R. G. 2004, Photometric modeling of Saturn’s rings. II. Azimuthal asymmetry in reflected and transmitted light. Icarus, 170, 70–90
Schenk, P. M., & McKinnon, W. B. 2009, Global color variations on Saturn’s icy satellites, and new evidence for Rhea’s ring. AAS Div. Planet. Sci. Meet. Abstr., 41, 3.03
Schenk, P., Hamilton, D. P., Johnson, R. E., McKinnon, W. B., Paranicas, C., Schmidt, J., & Showalter, M. R. 2011, Plasma, plumes and rings: saturn system dynamics as recorded in global color patterns on its midsize icy satellites. Icarus, 211, 740–757
Schlichting, H. E., & Chang, P. 2011, Warm Saturns: on the nature of rings around extrasolar planets that reside inside the ice line. Astrophys. J., 734, 117
Schmidt, J., Brilliantov, N., Spahn, F., & Kempf, S. 2008, Slow dust in Enceladus’ plume from condensation and wall collisions in tiger stripe fractures. Nature, 451, 685–688
Schmidt, J., Ohtsuki, K., Rappaport, N., Salo, H., & Spahn, F. 2009, Dynamics of Saturn’s dense rings, in Saturn from Cassini-Huygens, ed. M. Dougherty, L. Esposito, & S. M. Krimigis (Dordrecht: Springer-Verlag), 413–458
Seager, S. (ed.), 2010, Exoplanets (Tucson: University of Arizona Press)
Seal, D. A., & Buffington, B. B. 2009, The Cassini extended mission, in Saturn from Cassini-Huygens, ed. M. Dougherty, L. Esposito, & S. M. Krimigis (Dordrecht: Springer), 725–744
Seiß, M., Spahn, F., Sremčević, M., & Salo, H. 2005, Structures induced by small moonlets in Saturn’s rings: implications for the Cassini mission. Geophys. Res. Lett., 32, L11205.
Showalter, M. R. 1991, Visual detection of 1981S13, Saturn’s eighteenth satellite, and its role in the Encke gap. Nature, 351, 709–713
Showalter, M. R. 2011, The rings of Uranus: shepherded or not? AAS Div. Planet. Sci. Meet. Abstr., 43, 1224
Showalter, M. R., & Cuzzi, J. N. 1992, Physical properties of Neptune’s ring system. Bull. Am. Astron. Soc. 24, 1029
Showalter, M. R., & Lissauer, J. J. 2006, The second ring-moon system of Uranus: discovery and dynamics. Science, 311, 973–977
Showalter, M. R., Cuzzi, J. N., Marouf, E. A., & Esposito, L. W. 1986, Satellite “wakes” and the orbit of the Encke Gap moonlet. Icarus, 66, 297–323
Showalter, M. R., Cuzzi, J. N., & Larson, S. M. 1991, Structure and particle properties of Saturn’s E ring. Icarus, 94, 451–473
Showalter, M. R., Hamilton, D. P., & Nicholson, P. D. 2006, A deep search for Martian dust rings and inner moons using the Hubble Space Telescope. Planet. Space Sci., 54, 844–854
Showalter, M. R., Cheng, A. F., Weaver, H. A., Stern, S. A., Spencer, J. R., Throop, H. B., Birath, E. M., Rose, D., & Moore, J. M. 2007, Clump detections and limits on moons in Jupiter’s ring system. Science, 318, 232–234
Showalter, M. R., French, R., Sfair, R., Argüelles, C., Pajuelo, M., Becerra, P., Hedman, M., & Nicholson, P. 2009, The brightening of Saturn’s F ring. AAS Div. Planet. Sci. Meet. Abstr., 41, 22.07
Showalter, M. R., Hamilton, D. P., Stern, S. A., Weaver, H. A., Steffl, A. J., & Young, L. A. 2011a, New satellite of (134340) Pluto: S/2011 (134340) 1. Cent. Bur. Electron. Telegr., 2769, 1
Showalter, M. R., Hedman, M. M., & Burns, J. A. 2011b, The impact of Comet Shoemaker-Levy 9 sends ripples through the rings of Jupiter. Science, 332, 711–713
Shu, F. H. 1984, Waves in planetary rings, in Planetary Rings, ed. R. Greenberg, & A. Brahic (Tucson: University of Arizona Press), 513–561
Sicardy, B., Roddier, F., Roddier, C., Perozzi, E., Graves, J. E., Guyon, O., & Northcott, M. J. 1999, Images of Neptune’s ring arcs obtained by a ground-based telescope. Nature, 400, 731–733
Smith, B. A., et al. 1982, A new look at the Saturn system - The Voyager 2 images. Science, 215, 504–537
Soter, S. 1974, Remarks on the origin of Iapetus’ photometric asymmetry. IAU Colloq., 28
Spahn, F., & Sremčević, M. 2000, Density patterns induced by small moonlets in Saturn’s rings? Astron. Astrophys., 358, 368–372
Spencer, J. R., & Denk, T. 2010, Formation of Iapetus’ extreme albedo dichotomy by exogenically triggered thermal ice migration. Science, 327, 432–435
Spitale, J., & Porco, C. C. 2006, Shapes and kinematics of eccentric features in Saturn’s C ring and Cassini division. AAS Div. Dyn. Astron. Meet. Abstr., 37, 7.02
Spitale, J. N., & Porco, C. C. 2009, Time variability in the outer edge of Saturn’s A-ring revealed by Cassini imaging. Astron. J., 138, 1520–1528
Spitale, J. N., & Porco, C. C. 2010, Detection of free unstable modes and massive bodies in Saturn’s outer B ring. Astron. J., 140, 1747–1757
Spitale, J. N., Porco, C. C., & Colwell, J. 2008, An inclined saturnian ringlet at 1.954 Rs. AAS Div. Planet. Sci. Meet. Abstr., 40, 21.02
Sremčević, M., Spahn, F., & Duschl, W. J. 2002, Density structures in perturbed thin cold discs. Mon. Not. Roy. Astron. Soc., 337, 1139–1152
Sremčević, M., Schmidt, J., Salo, H., Seiß, M., Spahn, F., & Albers, N. 2007, A belt of moonlets in Saturn’s A ring. Nature, 449, 1019–1021
Sremčević, M., Colwell, J. E., & Esposito, L. W. 2009, Small-scale ring structure observed in Cassini UVIS occultations. AGU Fall Meeting Abstracts, P54A–05
Steffl, A. J., & Stern, S. A. 2007, First constraints on rings in the Pluto system. Astron. J., 133, 1485–1489
Stern, S. A., Weaver, H. A., Steffl, A. J., Mutchler, M. J., Merline, W. J., Buie, M. W., Young, E. F., Young, L. A., & Spencer, J. R. 2006, A giant impact origin for Pluto’s small moons and satellite multiplicity in the Kuiper belt. Nature, 439, 946–948
Supulver, K. D., Bridges, F. G., & Lin, D. N. C. 1995, The coefficient of restitution of ice particles in glancing collisions: experimental results for unfrosted surfaces. Icarus, 113, 188–199
Tamayo, D., Burns, J. A., Hamilton, D. P., & Hedman, M. M. 2011, Finding the trigger to Iapetus’ odd global albedo pattern: dynamics of dust from Saturn’s irregular satellites. Icarus, 215, 260–278
Thomson, F. S., Marouf, E. A., Tyler, G. L., French, R. G., & Rappoport, N. J. 2007, Periodic microstructure in Saturn’s rings A and B. Geophys. Res. Lett., 34, L24203
Tiscareno, M. S. 2012, A modified “Type I migration” model for propeller moons in Saturn’s rings. Planet. Space Sci., in press (arXiv:1206.4942)
Tiscareno, M. S., Burns, J. A., Hedman, M. M., Spitale, J. N., Porco, C. C., Murray, C. D., & Cassini Imaging Team, 2005, Wavy edges and other disturbances in Saturn’s Encke and Keeler gaps. AAS Div. Planet. Sci. Meet. Abstr., 37, 64.02
Tiscareno, M. S., Burns, J. A., Hedman, M. M., Porco, C. C., Weiss, J. W., Dones, L., Richardson, D. C., & Murray, C. D. 2006a, 100-metre-diameter moonlets in Saturn’s A ring from observations of “propeller” structures. Nature, 440, 648–650
Tiscareno, M. S., Nicholson, P. D., Burns, J. A., Hedman, M. M., & Porco, C. C. 2006b, Unravelling temporal variability in Saturn’s spiral density waves: results and predictions. Astrophys. J. Lett., 651, L65–L68
Tiscareno, M. S., Burns, J. A., Nicholson, P. D., Hedman, M. M., & Porco, C. C. 2007, Cassini imaging of Saturn’s rings II. a wavelet technique for analysis of density waves and other radial structure in the rings. Icarus, 189, 14–34
Tiscareno, M. S., Burns, J. A., Hedman, M. M., & Porco, C. C. 2008, The population of propellers in Saturn’s A ring. Astron. J., 135, 1083–1091
Tiscareno, M. S., Hedman, M. M., Burns, J. A., Weiss, J. W., & Porco, C. C. 2009a, Saturn’s A ring has no inner edge. AAS Div. Planet. Sci. Meet. Abstr., 41, 25.04
Tiscareno, M. S., Burns, J. A., Hedman, M. M., DiNino, D., Porco, C. C., Beurle, K., & Evans, M. W. 2009b, Observations of ejecta clouds produced by impacts onto Saturn’s rings. AGU Fall Meeting Abstracts, P54A–08
Tiscareno, M. S., Perrine, R. P., Richardson, D. C., Hedman, M. M., Weiss, J. W., Porco, C. C., & Burns, J. A. 2010a, An analytic parameterization of self-gravity wakes in Saturn’s rings. Astron. J., 139, 492–503
Tiscareno, M. S., Burns, J. A., Cuzzi, J. N., & Hedman, M. M. 2010b, Cassini imaging search rules out rings around Rhea. Geophys. Res. Lett., 37, L14205
Tiscareno, M. S., et al. 2010c, Physical characteristics and non-keplerian orbital motion of “propeller” moons embedded in Saturn’s rings. Astrophys. J. Lett., 718, L92–L96
Torrence, C., & Compo, G. P. 1998, A practical guide to wavelet analysis. Bull. Am. Meteorol. Soc., 79, 61–78 http://atoc.colorado.edu/research/wavelets/
Torrey, P. A., Tiscareno, M. S., Burns, J. A., & Porco, C. C. 2008, Mapping complexity: the wavy edges of the Encke and Keeler gaps in Saturn’s rings. AAS Div. Dyn. Astron. Meet. Abstr., 39, 15.19
Van Helden, A. 1984, Saturn through the telescope: a brief historical survey, in Saturn, ed. T. Gehrels, & M. S. Matthews (Tucson: University of Arizona Press), 23–43
Verbiscer, A. J., Skrutskie, M. F., & Hamilton, D. P. 2009, Saturn’s largest ring. Nature, 461, 1098–1100
Ward, W. R. 1986, Density waves in the solar nebula: differential Lindblad torque. Icarus, 67, 164–180
Ward, W. R. 1997, Survival of planetary systems. Astrophys. J. Lett., 482, L211–L214
Weiss, J. W. 2005, The physics of unconstrained edges in planetary rings. Ph.D. Thesis, University of Colorado
Weiss, J. W., Porco, C. C., & Tiscareno, M. S. 2009, Ring edge waves and the masses of nearby satellites. Astron. J., 138, 272–286
Winter, O. C., Mourão, D. C., Giuliatti Winter, S. M., Spahn, F., & da Cruz, C. 2007, Moonlets wandering on a leash-ring. Mon. Not. Roy. Astron. Soc., 380, L54–L57
Wisdom, J., & Holman, M. 1991, Symplectic maps for the n-body problem. Astron. J., 102, 1528–1538
Wisdom, J., & Tremaine, S. 1988, Local simulations of planetary rings. Astron. J., 95, 925–940
Zebker, H. A., Marouf, E. A., & Tyler, G. L. 1985, Saturn’s rings: particle size distributions for thin layer model. Icarus, 64, 531–548
Acknowledgments
I thank Mark Showalter, Joe Burns, Josh Colwell, Jeff Cuzzi, Jonathan Fortney, Doug Hamilton, Matt Hedman, Doug Lin, Phil Nicholson, and John Weiss for helpful conversations. I additionally thank Robin Canup, John Cooper, Estelle Deau, Larry Esposito, and Rob French for valuable comments on the manuscript, and Hanno Rein for help in creating Fig. 7-3. I acknowledge funding from NASA Outer Planets Research (NNX10AP94G), NASA Cassini Data Analysis (NNX08AQ72G and NNX10AG67G), and the Cassini Project.
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Tiscareno, M.S. (2013). Planetary Rings. In: Oswalt, T.D., French, L.M., Kalas, P. (eds) Planets, Stars and Stellar Systems. Springer, Dordrecht. https://doi.org/10.1007/978-94-007-5606-9_7
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