solar system physics i dr martin hendry 5 lectures, beginning autumn 2007 department of physics and...
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Solar System Physics ISolar System Physics IDr Martin Hendry
5 lectures, beginning Autumn 2007
Department of Physics and Astronomy
Astronomy 1XSession 2007-08
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.
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).
A ringCassini division
B ringC 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.
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.
A ringCassini division
B ringC ring
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
The F ring shows braided structure, is very narrow, and contains large numbers of micron-sized particles.
Solar System Physics ISolar System Physics IDr Martin Hendry
5 lectures, beginning Autumn 2007
Department of Physics and Astronomy
Astronomy 1XSession 2007-08
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.
Ring Systems of the other Jovian Planets
Why are the ring systems so thin?
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
y
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 and radius , orbiting at a distance (centre to centre) from a planet of mass and radius .
Section 10: Formation of ring systems
r A
PM
SM SR
r PM PR
( Assume that the planet and moon are spherical )
SM
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 and radius , orbiting at a distance (centre to centre) from a planet of mass and radius .
Section 10: Formation of ring systems
r
PM
SM SR
r PM PR
( Assume that the planet and moon are spherical )
Force on a unit mass at A due to gravity of moon alone is
2S
SG
R
MGF (10.1)
A
GFSM
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 and radius , orbiting at a distance (centre to centre) from a planet of mass and radius .
Section 10: Formation of ring systems
r
PM
SM SR
r PM PR
This follows from eq. (4.3) putting
Tidal force on a unit mass at A due to gravity of planet is
(10.2)
SR
3
2
r
RMGF SPT
A
TFSM
We assume, as an order-of-magnitude estimate that the
moon is tidally disrupted if
In other words, if
This rearranges further to
23
2
S
SSP
R
MG
r
RMG
GT FF (10.3)
(10.4)
SS
P RM
Mr
3/1
3/12
(10.5)
We can re-cast eq. (10.5) in terms of the planet’s radius, by
writing mass = density x volume.
Substituting
So the moon is tidally disrupted if
3
34
PPP RM
3
34
SSS RM
PS
P Rr3/1
3/12
(10.6)
We can re-cast eq. (10.5) in terms of the planet’s radius, by
writing mass = density x volume.
Substituting
So the moon is tidally disrupted if
More careful analysis gives
the Roche Stability Limit
3
34
PPP RM
3
34
SSS RM
PS
P Rr3/1
3/12
(10.6)
Pm
P Rr3/1
456.2
(10.7)
e.g. for Saturn, from the Table of planetary data
Take a mean density typical of the other moons
This implies
Most of Saturn’s ring system does lie within this
Roche stability limit. Conversely all of its moons
lie further out!
-3mkg700P
-3mkg1200m
PPRL RRr 05.21200
700456.2
3/1
(10.8)
Roche stability limit
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)
Section 11: More on Tidal Forces
The Sun also exerts a tide on the Earth.
Now, so
and
so that
3r
MF PT
3
Sun
Moon
Moon
Sun
Moon,
Sun,
r
r
M
M
F
F
T
T (11.1)
kg10989.1 30Sun M kg1035.7 22
Moon M
m10496.1 11Sun r m10844.3 8
Moon r
5.03
Sun
Moon
Moon
Sun
Moon,
Sun,
r
r
M
M
F
F
T
T (11.2)
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.
The Sun and Moon exert a tidal force similar in magnitude. The size of their combined tide on the Earth depends on their alignment.
Earth
Moon
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.
Earth’s rotation
Earth
Moon
The Earth’s rotation carries the tidal bulge ahead of the
Earth-Moon axis. (The Earth’s crust and oceans cannot
instantaneously redstribute themselves along the axis due
to friction)
Moon’s orbital motion
Earth’s rotation
Earth
Moon
A ‘Drag’ force
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.
Moon’s orbital motion
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
Earth
Moon
A ‘Drag’ force
Moon’s orbital motion
Earth’s rotation
Earth
Moon
A ‘Drag’ force
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 !!!
Moon’s orbital motion
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 The moons of Jupiterof 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
Neptune
Triton
ATriton’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)
Tidal forces have a major influence on the Galilean Moons of Jupiter
Name Diameter Semi-major Orbital Period Mass (m) axis (m) (days) (kg)
Io 610642.3
610120.3
610268.5
610800.4
Europa
Ganymede
Callisto
The Moon
Mercury
610476.3
610880.4
810216.4
810709.6
910070.1
910883.1
810844.3
1.769
3.551
7.155
16.689
27.322
2210932.8
2210791.4
2310482.1
2310077.1
2210349.7
2310302.3
Section 12: The Galilean Moons of Jupiter
Io Europa
Ganymede 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
IoEuropa
Ganymede
Callisto
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