EART 160: Planetary Science
25 February 2008
Homework 4 Graded
• Wikipedia is not a peer-reviewed journal
• I gave an incorrect value for H in problem
3, but it didn’t seem to trip anybody up.
• Convection in mantle, Conduction in
lithosphere
• Max: 50, Min: 21, Mean 36, St. Dev. 10
Last Time
• Coriolis Force Demo
• Planetary Atmospheres
– Thermal Balance
– Origin / Geochemistry
– Climate Change
Jeans Escape
• This expression for Jeans Escape IS
correct after all.
• Escape velocity ve= (2 g R)1/2
• Recall: g = GM / R2
Today
• Giant Planets
– Atmospheres
– Interiors
– Magnetospheres?
• Questions to Ponder:
– What determines their internal structure?
– How did they form and evolve?
– What controls their atmospheric dynamics?
• Moons: Tour of Icy Satellites
Giant Planets
Image not
to scale!
Basic Parameters
a
(AU)
Porb
(yrs)
Prot
(hrs)
R
(km)
M
(1026 kg)
Obliquity
Density
g/cc
Ts
K
Jupiter
5.2
11.8
9.9
71492
19.0
3.1o
1.33
165
Saturn
9.6
29.4
10.6
60268
5.7
26.7o
0.69
134
Uranus
19.2
84.1
17.2R
24973
0.86
97.9o
1.32
76
Neptune
30.1
165
16.1
24764
1.02
29.6o
1.64
72
Data from Lodders and Fegley 1998. Surface temperature Ts and radius R are
measured at 1 bar level.
Compositions
• We’ll discuss in more detail later, but briefly:
– (Surface) compositions based mainly on
spectroscopy
– Interior composition relies on a combination of models
and inferences of density structure from observations
– We expect the basic starting materials to be similar to
the composition of the original solar nebula
• Surface atmospheres dominated by H2 or He:
Solar
Jupiter Saturn
Uranus
Neptune
H2
83.3%
86.2%
96.3%
82.5%
80%
He
16.7%
13.6%
3.3%
15.2%
(2.3% CH4)
19%
(1% CH4)
(Lodders and Fegley 1998)
Pressure
dP
• Hydrostatic approximation
dr    (r ) g (r )
dM ( r )
2
• Mass-density relation

4

(
r
)
r
dr
• These two can be combined (how?) to get the pressure
at the centre of a uniform body Pc:
2
3GM
Pc 
8R 4
• Jupiter Pc=7 Mbar, Saturn Pc=1.3 Mbar, U/N Pc=0.9 Mbar
• This expression is only approximate (why?) (estimated true
central pressures are 70 Mbar, 42 Mbar, 7 Mbar)
• But it gives us a good idea of the orders of magnitude
involved
Equation of State
• If parcel of gas moves up/down fast enough that it doesn’t exchange
energy with surroundings, it is adiabatic
• In this case, the energy required to cause expansion comes from
cooling (and possible release of latent heat); and vice versa
• For an ideal, adiabatic gas we have two key relationships:
Ideal Gas Law
RT
P

Polytropic Law
P  K 
Here P is pressure,  is density, R is gas constant (8.3 J mol-1 K-1), T is temperature,
 is the mass of one mole of the gas,  is a constant (ratio of specific heats, ~ 3/2)
• So:
T 
• Adiabatic Lapse Rate
dT g

dz C p
At 1 bar level on Jupiter:
T=112 K, g=23 ms-2, Cp = 25 J mol-1 K-1,
=0.002 kg mol-1
dT/dz = 1.4 K/km
Hydrogen phase diagram
Hydrogen undergoes a
phase change at ~100
GPa to metallic
hydrogen (conductive)
It is also theorized that
He may be insoluble in
metallic H. This has
implications for Saturn.
Interior temperatures
are adiabats
• Jupiter – interior mostly metallic hydrogen
• Saturn – some metallic hydrogen
• Uranus/Neptune – molecular hydrogen only
Compressibility & Density
• As mass increases, radius
also increases
• But beyond a certain mass,
radius decreases as mass
increases.
• This is because the increasing
pressure compresses the
deeper material enough that
the overall density increases
faster than the mass
• The observed masses and
radii are consistent with a
mixture of mainly H+He (J,S)
or H/He+ice (U,N)
radius
mass
From Guillot,
2004
Giant Planet Formation
• Recall the first week of class
• Initially solid bodies (rock + ice; beyond snow line)
• When solid mass exceeded ~10 M, gravitational
acceleration sufficient to trap an envelope of H and He
• Process accelerated until nebular gas was lost
• So initial accretion was rapid (few Myr)
• Uranus and Neptune didn’t acquire so much gas because
they were further out and accreted more slowly
• Planets will have initially been hot (gravitational energy)
and subsequently cooled and contracted
• We can investigate how rapidly they are cooling at the
present day . . .
Energy budget observations
• Incident solar radiation much less than that at Earth
• So surface temperatures are lower
• We can compare the amount of solar energy absorbed
with that emitted. It turns out that there is usually an
excess. Why?
All units in
After Hubbard,
in New Solar System (1999)
1.4
W/m2
reflected
48
3.5
14
incident
8.1
5.4
Jupiter
0.6
0.6
4.6
13.5
2.6
0.6
0.3
2.0
Saturn
0.3
Uranus
Neptune
Sources of Energy
• One major one is contraction – gravitational energy
converts to thermal energy. Helium sinking is another.
• Gravitational energy of a uniform sphere is
Eg  0.6GM / R
2
• So the rate of energy release during contraction is
GM 2 dR
 0.6 2
dt
R dt
dE g
e.g.Jupiter is radiating 3.5x1017 W in excess of incident solar radiation.
This implies it is contracting at a rate of 0.4 km / million years
• Other sources?
– Tidal dissipation
– Radioactive decay
small compared to grav. energy
Uranus – What The Hell?
• Why is Uranus’ heat budget so different?
– Perhaps due to compositional density differences inhibiting
convection at levels deeper than ~0.6Rp .May explain different
abundances in HCN,CO between Uranus and Neptune
atmospheres.
– This story is also consistent with generation of magnetic fields in
the near-surface region (see earlier slide)
• Why is Uranus tilted on its side?
– Nobody really knows, but a possible explanation is an oblique
impact with a large planetesimal (c.f. Earth-Moon)
– This impact might even help to explain the compositional
gradients which (possibly) explain Uranus’ heat budget
Atmospheric Structure
• Lower atmosphere (opaque) is dominantly heated from below and will
be conductive or convective (adiabatic)
• Upper atmosphere intercepts solar radiation and re-radiates it
• There will be a temperature minimum where radiative cooling is most
efficient; in giant planets, it occurs at ~0.1 bar
• Condensation of species will occur mainly in lower atmosphere
mesosphere
radiation
Temperature
(schematic)
Theoretical cloud distribution
CH4 (U,N only)
stratosphere
tropopause
140 K
~0.1 bar
NH3
clouds
troposphere
80 K
adiabat
NH3+H2S
H2O
230 K
270 K
Giant planet atmospheric
structure
• Note position and order of cloud decks
Bands and Zones
Jupiter’s Clouds – New Horizons
Different colors indicate different gases
You’re seeing to different depths in the atmosphere
Zonal winds affect opacity
Galileo went into a boring spot – crushed before it got to
anything interesting
Magnetic fields
How are they generated?
•
•
•
•
•
Dynamos require convection in a conductive medium
Jupiter/Saturn – metallic hydrogen (deep)
Uranus/Neptune - near-surface convecting ices (?)
Terrestrial Planets – convection in liquid iron core
Icy Satellites – salty ocean
Van Allen Belts
• Torus of charged particles trapped in Earth’s
magnetic field
• Shield Earth’s surface against high-energy
particles
• Hazard to satellite navigation, manned space
missions
• Similar radiation belts observed at other planets
– Jupiter’s belt poses problem for dedicated Europa
mission
Aurora
• Collisions between charged particles with
the atmosphere.
– Gas controls color (Red: N, Green: O)
• Magnetic reconnection between solar
magnetic field and Earth’s magnetosphere
at poles
Summary
• Jupiter - mainly metallic hydrogen. Rock-ice core ~10
M E.
• Saturn - mix of metallic and molecular hydrogen; helium
may have migrated to centre due to insolubility. Similar
rock-ice core to Jupiter. Mean density lower than Jupiter
because of smaller self-compression effect (pressures
lower).
• Uranus/Neptune – thin envelope of hydrogen gas.
Pressures too low to generate metallic hydrogen.
Densities (and moment of inertia data) require large
rock-ice cores in the interior.
• All four planets have large magnetic fields, presumably
generated by convection in either metallic hydrogen (J,S)
or conductive ices (U,N)
Moons
• What are they?
• Natural things that orbit about other
natural things that aren’t stars
• Terrestrial planets have few if any
• Jovian planets have whole bunches
• Even some asteroids and comets have
them.
The Magnificent Seven
1. Ganymede
4. Io
2. Titan
3. Callisto
6. Europa
5. The Moon
7. Triton
Earth: The Moon
Maria: Lava plains
Only on near side
Terrae: Cratered
Highlands
Mars: Phobos and Deimos
Captured Asteroids
Crater: Stickney
Jupiter: The Inner Moons
Metis
Adrastea
Thebe
Amalthea
Jupiter: Io
The Volcanic Moon
Tvashtar Plume
The lavas of violent Io,
Though they may look like pico de gallo,
Erupt and then rain
On the sulphurous plain,
Looking nothing at all like Ohio.
Jupiter: Europa
ALL THESE WORLDS
ARE YOURS EXCEPT
EUROPA
ATTEMPT NO
LANDING THERE
USE THEM TOGETHER
USE THEM IN PEACE
A promising place is Europa
Where astrobiologists hope a
Critter or three
May swim in the sea
Far beneath the icy dystopia
Jupiter: Callisto
Jupiter: The Outer Moons
• Seven in prograde orbits
– Themisto, Leda, Himalia, Lysithia, Elara
• 46 in retrograde orbits
– Probably Captured
– Ananke, Came, Pasiphae, Sinope
Saturn
MET DR THIP
For a sickeningly huge number of awesome
images, go to:
Some share orbits!
http://ciclops.org
Saturn: Mimas
Herschel
That’s no moon . . . it’s a space station!
Now Mimas has one giant crater
That’s sitting right on the equator
Because it’s a hole
It should be at the pole.
It could maybe reorient later.
Saturn: Enceladus
South Polar Plumes
Tiger-Stripes
Possible liquid ocean
Tidally heated?
There once was a moon called Enceladus,
Whose Tiger-stripes have cast a spell at us.
The south polar plume
Like a vapor mushroom,
Has poked its way through
the ice shell at us.
Saturn: Tethys
•Heavily cratered
•Active early on
•Some
Resurfacing
•Dark Belt
•Polar caps
Odysseus
Calypso and Telesto on same orbit
Saturn: Dione and Rhea
Wispy streaks
Eruptions of Snow?
Shares orbit with Helene
The ice shell of distant Dione
Lies over a core that is stony.
Its wispy terrain
In extensional strain
Is as brittle as dry macaroni.
Saturn: Titan
Xanadu
Haze
Volcano?
The tholins surrounding old Titan
Raise the following question. “Might an
Airborne balloon
Get a look at this moon
And see if the dark patches brighten?”
Saturn: Iapetus
Black on White or White on Black?
20 km high
ridge!
Cassini Regio
Huge Fracture
Uranus
• 11 small inner moons
– Cordelia, Ophelia, Bianca, Cressida,
Desdemona, Juliet, Portia, Rosalind, Belinda,
Puck
• MAUTO
– Miranda, Ariel, Umbriel, Titania, Oberon
• 5 small outer moons
– Caliban, Sycorax, Stephano, Prospero,
Setebos
Uranus: Miranda
Iapetus said to Miranda
“You’re no place at all for a
lander.
Your canyons have rocks
Like the teeth on some crocs
Whereas I’m black and white
like a panda.”
Broken apart and reassembled
Uranus: Ariel and Umbriel
Fluorescent Cheerio
(north polar crater)
Interconnected valleys
100s km long, 10 km deep
Uranus: Titania and Oberon
Queen and King of the Faeries
Chasms all over
6 km high mountain,
craters
Neptune: Moons
• 5 small inner moons
• Proteus
• Triton, the big retrograde moon
– Captured KBO?
– Going to collide – more on this tomorrow
• Nereid (medium size moon)
• 3 small retrograde outer moons
Neptune: Triton
•Orbits retrograde
•Unstable orbit
•Going to impact Neptune
A big KBO in disguise or
A moon with a nitrogen geyser?
The retrograde moon
Of sea-king Neptune
Triton thinks we’ll all be none the wiser.
Ice Lava
Next time
• Icy Satellites
• Ring Systems of Giant Planets
• Tidal Interactions
• Paper Discussions
– Namouni and Porco (2002)
– Porco et al. (2006)