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Department of Physics and Astronomy
Astronomy 1X
Session 2007-08
Solar System Physics I
Dr Martin Hendry
5 lectures, beginning Autumn 2007
Section 9: Ring Systems of the Jovian Planets
All four Jovian planets have RING SYSTEMS. e.g. Saturn’s rings
are easily visible from Earth with a small telescope, and appear solid.
Section 9: Ring Systems of the Jovian Planets
All four Jovian planets have RING SYSTEMS. e.g. Saturn’s rings
are easily visible from Earth with a small telescope, and appear solid.
The rings consist of countless lumps of ice and rock, ranging from
~1cm to 5m in diameter, all independently orbiting Saturn in an
incredibly thin plane – less than 1 kilometre in thickness.
Section 9: Ring Systems of the Jovian Planets
All four Jovian planets have RING SYSTEMS. e.g. Saturn’s rings
are easily visible from Earth with a small telescope, and appear solid.
The rings consist of countless lumps of ice and rock, ranging from
~1cm to 5m in diameter, all independently orbiting Saturn in an
incredibly thin plane – less than 1 kilometre in thickness.
( Diameter of the outermost ring – 274000 km. If Saturn’s rings were the
thickness of a CD, they would still be more than 200m in diameter! )
Section 9: Ring Systems of the Jovian Planets
All four Jovian planets have RING SYSTEMS. e.g. Saturn’s rings
are easily visible from Earth with a small telescope, and appear solid.
The rings consist of countless lumps of ice and rock, ranging from
~1cm to 5m in diameter, all independently orbiting Saturn in an
incredibly thin plane – less than 1 kilometre in thickness.
( Diameter of the outermost ring – 274000 km. If Saturn’s rings were the
thickness of a CD, they would still be more than 200m in diameter! )
James Clerk Maxwell proved that Saturn’s
rings couldn’t be solid; if they were then
tidal forces would tear them apart. He
concluded that the rings were made of ‘an
indefinite number of unconnected particles’
Saturn’s rings are bright; they reflect ~80% of the sunlight that
falls on them. Their ice/rock composition was confirmed in the
1970s when absorption lines of water were observed in the
spectrum of light from the rings.
(See A1Y Stellar astrophysics for more on spectra and absorption lines)
Saturn’s rings are bright; they reflect ~80% of the sunlight that
falls on them. Their ice/rock composition was confirmed in the
1970s when absorption lines of water were observed in the
spectrum of light from the rings.
(See A1Y Stellar astrophysics for more on spectra and absorption lines)
Ground-based observations show only the
A, B and C rings.
B ring
C ring
In the 1980s the Voyager spacecraft flew
past Saturn, and observed thousands of
‘ringlets’ – even in the Cassini Division
(previously believed to be a gap).
Cassini division
A ring
Saturn’s rings are bright; they reflect ~80% of the sunlight that
falls on them. Their ice/rock composition was confirmed in the
1970s when absorption lines of water were observed in the
spectrum of light from the rings.
(See A1Y Stellar astrophysics for more on spectra and absorption lines)
Ground-based observations show only the
A, B and C rings.
B ring
C ring
In the 1980s the Voyager spacecraft flew
past Saturn, and observed thousands of
‘ringlets’ – even in the Cassini Division
(previously believed to be a gap).
They also discovered a D ring, (inside the
C ring), and very tenuous E, F and G rings
outside the A ring, out to ~5 planetary radii.
Cassini division
A ring
The F ring shows braided structure,
is very narrow, and contains large
numbers of micron-sized particles.
The structure of the F ring is
controlled by the two
‘shepherd moons’ – Pandora
and Prometheus – which orbit
just inside and outside it.
The gravitational influence of
these moons confine the F
ring to a band about 100km
wide
Department of Physics and Astronomy
Astronomy 1X
Session 2007-08
Solar System Physics I
Dr Martin Hendry
5 lectures, beginning Autumn 2007
Ring Systems of the other Jovian Planets
Jupiter’s ring system is much more tenuous than Saturn’s. It
was only detected by the Voyager space probes. The ring
material is primarily dust, and extends to about 3 Jupiter radii.
Ring Systems of the other Jovian Planets
Jupiter’s ring system is much more tenuous than Saturn’s. It
was only detected by the Voyager space probes. The ring
material is primarily dust, and extends to about 3 Jupiter radii.
Uranus’ rings were discovered in 1977, during the occultation
of a star, and first studied in detail by Voyager 2 in 1986
There are 11 rings, ranging in width from 10km to 100km. The
ring particles are very dark and ~1m across. Some rings are
‘braided’, and the thickest ring has shepherd moons. There is a
thin layer of dust between the rings, due to collisions.
Ring Systems of the other Jovian Planets
Jupiter’s ring system is much more tenuous than Saturn’s. It
was only detected by the Voyager space probes. The ring
material is primarily dust, and extends to about 3 Jupiter radii.
Uranus’ rings were discovered in 1977, during the occultation
of a star, and first studied in detail by Voyager 2 in 1986
There are 11 rings, ranging in width from 10km to 100km. The
ring particles are very dark and ~1m across. Some rings are
‘braided’, and the thickest ring has shepherd moons. There is a
thin layer of dust between the rings, due to collisions.
Neptune’s rings were first photographed by Voyager 2 in 1989.
There are 4 rings: two narrow and two diffuse sheets of dust.
One of the rings has 4 ‘arcs’ of concentrated material.
Why are the ring systems so thin?
y
Collisions of ring particles are partially inelastic.
Consider two particles orbiting
e.g. Saturn in orbits which are
slightly tilted with respect to
each other.
Collision reduces difference of
y components, but has little
effect on x components
 this thins out the disk of
ring particles
x
Section 10: Formation of ring systems
The ring systems of the Jovian planets result from tidal forces.
During planetary formation, these prevented any material that was too
close to the planet clumping together to form moons. Also, any moons
which later strayed too close to the planet would be disrupted.
Consider a moon of mass M S and radius RS , orbiting at a distance
(centre to centre) r from a planet of mass M P and radius RP .
MP
r
A
MS
( Assume that the planet and moon are spherical )
Section 10: Formation of ring systems
The ring systems of the Jovian planets result from tidal forces.
During planetary formation, these prevented any material that was too
close to the planet clumping together to form moons. Also, any moons
which later strayed too close to the planet would be disrupted.
Consider a moon of mass M S and radius RS , orbiting at a distance
(centre to centre) r from a planet of mass M P and radius RP .
Force on a unit mass
at A due to gravity of
moon alone is
MP
FG
r
A
MS
( Assume that the planet and moon are spherical )
G MS
FG 
2
RS
(10.1)
Section 10: Formation of ring systems
The ring systems of the Jovian planets result from tidal forces.
During planetary formation, these prevented any material that was too
close to the planet clumping together to form moons. Also, any moons
which later strayed too close to the planet would be disrupted.
Consider a moon of mass M S and radius RS , orbiting at a distance
(centre to centre) r from a planet of mass M P and radius RP .
Tidal force on a unit
mass at A due to
gravity of planet is
MP
FT
r
A
MS
2G M P RS
FT 
r3
This follows from eq. (4.3) putting   RS
(10.2)
We assume, as an order-of-magnitude estimate that the moon
is tidally disrupted if
FT  FG
In other words, if
(10.3)
2G M P RS G M S

2
3
r
RS
(10.4)
1/ 3
This rearranges further to
 MP 
 RS
r  2 
 MS 
1/ 3
(10.5)
We can re-cast eq. (10.5) in terms of the planet’s radius, by
writing mass = density x volume.
Substituting
MP 
4
3
 P RP
MS 
4
3
S RS
3
3
1/ 3
So the moon is tidally disrupted if
 P 
r  2   RP
 S 
1/ 3
(10.6)
We can re-cast eq. (10.5) in terms of the planet’s radius, by
writing mass = density x volume.
Substituting
MP 
4
3
 P RP
MS 
4
3
S RS
3
3
1/ 3
So the moon is tidally disrupted if
More careful analysis gives
the Roche Stability Limit
 P 
r  2   RP
 S 
1/ 3
1/ 3
 P 

r  2.456 
 m 
RP
(10.7)
(10.6)
e.g. for Saturn, from the Table of planetary data
Take a mean density typical of the other moons
 P  700 kg m-3
 m  1200 kg m -3
This implies
1/ 3
 700 
rRL  2.456  

 1200 
 RP
 2.05 RP
Most of Saturn’s ring system does lie within this
Roche stability limit. Conversely all of its moons
lie further out!
(10.8)
Roche stability limit
Section 11: More on Tidal Forces
Tidal forces also have an effect (albeit less destructive) outside
the Roche stability limit.
Consider the Moon’s tide on
the Earth (and vice versa).
The tidal force produces an
oval bulge in the shape of the
Earth (and the Moon)
Section 11: More on Tidal Forces
Tidal forces also have an effect (albeit less destructive) outside
the Roche stability limit.
Consider the Moon’s tide on
the Earth (and vice versa).
The tidal force produces an
oval bulge in the shape of the
Earth (and the Moon)
There are, therefore, two high
and low tides every ~25 hours.
(Note: not every 24 hours, as the Moon
has moved a little way along its orbit by
the time the Earth has completed one rotation)
The Sun also exerts a tide on the Earth.
Now,
and
so that
MP
FT  3
r
so
FT ,Sun
FT ,Moon
M Sun  rMoon 



M Moon  rSun 
M Sun  1.989 1030 kg
M Moon  7.35 10 22 kg
rSun  1.496 1011 m
rMoon  3.844 108 m
FT ,Sun
FT ,Moon
3
(11.1)
3
M Sun  rMoon 

  0.5

M Moon  rSun 
(11.2)
The Sun and Moon exert a tidal force similar in magnitude.
The size of their combined tide on the Earth depends on
their alignment.
Spring tides occur when the
Sun, Moon and Earth are
aligned (at Full Moon and New
Moon). High tides are much
higher at these times.
Neap tides occur when the Sun,
Moon and Earth are at right
angles (at First Quarter and
Third Quarter). Low tides are
much lower at these times.
Even if there were no tidal force on the Earth from the Sun, the
Earth’s tidal bulge would not lie along the Earth-Moon axis. This
is because of the Earth’s rotation.
Moon
Earth
The Earth’s rotation carries the tidal bulge ahead of the EarthMoon axis. (The Earth’s crust and oceans cannot instantaneously
redstribute themselves along the axis due to friction)
Earth’s rotation
Moon’s orbital
motion
Moon
Earth
The Moon exerts a drag force on the tidal bulge at A, which
slows down the Earth’s rotation.
The length of the Earth’s day is increasing by 0.0016 sec per century.
Earth’s rotation
A
‘Drag’ force
Moon’s orbital
motion
Moon
Earth
At the same time, bulge A is pulling the Moon forward, speeding
it up and causing the Moon to spiral outwards. This follows from
the conservation of angular momentum.
The Moon’s semi-major axis is increasing by about 3cm per year.
Earth’s rotation
A
‘Drag’ force
Moon’s orbital
motion
Moon
Earth
Given sufficient time, the Earth’s rotation period would slow down
until it equals the Moon’s orbital period – so that the same face
of the Earth would face the Moon at all times.
(This will happen when the Earth’s “day” is 47 days long)
In the case of the Moon, this has already happened !!!
Earth’s rotation
A
‘Drag’ force
Moon’s orbital
motion
Moon
Earth
Given sufficient time, the Earth’s rotation period would slow down
until it equals the Moon’s orbital period – so that the same face
of the Earth would face the Moon at all times.
(This will happen when the Earth’s “day” is 47 days long)
In the case of the Moon, this has already happened !!!
Tidal locking has occurred much more rapidly for the Moon than
for the Earth because the Moon is much smaller, and the Earth
produces larger tidal deformations on the Moon than vice versa.
Given sufficient time, the Earth’s rotation period would slow down
until it equals the Moon’s orbital period – so that the same face
of the Earth would face the Moon at all times.
(This will happen when the Earth’s “day” is 47 days long)
In the case of the Moon, this has already happened !!!
Tidal locking has occurred much more rapidly for the Moon than
for the Earth because the Moon is much smaller, and the Earth
produces larger tidal deformations on the Moon than vice versa.
The Moon isn’t exactly tidally locked. It ‘wobbles’ due to the
perturbing effect of the Sun and other planets, and because its
orbit is elliptical. Over about 30 years, we see 59% of the
Moon’s surface.
Many of the satellites in Solar System are in synchronous
rotation, e.g.
Mars:
Phobos and Deimos
Jupiter:
Galilean moons + Amalthea
Saturn:
All major moons, except Phoebe + Hyperion
Neptune:
Triton
Pluto:
Charon
The moons of
Jupiter
Many of the satellites in Solar System are in synchronous
rotation, e.g.
Mars:
Phobos and Deimos
Jupiter:
Galilean moons + Amalthea
Saturn:
All major moons, except Phoebe + Hyperion
Neptune:
Triton
Pluto:
Charon
Pluto and Charon are in mutual synchronous rotation: i.e. the
same face of Charon is always turned towards the same face of
Pluto, and vice versa.
Many of the satellites in Solar System are in synchronous
rotation, e.g.
Mars:
Phobos and Deimos
Jupiter:
Galilean moons + Amalthea
Saturn:
All major moons, except Phoebe + Hyperion
Neptune:
Triton
Pluto:
Charon
Pluto and Charon are in mutual synchronous rotation: i.e. the
same face of Charon is always turned towards the same face of
Pluto, and vice versa.
Triton orbits Neptune in a retrograde orbit (i.e. opposite
direction to Neptune’s rotation).
Neptune’s rotation
Triton
A
Neptune
Triton’s orbital
motion
In this case Neptune’s tidal bulge acts to slow down Triton. The
moon is spiralling toward Neptune (although it will take billions of
years before it reaches the Roche stability limit)
Section 12: The Galilean Moons of Jupiter
Tidal forces have a major influence on the Galilean Moons of Jupiter
Name
Diameter
(m)
Semi-major
axis (m)
Orbital Period
(days)
Mass
(kg)
Io
3.642 106
4.216 108
1.769
8.932 10 22
Europa
3.120 106
6.709 108
3.551
4.79110 22
Ganymede
5.268 106
1.070  109
7.155
1.482 10 23
Callisto
4.800 106
1.883  109
16.689
1.077 10 23
The Moon
3.476 106
3.844 108
27.322
7.349 10 22
Mercury
4.880 106
3.302 10 23
Io
Ganymede
Europa
Callisto
The orbital periods of Io, Europa and Ganymede are almost
exactly in the ratio 1:2:4. This leads to resonant effects :
The orbit of Io is perturbed by Europa and Callisto, because
the moons regularly line up on one side of Jupiter. The
gravitational pull of the outer moons is enough to produce a
small eccentricity in the orbit of Io. This causes the tidal
bulges of Io to ‘wobble’ (same as the Moon) which produces
large amount of frictional heating.
The surface of Io is almost totally molten, yellowish-orange
in colour due to sulphur from its continually erupting
volcanoes.
Tidal friction effects on Europa are weaker than on Io, but
still produce striking results. The icy crust of the moon is
covered in ‘cracks’ due to tidal stresses, and beneath the crust
it is thought frictional heating results in a thin ocean layer
Inside Europa
Interior structure of the Galilean Moons
Io
Europa
Callisto
Ganymede
Structure of the Galilean Moons
Their mean density decreases with distance from Jupiter
The fraction of ice which the moons contain increases with
distance from Jupiter
This is because the heat from ‘proto-Jupiter’ prevented ice grains from
surviving too close to the planet. Thus, Io and Europa are mainly rock;
Ganymede and Callisto are a mixture of rock and ice.
The surface of the Moons reflects their formation history:
Io:
surface continually renewed by volcanic activity. No
impact craters
Europa:
surface young ( < 100 million years), regularly
‘refreshed’ – hardly any impact craters
Structure of the Galilean Moons
Their mean density decreases with distance from Jupiter
The fraction of ice which the moons contain increases with
distance from Jupiter
This is because the heat from ‘proto-Jupiter’ prevented ice grains from
surviving too close to the planet. Thus, Io and Europa are mainly rock;
Ganymede and Callisto are a mixture of rock and ice.
The surface of the Moons reflects their formation history:
Ganymede:
Cooled much earlier than Io and Europa.
Considerable impact cratering; also ‘grooves’
and ridges suggest history of tectonic activity
Structure of the Galilean Moons
Their mean density decreases with distance from Jupiter
The fraction of ice which the moons contain increases with
distance from Jupiter
This is because the heat from ‘proto-Jupiter’ prevented ice grains from
surviving too close to the planet. Thus, Io and Europa are mainly rock;
Ganymede and Callisto are a mixture of rock and ice.
The surface of the Moons reflects their formation history:
Ganymede:
Cooled much earlier than Io and Europa.
Considerable impact cratering; also ‘grooves’
and ridges suggest history of tectonic activity
Callisto:
Cooled even earlier; extensive impact cratering