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.

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.

appear solid.

( 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! )

appear solid.

( 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)

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

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

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.

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?

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

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 PR

( Assume that the planet and moon are spherical )

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

MGF (10.1)

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)

RMGF SPT

We assume, as an order-of-magnitude estimate that the

moon is tidally disrupted if

In other words, if

This rearranges further to

GT FF (10.3)

(10.4)

(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

PPP RM

SSS RM

P Rr3/1

(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

PPP RM

SSS RM

P Rr3/1

(10.6)

P Rr3/1

(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

(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

so that

T (11.1)

kg10989.1 30Sun M kg1035.7 22

Moon M

m10496.1 11Sun r m10844.3 8

Moon r

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.

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

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

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.

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

Earth’s rotation

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 !!!

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.

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

rotation, e.g.

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.

rotation, e.g.

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

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

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

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.

Ganymede: Cooled much earlier than Io and Europa.

Considerable impact cratering; also

‘grooves’ and ridges suggest history of

tectonic activity

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.

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

Solar System Physics I Dr Martin Hendry 5 lectures, beginning Autumn 2007 Department of Physics and...

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