ASTR 330: The Solar System
Announcements
• Mid-term #2 exams returned today.
• Class average =148.6 = 74.3%
• Range: 76-194 pts.
• Compare to Mid-term #1: avg. 167.8 (83.9%)
• What were the problem areas?
• Course class average so far: 457/600 = 76%.
• HW#5 due today.
Dr Conor Nixon Fall 2006
ASTR 330: The Solar System
Lecture 24:
Rings and Shepherds
Picture credit: solarviews.com (Voy 1: 11-12-81)
Dr Conor Nixon Fall 2006
ASTR 330: The Solar System
Saturn’s Rings: Discovery
• Whenever you think of a planet with rings, you probably think of Saturn.
Saturn’s rings were first seen in 1610 by the first ever astronomical
observer to possess a telescope: Galileo Galilei.
• Galileo was mystified by the
phenomenon: it looked like the planet had
‘ears’ ! In fact, many of his contemporaries
argued that he was seeing illusions through
his new-fangled device.
• This taunt was not helped any when the
‘ears’ disappeared several years later!
Why?
• Galileo theorized that he was seeing
‘bumps’ on the planet, or perhaps a triple
planet.
Picture credit: St Andrews Univ
Dr Conor Nixon Fall 2006
ASTR 330: The Solar System
An Explanation At Last
• The mystery of the ‘ears’ was eventually
cleared up by further observation: The
Dutch Astronomer Christian Huygens in
1659 correctly guessed that Saturn was
surrounded by “a thin flat ring, nowhere
touching” the planet and lying in the
equatorial plane.
• The reason for the periodic
disappearance also became apparent to
observers over time: as the planet orbits
the Sun on its inclined axis, over one full
orbit we see the ring(s) change from edge
on, to more face on, and back again, with
a 15 (Earth) year cycle.
Picture credit: (I) St Andrews University
(ii) NASA / Hubble Heritage Team (STScI / AURA)
Dr Conor Nixon Fall 2006
ASTR 330: The Solar System
First Structure in the Rings
• In 1675 another major event took place:
the astronomer Giovanni Cassini (right)
spotted a dark lane, or division in the ring.
The ring was therefore two rings: an outer
‘A’ Ring and an inner ‘B’ Ring.
• In 1837, J.F. Encke (who, like Halley,
connected 4 comet sightings as one)
spotted a dark lane (minimum) in the A
Ring. This was confirmed to be a gap, or
division, in 1888 by James Keeler.
Keeler’s original drawing is shown (right).
• Meanwhile, in 1850 the third ring, the
inner C or Crepe Ring was found by W.
Bond, G. Bond and W. Dawes. You can
also see it on the sketch.
Picture credit: (I) wikipedia.com (ii) Eric Jamison
Dr Conor Nixon Fall 2006
ASTR 330: The Solar System
1850-1973: Ring Particles
• Until the mid-1800s, it was not conclusively known whether the rings
were solid or composed of orbiting pieces, although there were sound
mathematical reasons for preferring the latter.
• We now know that the rings are indeed composed of billions of tiny
moons, with the inner ones traveling faster than the outer ones, each on
a circular Keplerian orbit around Saturn (with a few exceptions).
• At the inner edge, the particles take just 5.6 hrs to orbit once, compared
to 14.2 hours at the outer edge.
• In 1970, infrared spectroscopy revealed that the rings were made
primarily of water ice.
• Radar signals bounced off the rings were able to give a size estimate in
1973, with the typical size turning out to be around 10 cm.
Dr Conor Nixon Fall 2006
ASTR 330: The Solar System
1980-1981: Voyager Results
• The encounters of Voyagers 1 and 2 were the main sources of
knowledge about the rings prior to Cassini.
• The Voyagers found that the ring particles range in size from ‘grain of
sand’ size, up to boulders as big as a house. Small particles greatly
outnumber large ones: as we saw in the case of the main asteroid belt.
• Most of the particles have a visible albedo of 50-60%, with a spectrum
of water ice.
• Some are darker, perhaps composed of organics or silicates.
• Almost all the particles move in circular orbits in the equatorial plane,
as they must. Why do we say this? Because any particle moving out of a
circular orbit would bump against others, and lose energy. The effect is
to circularize the orbits.
Dr Conor Nixon Fall 2006
ASTR 330: The Solar System
The Main Rings of Saturn
• The rings are very broad and thin. They stretch from 7000 km above
the cloud tops, to 70,000 km and more. However, they are just 20 meters
thick (yes, I did write meters!).
• The analogy (from M&O) is that if the rings were as thick as notepaper,
then they would be eight city blocks (1 km) across!
• The main rings we have mentioned already are the A and B Rings; and
the inner Crepe (C) Ring. We will discuss others as well.
Name
D
C
B
Cassini Division
A
F
Table: Morrison and Owen
Outer Edge
(Rplanet )
1.233
1.524
1.946
2.212
2.265
2.324
Outer Edge
(km)
74,400
91,900
117,400
133,400
136,600
140,180
Dr Conor Nixon Fall 2006
ASTR 330: The Solar System
Picture credit: JPL/NASA
Lord of the Rings
Dr Conor Nixon Fall 2006
ASTR 330: The Solar System
Gaps in the Rings
• The spectacular Voyager (false color) image of C-Ring detail below
emphasizes one fact: every one of the ‘lettered’ rings is not a single ring
at all, but rather many hundreds of individual ‘ringlets’.
• Each ring is separated
by an apparent ‘gap’ (or
division), but few of these
divisions are really empty:
they are merely regions of
thinner material.
• A few of the gaps are
really empty (we will see
the reason for that later).
Picture credit: JPL/NASA
Dr Conor Nixon Fall 2006
ASTR 330: The Solar System
Inner rings: C and D
• Voyager discovered several thin rings between the planet
and the start of the C-Ring proper at 7000 km: collectively
these are called the D-Ring.
• The C-Ring is dense enough to reflect substantial sunlight,
and be seen from the Earth, although it is more transparent
than the A and B Rings.
• The C-Ring has two major gaps (several hundred km
wide).
• In one of these gaps is at least one narrow eccentric
ribbon ringlet. The color of this ring is different from the
nearby C-Ring material, hinting at a different composition
and origin. More have now been found.
Dr Conor Nixon Fall 2006
ASTR 330: The Solar System
The B-ring
• The B-ring is what we would
consider the ‘main’ ring of Saturn,
being the brightest, and
containing most of the mass.
• It begins 32,000 km from
Saturn, and continues unbroken
out to 57,000 km. The structure is
very complex, and although we
see thousands of individual
separate ringlets; the ‘gaps’
between them are not empty, just
less dense.
• The ring particles here range
from 10s of cm to meters in
diameter.
Picture credit: JPL/NASA/Space Science Institute
Dr Conor Nixon Fall 2006
ASTR 330: The Solar System
• At the outer edge of the BRing is the famous Cassini
Division. Far from being
empty space, as it appears
from the Earth, there are in
fact:
Cassini Division
• several faint sparse rings,
with ‘real’ gaps between
them.
• one known eccentric
ringlet (Huygens).
• Scientists considered
whether to target the Pioneer
11 spacecraft to pass
through the Cassini Division,
but the idea was luckily
rejected!
Picture credit: JPL/NASA/Space Science Institute
Dr Conor Nixon Fall 2006
ASTR 330: The Solar System
The A-ring
• Beyond the Cassini Division, at 61,000 km, the A-Ring begins. The ARing is intermediate in brightness and density to the B and C Rings.
• The A-ring contains two main gaps or divisions - Encke and Keeler - and
then ends sharply at 96,000 km from Saturn
• The image
(left) shows
clumping in
the A-ring
(falsely
colored from
ultraviolet)
compared to
a computer
simulation
(right).
Picture credit: JPL/NASA/Univ. of Colorado
Dr Conor Nixon Fall 2006
ASTR 330: The Solar System
A-ring: Encke Division
• The most interesting feature is the 360
km wide Encke Division (1/10 the width of
the Cassini Division).
• In this gap we see:
• 2 discontinuous, kinky ringlets: 20
km wide ribbons of material (above).
• at least one small satellite (Pan)
(left).
Picture credit: JPL/NASA
Dr Conor Nixon Fall 2006
ASTR 330: The Solar System
Voyager 2: Saturn’s Rings (False Color)
• Can you spot
the:
• A RING
• B RING
• C RING
• CASSINI
DIVISION
• ENCKE
DIVISION
Picture credit: JPL/NASA
Dr Conor Nixon Fall 2006
ASTR 330: The Solar System
The F-Ring
• 4000 km beyond the edge of the ARing is the interesting, faint F-Ring.
Unlike the previous A-D Rings we have
looked at, which were broad bands, the
F-Ring is an isolated bright ribbon.
• The width varies along its length: from
30 km to 500 km. It is also eccentric,
like the ones inside the C-Ring and the
Cassini Division.
• The F-Ring appears to split in places,
and divide into multiple strands which
appear intertwined or braided!
• Much of the structure in the F-Ring
may be caused by small nearby moons..
Image credit: NASA/JPL
Dr Conor Nixon Fall 2006
ASTR 330: The Solar System
The G and E Rings
• Beyond the F-Ring are two extremely faint outer rings: the G and ERings.
• The G-Ring is just 8 km wide and composed of small particles of
neutral tint.
• The very broad E-Ring (180,000 to 640,000 km from the planet), is
composed of very small (1-micron), same-sized particles, which have a
distinct blue color.
• The E-Ring stretches from the orbit of Mimas, peaking in density at
Enceladus, and then tapering off to Tethys and Dione.
• Enceladus is now known to be the source of E-ring particles, which are
the result of its active geysering.
Dr Conor Nixon Fall 2006
ASTR 330: The Solar System
Enceladus and the E-ring
• This Cassini image shows amazing detail of the moon Enceladus
encased within the E-ring. Bright streamers of material can be seen
leaving the moon.
Picture credit: NASA/JPL/Space Science Institute
Dr Conor Nixon Fall 2006
ASTR 330: The Solar System
Discovery of the Rings of Uranus
• On March 10th 1977, a group of scientists were set to observe an
occultation of a star by Uranus. (What do you think they were trying to
see?)
• The most important results came not from the planet, but from before
and after the planet went in front of the star.
• Scientists observing the occultation around the world all saw the same
thing: the starlight flickered on and off several times before the main
eclipse, and then on and off again in the same pattern after the eclipse.
• At first the scientists thought that they might be seeing a swarm of small
satellites.
• However, the fact that the same pattern was seen from different places
on the Earth ultimately led to the conclusion that Uranus was surrounded
by several narrow dark rings.
Dr Conor Nixon Fall 2006
ASTR 330: The Solar System
Studying Rings with Occultations
• The occultation technique is now a well-established method for
studying the ring structure of Uranus.
• This technique has one particular advantage over direct observation:
the resolution (fineness of detail seen) is not limited by the size of the
telescope or by the turbulence in the Earth’s atmosphere, as is
regular astronomy. The limit on resolution is how fast we can sample
the changing brightness of the star.
• In the case of Uranus additional advantages are that:
1. The rings are dark, so do not reflect sunlight to interfere with the
starlight.
2. At near-infrared wavelengths, the planet is also dark.
3. Uranus has a high tilt, so we can see the rings almost full-face on
(at certain times).
• Would these advantages also apply when observing Saturn’s rings?
Dr Conor Nixon Fall 2006
ASTR 330: The Solar System
Uranian Rings
• How do these compare to Saturn’s rings in width?
Ring
Name
6 Ring
5 Ring
4 Ring
Alpha
Beta
Eta
Gamma
Delta
Lambda
Epsilon
Distance
(km)
41,850
42,240
42,580
44,730
45,670
47,180
47,630
48,310
50,040
51,160
Width
(km)
1-3
2-3
2
8-11
7-11
55
1-4
3-9
1-2
22-93
Eccentricity
0.0010
0.0019
0.0011
0.0008
0.0004
0.0000
0.0000
0.0000
?
0.0079
Dr Conor Nixon Fall 2006
ASTR 330: The Solar System
From Moons to Rings
• This image shows the
Uranian ring system in false
color, from right to left:
• Epsilon (white)
• Delta (green)
• Gamma (blue)
• Eta (blue)
• Beta (light blue)
• Alpha (light blue)
•4
•5
•6
Picture credit: JPL/NASA
Dr Conor Nixon Fall 2006
ASTR 330: The Solar System
Uranian rings: description
• The Uranian rings are almost the opposite of the Saturnian ones: rather
than having mainly broad rings with a few narrow gaps; instead we have
a few narrow rings with large spaces in between.
• Also, the Uranian rings are dark, unlike the bright, reflective rings of
Saturn. Hence they cannot be composed of ice; and must instead be
made of some dark carbonaceous material.
• Most of the 10 rings are nearly circular and very narrow: typically less
than 10 km. Voyager 2 made close-up occultation measurements in
1986, determining fine structure.
• The Epsilon Ring probably contains as much mass as the rest put
together: it also has a variable width: 22 km closest to Uranus, and 93
km when furthest away.
• The Eta Ring is also strange: having a broad, diffuse ring 55 km wide,
and a narrow denser component at the inner edge.
Dr Conor Nixon Fall 2006
ASTR 330: The Solar System
View From the Shadows
• This image was taken
while Voyager 2 was in the
shadow of Uranus.
• This is a high phase angle
image, meaning that the
Sun is lighting up the ring
particles from behind, which
are scattering the light
forward to the camera
rather than blocking it.
• The broader dust lanes
are un-named. What are the
streaks on the image?
Picture credit: JPL/NASA
Dr Conor Nixon Fall 2006
ASTR 330: The Solar System
Does Jupiter Have Rings?
• When the Voyager 1 spacecraft arrived at Jupiter in 1979, it was
deliberately set to make a long exposure of the planet near the equator,
seen from behind to look for rings. The image below was the result: a
positive one! Voyager 2 was then programmed to take more pictures.
Picture credit: JPL/NASA - Voyager
Dr Conor Nixon Fall 2006
ASTR 330: The Solar System
Jovian Rings
• The main ring of Jupiter is a relatively narrow (5000 km) ring 54,000 km
from the cloud tops.
• The Jovian ring is much fainter than those of the other planets: the ring
material is 10,000 times less absorbing than window glass - we can only
see it when we look across the densest part.
• Inside the main ring, are the orbits of the small moons Adrastea and
Metis, which may serve as sources of ring material.
• The main rings merges inwards into the halo: a faint broad torus about
10,000 thick (north-south) which extends halfway from the main ring to
the cloud tops.
• Outside the main ring are two very faint gossamer rings: one bounded
by the orbit of the moon Amalthea, and the other by the orbit of Thebe.
Dr Conor Nixon Fall 2006
ASTR 330: The Solar System
Picture credit: JPL/NASA - Galileo
Dr Conor Nixon Fall 2006
ASTR 330: The Solar System
Rings of Neptune?
• Once rings were discovered at Uranus, it was natural to search for
rings of Neptune.
• Several occultations were observed, but the evidence was
contradictory. Sometimes the starlight dimmed on one side the planet
only, not on both as you might expect. This led to the idea that the rings
were in fact ‘arcs’ if they were there at all.
• When Voyager 2 arrived at Neptune, it found an even more complex
picture. There are in fact 3 major continuous rings, named Galle,
Leverrier and Adams in increasing order of distance (who were they?).
• The Adams Ring is the one with the arcs: three enhancements of
material at different points along its length. Why has the material not
spread out uniformly? We do not know.
Dr Conor Nixon Fall 2006
ASTR 330: The Solar System
Rings and Arcs
• The upper image (right)
shows 3 prominent arcs in
the Adams Ring: now
named Liberty, Equality and
Fraternity! From Voyager 2.
• The lower image shows
the three main rings, with
the glare of Neptune
masked out.
Picture credit: JPL/NASA
Dr Conor Nixon Fall 2006
ASTR 330: The Solar System
Patterns In The Rings
• Over time, as our knowledge of Saturn’s rings has improved, and
especially the technology for taking images, we have discovered
structure at finer and finer scales.
• From the Earth we were able to see the major Divisions of the rings,
but when the Voyagers arrived we saw much more detail: thousands of
ringlets, and strange spokes and wave patterns.
• The fine structure of the rings changes in a matter of hours, like the
surface of the sea. Two mathematical types of waves were predicted to
occur, and both were seen:
• Spiral density waves: ripples of more and less dense material,
like sound waves in air, or P-waves in the Earth.
• Spiral bending waves: vertical oscillations of ring material, like
EM radiation or S-waves in the Earth.
Dr Conor Nixon Fall 2006
ASTR 330: The Solar System
Waves in the A-Ring
• This Voyager image shows
both types of waves in the ARing, 400 km apart.
• The outer (left side) ripples are
the spiral density wave,
propagating outwards.
• The inner (right side)
disturbance is the spiral bending
wave, propagating inwards.
• These were formed due to
resonance perturbations from
the satellite Mimas, in this case
a 5:3 resonance.
Picture credit: solarviews.com
Dr Conor Nixon Fall 2006
ASTR 330: The Solar System
Ring Spokes
• Spokes are an even stranger effect. These are dark radial markings up
to 20,000 km long, which initially perplexed Voyager scientists, as they
seemed to defy gravity.
• Spokes are seen on both sides of the ring plane, near the densest part
of the B-Ring. They start at about 104,000 km from Saturn center and
extend to the Cassini Division, with a characteristic hour-glass shape.
• These are now thought to be made of dust particles suspended above
the ring plane. They rotate synchronously with the magnetic field, which
indicates that they are charged.
• Possible explanations are:
(i) material which has been ‘punched out’ by the passage of a small moonlet, or,
(ii) particles which have acquired charge and been drawn off the ring plane.
Dr Conor Nixon Fall 2006
ASTR 330: The Solar System
Spoke
Formation
Sequence
• This 35-minute
sequence of
images from
Voyager 2
shows the rapid
formation of a
new spoke,
indicated by the
arrow in the
lowermost
frame.
Picture credit: solarviews.com
Dr Conor Nixon Fall 2006
ASTR 330: The Solar System
Stability of Rings over time
• Over time, science predicts that the rings should spread out, both away
from the planet and towards it, due to interactions between the ring
particles and fragments (gravity, friction, collisions etc).
• At the inner edge, the pieces would fall into Saturn as meteors: at the
outer edge, the pieces would disperse to greater and greater distances.
• If the rings are to last then, something must be keeping them in place.
In fact, we now know that the outer edge of the A-Ring is ‘policed’ by the
co-orbital satellites, Janus and Epimetheus, in a 6:7 resonance. Their
gravity keeps the ring pieces trapped.
• The F-Ring is also confined by the action of moons: in this case, the
shepherd moons Prometheus and Pandora, one on each side. It is
probably the influence of these moons which causes the ‘braiding’ effect,
but our understanding is incomplete.
Dr Conor Nixon Fall 2006
ASTR 330: The Solar System
F-Ring Shepherds
• The left image from Voyager
2 shows the shepherd moons
Prometheus (inner) and
Pandora (outer), either side of
the F-Ring.
Picture credit: (I) solarviews.com (ii) NASA ARC.
• The right image shows a closer
view of Prometheus from Voyager 2.
The shape of the moon is clearly
seen, but there are no kinks in the
Ring evident near the satellite.
Dr Conor Nixon Fall 2006
ASTR 330: The Solar System
U-Ring Shepherds
• The narrow rings of Uranus seemed to be a slam-dunk case for
shepherd moons, in an analogue to the F-Ring of Saturn.
• Therefore, Voyager 2 was tasked to search for ring shepherds during
the Uranus encounter, a search which was not as successful as
anticipated.
• The image (right) shows two Epsilon
Ring shepherds discovered, now
named Cordelia and Ophelia. Each is
less than 50 km in size, and they orbit
some 2000 km either side of the Ring.
• No other shepherd satellites were
found, leaving a mystery for the other
rings: however the cameras could only
resolve detail down to 10 km in size.
Picture credit: JPL/NASA ARC
Dr Conor Nixon Fall 2006
ASTR 330: The Solar System
New Moons and Rings
Picture credit: wikipedia.org
Dr Conor Nixon Fall 2006
ASTR 330: The Solar System
Resonances with large satellites
• It is not only the small satellites close to the rings which have an effect
on ring structure: the larger, further moons also play a part.
• Mimas is particularly
influential: in fact, the inner
edge of the Cassini Division
is an exact 2:1 resonance
with Mimas (remember the
gaps in the asteroid belt?).
• This Voyager 1 image was
taken looking across the
‘dark side’ (shadowed) of
the rings, showing the ARing, thin F-Ring, and the
moon Mimas.
Picture credit: JPL/NASA ARC
Dr Conor Nixon Fall 2006
ASTR 330: The Solar System
Origin of Rings and Small Satellites
•
There are two main theories of ring formation, and both
are closely tied to the presence of the small satellites.
1. The ‘break-up’ theory: in essence, this theory suggests
that the rings are the remains of a shattered small
satellite.
2. The second theory suggests that the rings are material
which was unable to form an actual satellite, due
gravitational interference.
•
We will examine each of these theories in turn.
Dr Conor Nixon Fall 2006
ASTR 330: The Solar System
Tidal Stability
• The tidal stability limit is the distance from a planet where tidal forces
become stronger than the forces keeping a body together.
• This limit, known as the Roche Limit after the 19th century
mathematician who proposed it, depends on factors such as tensile
strength of the body, as well as its self gravitation.
• For example, two bodies just touching (zero tensile strength) will pull
apart at about 2.5 planetary radii from the planet center.
• On the other hand, clearly objects such as the shuttle do not get tidally
pulled apart in orbit around the Earth: their intrinsic strength keeps them
whole.
• Therefore, we can propose that inside the Roche Limit of the planets,
the particles of the rings were unable to stay together long enough to
form an actual moon.
Dr Conor Nixon Fall 2006
ASTR 330: The Solar System
Simulation Of Ring Particles
• This image shows a
visualization (artists
impression) of the
ring particles.
• In this image, the
largest pieces are
house-sized.
• Clumps of boulders
are continuously
being created and
being pulled apart
again by tidal forces,
as in the foreground
(‘S’ shape).
Picture credit: William K Hartmann
Dr Conor Nixon Fall 2006
ASTR 330: The Solar System
Satellite Break-Up
• There are several ways in which we imagine a satellite being
destroyed. One is by tidal forces, if a moon or even a comet (e.g. S-L 9)
wandered too close to a planet.
• The other possibility is that a satellite suffered a massive impact, while
inside the Roche Limit and was unable to re-form again afterwards
(unlike Miranda).
• The embedded satellites provide evidence for this type of scenario: if
we could find a lot more larger pieces, the theory would be stronger.
• We can calculate the mass of ring systems, and see if the amount is
appropriate. For Saturn the total ring mass (that we know of) is 1018 kg:
about equivalent to a 250 km diameter satellite, very close to the size of
Janus.
• Hence, the theory is plausible, but by no means proven. We cannot rule
out that this material never formed a moon.
Dr Conor Nixon Fall 2006
ASTR 330: The Solar System
Long Term Stability
• Even if we know how the rings formed, we have not answered the
question of long-term stability. This depends on particle size. Small
particles would be eroded more quickly; in just a few 100 million years.
• Therefore,
either the rings
are a recent
occurrence, or
they are
constantly being
renewed by the
break-up of kmsized objects
which are now
been discovered
by Cassini (right).
Picture credit: NASA/JPL/Space Science Institute
Dr Conor Nixon Fall 2006
ASTR 330: The Solar System
Compositions
• The chemical compositions of the 4 ring systems must
also be explained. Saturn’s rings are mostly icy material: the
easiest to explain. Some silicates (rock dust) must also be
present.
• The J-Rings are mainly silicate: erosion from the rocky
satellites.
• The dark rings of Uranus and Neptune are the hardest to
explain, as the large satellites are mostly icy. However, the
dark coatings seen on the inner satellites seems to suggest
that they were formed from a moon break-up which also
created the rings.
Dr Conor Nixon Fall 2006
ASTR 330: The Solar System
Quiz-Summary
1. Who discovered (a) the main rings of Saturn (b) the explanation for the
‘ears’ (c) the two major Divisions?
2. How was the ring particle size and composition first measured? What
results were obtained?
3. Why are the ring particles mainly in circular, low-inclination orbits?
4. Are the ring divisions or gaps really empty?
5. What types off outer rings (beyond the A-Ring) do we see?
6. How were the rings of Uranus discovered, and what advantages are
there to this method?
7. What are the main similarities and differences between the rings of
Saturn, and Uranus?
Dr Conor Nixon Fall 2006
ASTR 330: The Solar System
Quiz-Summary
8. How were the rings of Jupiter discovered, and what are they?
9. The rings off Neptune were once thought to be incomplete ‘arcs’ of
material rather than true rings. Was this theory true? Describe them.
10. Why do we see (a) waves and (b) spokes in the rings?
11. What confines (a) the outer edge of the A-Ring (b) the F-Ring?
12. Do all the Uranian rings have shepherds?
13. What causes the Cassini Division?
14. What is the Roche or Tidal Stability Limit?
15.What two theories have been suggested for the origin of rings.
Dr Conor Nixon Fall 2006