- Collisions between objects in Saturn's rings flatten the rings to a thickness of about 10 meters. - Resonances with Saturn's moons produce the gross structure of the rings, while electromagnetic resonances generate waves. - The Encke and Keeler gaps contain the moons Pan and Daphnis, respectively, and have wavy, sculpted edges maintained by interactions with the embedded moons. - Ring moons like Pan, Daphnis, and Atlas have low densities and fill their Roche lobes, accumulating porous mantles through accretion until reaching a critical density.

1. Paolo Farinella

2. Dynamics and Collisions at
Saturn:
The View from
Cassini
Joe Burns, Cornell University
14 Giugno 2010

3. Simple causes of
structure
Thickness
Resonances and
C waves
Edge wiggles
Rubble piles and shapes
Ring moons
Hyperion
B Iapetus
Two new problems
CD Embedded moons
A Corrugations/collisions
F ORIGIN?
- Collisions or Nebula?

4. Collisions flatten the rings until they are only about 10 m thick.
Structure

5. Satellite resonances
Produce known gross form.
Through waves, drive radial evolution of ring & moons.
Electromagnetic resonances
Generate waves in faint rings

6. Overview of Rings’ Geography
Keeler
F Ring
B Ring Cassini Div. A Ring
Encke
• Encke Gap and Keeler Gap in the outer A Ring
• Each contains a moon – the only known embedded
moons.
– Pan was inferred from wavy edges in 1985, discovered in 1991
– Daphnis was discovered in 2005
• Gap edges are sculpted by the embedded moons.

7. STREAMLINES PAST A MOON
wakes
Chaotic
zone
Horseshoe
orbits
3s
M & D, p.
Units are Hill radii 121
s = radial separation PF’s book,
too

8. Waves Near the Encke Gap
Pan (~15 km, 0.4 g/cm3 opens 320-km gap. Three-body problem!
Gap contains variable faint rings; one shares Pan’s orbit.
Wavy edges induce wakes.
Density/bending waves populate region, transfer anglr. mom.

9. PIA06238
PIA06237 Daphnis 0pens Keeler Gap.
4-km moon clears
20-40 km gap
Inferred  = 0.4 g-cm
Lewis and Stewart, 2005

10. Encke Gap Wavy Edges
Outer Edge
Synodic Motion
Inner Edge
Synodic Motion
• Wavy edges persist until next encounter with Pan ( ~ 1000
orbits).
• Immediately after encounter, edges damp as expected, but
far downstream, wavelength deviates from 3s, sometimes
switches abruptly from sinusoid to “chirp”.
• Widths of Keeler and Encke Gaps consistent with mass
ratios.
• Is angular-momentum transfer affected?
Tiscareno et al. 2006

12. Accretion in the Ring Region
Atlas Pan
~ 15 km
Density: 0.4 g/cm3
41 x 36 x 20 km
Density: 0.4 g/cm3
• Ring-moons have low densities, fill their Roche lobes
• Dense cores accrete porous mantle until they reach
“Roche critical density” (Charnoz et al. 2007; Porco et al. 2007, Science)

13. Equipotential Surfaces: Roche Lobe or Hill Sphere

14. Shapes of Solar System Bodies

15. Saturn’s
Ring-
Moons
Were Atlas -> Janus/Epimetheus born
Nature, last week
in the rings and driven outwards by Charnoz et al., Burns, N&V
ring torques?

16. Spongy Tumbling Hyperion
• Hyperion’s
bright craters
have dark
floors
• Very low
density (~0.5 g-
cm-3)
• Impacts into
low-density
form shallow
craters
• Hyperion does
not rotate
synchronously
but tumbles
chaotically

17. Shape => 17 hr spin??

18. Recent models
involving collisions
in Saturn’s rings
- Propellers
-Corrugations in the C ring
- Phoebe’s ring and Iapetus

19. A Corrugated
Curiosity in Saturn’s
C ring
M.M. Hedman, J.A. Burns
M.S. Tiscareno
DDA Meeting, April 2010

20. Images at equinox with different illuminations demonstrate that
the periodic brightness variations represent vertical corrugations.
Sunlight Sunlight
The corrugation’s wavelength ranges from 30 to 80 km, and
its amplitude is only ~ 10 m.

21. The corrugation wavelengths vary smoothly with radius,
indicating that the corrugation is a single structure with one
cause.
D-ring C-ring

22. This structure is not static; its wavelength across the D ring
has decreased with time
k = 2π/λ = ( 2.5*10-5 km-1/day) δt
Cassini
Images
HST Occultation

23. 2
Model: Tilted ring becomes corrugated Ý 21
dk d GM Rs 
and winds up at a rate determined by   J2 5  
Saturn’s gravitational field dt dr 4 r  r 

24. We can extrapolate back in time to see when the ring
would have been flat (i.e., when k -> 0):
k = 2π/λ = ( 2.5*10-5 km-1/day) δt

25. The big question is: What happened in 1983?
Either the rings
angular momentum
shifted off Saturn’s
equatorial plane…
…or Saturn’s internal
structure changed and
tilted the planet’s equator
relative to the rings.

26. How much mass is needed to shift the ring’s H by 10-7?
A m impact v impactor
 sini ~ `
r m ring v ring
Where A is the corrugation amplitude ~ 10 m
r is the ring radius ~ 80,000 km
vring is the orbital speed ~ 24 km/s
vimpactor is the impactor’s speed ~ 40 km/s
mring is the ring’s mass ~ 5 x 1017 kg
For this scenario to work, the impacting mass needs to be:
mimpact ~ 3 x 10 10 kg
or, assuming the impactor was a single ice-rich object
rimpactor ~ 250 m

27. This is comparable to the sizes of
the fragments of Shoemaker-Levy 9
that hit Jupiter in 1994.
(and perhaps the 2009 impactor)
Showalter: Jupiter’s ring tilted in
1994!!
…maybe it is not so
unlikely that a similar-
sized impactor hit Saturn
25-30 years ago

30. Thanks