Paolo Farinella

Dynamics and Collisions at Saturn:

Joe Burns, Cornell University14 Giugno 2010

The View fromCassini

ORIGIN?- Collisions or Nebula?

A

B

C

C D

F

Simple causes of structure

ThicknessResonances and

wavesEdge wiggles

Rubble piles and shapesRing moonsHyperionIapetus

Two new problemsEmbedded moonsCorrugations/collisions

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

Structure

Satellite resonancesProduce known gross form.Through waves, drive radial evolution of ring & moons.

Electromagnetic resonancesGenerate waves in faint rings

• 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.

Overview of Rings’ Geography

B Ring A RingCassini Div.

F Ring

Keeler

Encke

STREAMLINES PAST A MOONwakes

Chaotic zone

Horseshoe orbits

3s

Units are Hill radiis = radial separation

M & D, p. 121PF’s book, too

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.

4-km moon clears20-40 km gap

Inferred = 0.4 g-cm

PIA06237

PIA06238

Daphnis 0pens Keeler Gap.

Lewis and Stewart, 2005

Encke Gap Wavy Edges

• Wavy edges persist until next encounter with Pan ( ~ 1000 orbits).

• Immediately after encounter, edges damp as expected, but far downstream, wavelength deviates from 3s, sometimes switches abruptly from sinusoid to “chirp”.

• Widths of Keeler and Encke Gaps consistent with mass ratios.

• Is angular-momentum transfer affected?

Inner Edge

Outer Edge

Synodic Motion

Synodic Motion

Tiscareno et al. 2006

41 x 36 x 20 kmDensity: 0.4 g/cm3

Atlas Pan

~ 15 kmDensity: 0.4 g/cm3

Accretion in the Ring Region

• 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)

Equipotential Surfaces: Roche Lobe or Hill Sphere

Shapes of Solar System Bodies

Nature, last weekCharnoz et al., Burns, N&V

Saturn’sRing-Moons

Were Atlas -> Janus/Epimetheus born in the rings and driven outwards by ring torques?

• Hyperion’sbright 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

Spongy Tumbling Hyperion

Shape => 17 hr spin??

- Propellers-Corrugations in the C ring- Phoebe’s ring and Iapetus

Recent models involving collisions in Saturn’s rings

A Corrugated Curiosity in Saturn’s C ring

M.M. Hedman, J.A. Burns M.S. TiscarenoDDA Meeting, April 2010

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.

The corrugation wavelengths vary smoothly with radius, indicating that the corrugation is a single structure with one cause.

D-ring C-ring

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

CassiniImages

HST Occultation

dkdt

d Ý dr

214

J2GMr5

Rs

r

2Model: Tilted ring becomes corrugated and winds up at a rate determined by Saturn’s gravitational field

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

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.

How much mass is needed to shift the ring’s H by 10-7?

Where A is the corrugation amplitude ~ 10 mr is the ring radius ~ 80,000 kmvring is the orbital speed ~ 24 km/svimpactor is the impactor’s speed ~ 40 km/smring 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

`Ar sini ~

mimpact

mring

v impactor

vring

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

Thanks