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RE: Ring A
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Title: Care and feeding of frogs
Authors: Margaret Pan, Eugene Chiang (UC Berkeley)

"Propellers" are features in Saturn's A ring associated with moonlets that open partial gaps. They exhibit non-Keplerian motion (Tiscareno 2010); the longitude residuals of the best-observed propeller, "Bleriot," appear consistent with a sinusoid of period ~4 years. Pan and Chiang (2010) proposed that propeller moonlets librate in "frog resonances" with co-orbiting ring material. By analogy with the restricted three-body problem, they treated the co-orbital material as stationary in the rotating frame and neglected non-co-orbital material. Here we use simple numerical experiments to extend the frog model, including feedback due to the gap's motion, and drag associated with the Lindblad disk torques that cause Type I migration. Because the moonlet creates the gap, we expect the gap centroid to track the moonlet, but only after a time delay t_diff, the time for a ring particle to travel from conjunction with the moonlet to the end of the gap. We find that frog librations can persist only if t_diff exceeds the frog libration period P_lib, and if damping from Lindblad torques balances driving from co-orbital torques. If t_diff << P_lib, then the libration amplitude damps to zero. In the case of Bleriot, the frog resonance model can reproduce the observed libration period P_lib ~ 4 yr. However, our simple feedback prescription suggests that Bleriot's t_diff ~ 0.01P_lib, which is inconsistent with the observed libration amplitude of 260 km. We urge more accurate treatments of feedback to test the assumptions of our toy models.

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Propeller Structure
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Title: Formation of a Propeller Structure by a Moonlet in a Dense Planetary Ring
Authors: Shugo Michikoshi, Eiichiro Kokubo

The Cassini spacecraft discovered a propeller-shaped structure in Saturn's A ring. This propeller structure is thought to be formed by gravitational scattering of ring particles by an unseen embedded moonlet. Self-gravity wakes are prevalent in dense rings due to gravitational instability. Strong gravitational wakes affect the propeller structure. Here, we derive the condition for formation of a propeller structure by a moonlet embedded in a dense ring with gravitational wakes. We find that a propeller structure is formed when the wavelength of the gravitational wakes is smaller than the Hill radius of the moonlet. We confirm this formation condition by performing numerical simulations. This condition is consistent with observations of propeller structures in Saturn's A ring.

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Saturn Propellers Reflect Solar System Origins

Scientists using NASA's Cassini spacecraft at Saturn have stalked a new class of moons in the rings of Saturn that create distinctive propeller-shaped gaps in ring material. It marks the first time scientists have been able to track the orbits of individual objects in a debris disk. The research gives scientists an opportunity to time-travel back into the history of our solar system to reveal clues about disks around other stars in our universe that are too far away to observe directly.
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Title: Migration of a moonlet in a ring of solid particles : Theory and application to Saturn's propellers
Authors: A. Crida, J. C. B. Papaloizou, H. Rein, S. Charnoz, J. Salmon

Hundred meter sized objects have been identified by the Cassini spacecraft in Saturn's A ring through the so-called "propeller" features they create in the ring. These moonlets should migrate, due to their gravitational interaction with the ring ; in fact, some orbital variation have been detected. The standard theory of type I migration of planets in protoplanetary disks can't be applied to the ring system, as it is pressureless. Thus, we compute the differential torque felt by a moonlet embedded in a two-dimensional disk of solid particles, with flat surface density profile, both analytically and numerically. We find that the corresponding migration rate is too small to explain the observed variations of the propeller's orbit in Saturn's A-ring.
However, local density fluctuations (due to gravity wakes in the marginally gravitationally stable A-ring) may exert a stochastic torque on a moonlet. Our simulations show that this torque can be large enough to account for the observations, depending on the parameters of the rings. We find that on time scales of several years the migration of propellers is likely to be dominated by stochastic effects (while the former, non-stochastic migration dominates after ~ 10^{4-5} years). In that case, the migration rates provided by observations so far suggests that the surface density of the A ring should be of the order of 700 kg/mē. The age of the propellers shouldn't exceed 1 to 100 million years, depending on the dominant migration regime.

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Saturn's A ring
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This image of Saturn's A ring was taken in visible green light by the Cassini spacecraft narrow-angle camera on the 11th January, 2010, when it was approximately 279,000 kilometres away.
The image scale is about 1 kilometre per pixel.

Aring1.jpg
Expand (210kb, 1016 x 1016)
Credit: NASA/JPL/Space Science Institute

The Cassini spacecraft imaged Saturn's A ring and captured two types of waves; a spiral density wave (left of the image) and a spiral bending wave (near the middle).

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Ring A
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Waves and Small Particles in Ring A:

Specially designed Cassini orbits place Earth and Cassini on opposite sides of Saturn's rings, a geometry known as occultation. Cassini conducted the first radio occultation observation of Saturn's rings on May 3, 2005.

Three simultaneous radio signals at wavelengths of 0.94, 3.6, and 13 centimetres (Ka-, X-, and S-bands) were sent from Cassini through the rings to Earth. The observed change of each signal as Cassini moved behind the rings provided a profile of the distribution of ring material and an optical depth profile.
This simulated image was constructed from the measured optical depth profiles of the Cassini Division and ring A.


Expand (1024 x 571)

It depicts the observed structure at about 10 kilometres in resolution. The image shows the same ring A region depicted in a similar image (
Multiple Eyes of Cassini), using a different color scheme to enhance the view of a remarkable array of over 40 wavy features called "density waves" uncovered in the May 3 radio occultation throughout ring A.


Colour is used to represent information about ring particle sizes based on the measured effects of the three radio signals. Shades of red indicate regions where there is a lack of particles less than 5 centimetres in diameter. Green and blue shades indicate regions where there are particles of sizes smaller than 5 centimetres and 1 centimetre, respectively.
Note the gradual increase in shades of green towards the outer edge of ring A. It indicates gradual increase in the abundance of 5-centimeter and smaller particles. Note also the blue shades in the vicinity of the Keeler gap (the narrow dark band near the edge of ring A).
They indicate increased abundance of even smaller particles of diameter less than a centimetre. Frequent collisions between large ring particles in this dynamically active region likely fragment the larger particles into more numerous smaller ones.

The Cassini-Huygens mission is a cooperative project of NASA, the European Space Agency and the Italian Space Agency. The Jet Propulsion Laboratory, a division of the California Institute of Technology in Pasadena, manages the mission for NASA's Science Mission Directorate, Washington, D.C. The Cassini orbiter was designed, developed and assembled at JPL. The radio science team is based at JPL.

http://photojournal.jpl.nasa.gov/jpeg/PIA07874.jpg Multiple Eyes of Cassini


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