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

Image not to scale!

Giant Planets

Basic Parameters

Data from Lodders and Fegley 1998. Surface temperature Ts and radius R are measured at 1 bar level.

a (AU)

Porb

(yrs)

Prot

(hrs)

R

(km)

M

(1026 kg)

Obli-quity

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

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:

(Lodders and Fegley 1998)

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)

Pressure• Hydrostatic approximation• Mass-density relation• These two can be combined (how?) to get the pressure

at the centre of a uniform body Pc:

)()( rgrdrdP

2)( )(4 rrdrrdM

4

2

8

3

R

GMPc

• 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:

T

RT

P KP Ideal Gas Law Polytropic Law

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:

• Adiabatic Lapse Rate

pC

g

dz

dT

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

• Jupiter – interior mostly metallic hydrogen

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

• 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)

mass

radius

Con

stan

t den

sity

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?

5.4

8.1

13.5

48

2.0

2.6

4.6

14

0.6

0.6

3.5

0.3

0.3

0.6

1.4

incidentreflected

After Hubbard, in New Solar System (1999)All units in W/m2

Jupiter Saturn 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

• So the rate of energy release during contraction is

RGMEg /6.0 2

dt

dR

R

GM

dt

dEg

2

2

6.0

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

Temperature (schematic)

tropopause

troposphere

stratosphere

mesosphere

~0.1 bar

radiation

adiabat

CH4 (U,N only)

NH3

NH3+H2S

H2O

80 K

140 K

230 K

270 K

Theoretical cloud distribution

clouds

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

ME.

• 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

4. Io 6. Europa

1. Ganymede 3. Callisto

2. Titan 5. The Moon 7. Triton

Earth: The Moon

Maria: Lava plainsOnly on near side

Terrae: Cratered Highlands

Mars: Phobos and Deimos

Crater: Stickney

Captured Asteroids

Jupiter: The Inner Moons

Metis AdrasteaThebe Amalthea

Jupiter: IoThe Volcanic Moon Tvashtar Plume

The lavas of violent Io,Though they may look like pico de gallo,Erupt and then rainOn the sulphurous plain,Looking nothing at all like Ohio.

Jupiter: Europa

A promising place is EuropaWhere astrobiologists hope a

Critter or threeMay swim in the sea

Far beneath the icy dystopia

ALL THESE WORLDSARE YOURS EXCEPT

EUROPA ATTEMPT NO LANDING THERE

USE THEM TOGETHERUSE THEM IN PEACE

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

Some share orbits!

MET DR THIP

For a sickeningly huge number of awesome images, go to:

http://ciclops.org

Saturn: Mimas

Herschel

That’s no moon . . . it’s a space station!

Now Mimas has one giant craterThat’s sitting right on the equator

Because it’s a holeIt should be at the pole.

It could maybe reorient later.

Saturn: EnceladusSouth 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 plumeLike 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 streaksEruptions of Snow?

Shares orbit with Helene

The ice shell of distant DioneLies over a core that is stony.

Its wispy terrainIn extensional strain

Is as brittle as dry macaroni.

Saturn: Titan

Haze

The tholins surrounding old TitanRaise the following question. “Might anAirborne balloonGet a look at this moonAnd see if the dark patches brighten?”

Xanadu

Volcano?

Saturn: Iapetus

Black on White or White on Black?

20 km highridge!

Cassini RegioHuge 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

Broken apart and reassembled

Iapetus said to Miranda“You’re no place at all for a

lander.Your canyons have rocksLike the teeth on some crocsWhereas I’m black and white

like a panda.”

Uranus: Ariel and Umbriel

Interconnected valleys100s km long, 10 km deep

Fluorescent Cheerio(north polar crater)

Uranus: Titania and OberonQueen 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

Ice Lava

A big KBO in disguise orA moon with a nitrogen geyser?

The retrograde moonOf sea-king Neptune

Triton thinks we’ll all be none the wiser.

Next time

• Icy Satellites

• Ring Systems of Giant Planets

• Tidal Interactions

• Paper Discussions– Namouni and Porco (2002)– Porco et al. (2006)