EART 160: Planetary Science

15 February 2008

Last Time

• Planetary Interiors– Cooling Mechanisms

• Conduction• Convection

– Rheology• Viscoelasticity

Today

• Elastic Flexure• Paper Discussion – Titan Atmosphere

– Tobie et al., 2005

• Planetary Atmospheres– General Description – Atmospheric Structure– General Circulation– Origin / Geochemistry– Thermal Balance

Elastic Flexure• The near-surface, cold parts of a planet (the

lithosphere) behaves elastically• This lithosphere can support loads (e.g. volcanoes)• We can use observations of how the lithosphere

deforms under these loads to assess how thick it is• The thickness of the lithosphere tells us about how

rapidly temperature increases with depth i.e. it helps us to deduce the thermal structure of the planet

• The deformation of the elastic lithosphere under loads is called flexure

• EART163: Planetary Surfaces

Flexural Stresses

• In general, a load will be supported by a combination of elastic stresses and buoyancy forces (due to the different density of crust and mantle)

• The elastic stresses will be both compressional and extensional (see diagram)

• Note that in this example the elastic portion includes both crust and mantle

Elastic plateCrust

Mantle

load

Flexural Parameter• Consider a load acting

on an elastic plate: Te

m

load

3

2

1

4

3 ( )(1 )e

m w

ET

g

w

• The plate has a particular elastic thickness Te

• If the load is narrow, then the width of deformation is controlled by the properties of the plate• The width of deformation is called the flexural parameter and is given by

E is Young’s modulus, g is gravity and is Poisson’s ratio (~0.3)

• If the applied load is much wider than , then the load cannot be supported elastically and must be supported by buoyancy (isostasy)

• If the applied load is much narrower than , then the width of deformation is given by

• If we can measure a flexural wavelength, that allows us to infer and thus Te directly.

• Inferring Te (elastic thickness) is useful because Te is controlled by a planet’s temperature structure

Example• This is an example of a

profile across a rift on Ganymede

• An eyeball estimate of would be about 10 km

• For ice, we take E=10 GPa, =900 kg m-3, g=1.3 ms-2 Distance, km

10 km

• If =10 km then Te=1.5 km

• So we can determine Te remotely

• This is useful because Te is ultimately controlled by the temperature structure of the subsurface

Te and temperature structure• Cold materials behave elastically• Warm materials flow in a viscous fashion• This means there is a characteristic temperature

(roughly 70% of the melting temperature) which defines the base of the elastic layer

110 K270 K

elastic

viscous

190 K•E.g. for ice the base of the elastic layer is at about 190 K• The measured elastic layer thickness is 1.4 km (from previous slide)• So the thermal gradient is 60 K/km• This tells us that the (conductive) ice shell thickness is 2.7 km (!)

Depth

1.4 km

Temperature

Te in the solar system• Remote sensing observations give us Te

• Te depends on the composition of the material (e.g. ice, rock) and the temperature structure

• If we can measure Te, we can determine the temperature structure (or heat flux)

• Typical (approx.) values for solar system objects:Body Te (km) dT/dz

(K/km)Body Te dT/dz

(K/km)

Earth (cont.)

30 15 Venus (450oC)

30 15

Mars (recent)

100 5 Moon (ancient)

15 30

Europa 2 40 Ganymede 2 40

Planetary Atmospheres

• Atmosphere – The layer of gases surrounding a planet

• Determines present surface conditions

• Controls long-term climatic history and evolution

• Greenhouse Effect

• Global Warming

Image Credit Brett Wilson

Planetary Atmospheres in the Solar System

Nothing to write home about

Moon, Mercury

(He, Ar, Na, O)

Microbars Io, Triton, Europa, Pluto

(S, N, C, H, O)

Millibars Earth, Mars, Venus, Titan

(C, H, O, N, Ar)

Gas Bags Jupiter, Saturn, Uranus, Neptune

(H, He, O, S, N, C)

Composition

P = 1 bar78% N2

21% O2

1% Ar1% H2OT = 287 K

P = 92 bars96.5% CO2

3.5% N2

T = 737 K

P = 6 millibars95% CO2

3% N2

2% Ar

T = 218 K

This Planet is too hot! This Planet is too cold!This Planet is just right!

Earth

• Same amount of Carbon as Venus– Where did it all go?

• Climate controlled by water vapor– Clouds, Rain, Oceans

• Near Triple-Point– Ice, Liquid, Vapor all

present

Image Credit Fabio Grasso

Image Credit Luca Galuzzi

Venus

• Similar to Earth’s bulk properties but VERY different

• Hot enough to melt lead• No water at all – where did it go?• Clouds of Sulfur, Rain of Sulfuric Acid• Surface not visible• MASSIVE CO2 greenhouse• Slow rotation stagnant

Mars

• Water vapor clouds• Polar Ice Caps• Liquid water unstable• Warmer, wetter in past?

• CO2 cycle

• Dust storms– Massive Dust Devils!

Titan

• The only Moon with an atmosphere

• Haze prevented Voyager from seeing the surface

• P = 1.5 bar– 98% N2

– 2% CH4

• T = 95 K

Atmospheric Compositions

Isotopes are useful for inferring outgassing and atmos. loss

Earth Venus Mars TitanPressure 1 bar 92 bar 0.006 bar 1.5 barN2 77% 3.5% 2.7% 98.4%

O2 21% - - -

H2O 1% 0.01% 0.006% -

Ar 0.93% 0.007% 1.6% 0.004%

CO2 0.035% 96% 95% ~1ppb

CH4 1.7ppm - ? 1.6%

40Ar 6.6x1016 kg 1.4x1016 kg 4.5x1014 kg 3.5x1014 kg

H/D 3000 63 1100 360014N/15N 272 273 170 183

Atmospheric Structure

Convection, Weather, Clouds

T increases with alt. Stable to convectionCools by radiation

Shooting stars burn up

Low density, heated by X-rays

Free electrons, ionsAffects radio wave propagation

Exobase – Height at which 1/e particles can escape(Thermosphere keeps going)

Atmospheric Pressure

• Atmosphere is hydrostatic:

• Ideal Gas Law:

• Combining these two:

gdzzdP )(

NRTPV

zRT

gPP

RT

gP

dz

dP

exp0

P Pressure Densityg Gravityz HeightV VolumeN Number of MolesR Gas ConstantT Temperature Mass of one Mole

Assuming Isothermal AtmosphereConstant Gravity

Scale Height

• Let H = RT/g:

• P = P0 e-z/H

• H is the scale height of the atmosphere– Distance over which P

drops by 1/e

• Mass of a column of atmosphere– Mc = P/g

Venus Earth Mars Jupiter Saturn Uranus Neptune

H (km) 16 8.5 18 18 35 20 19

Atmospheric Structure• Of course, temperature actually does vary with height• If a packet of gas rises rapidly (adiabatic), then it will expand and,

as a result, cool• Work done in cooling = work done in expanding

pC dT

pC

g

dz

dT

• Combining these two equations with hydrostatic equilibrium, we get the dry adiabatic lapse rate:

Cp is the specific heat capacityof the gas at constant pressure

• On Earth, the lapse rate is about 10 K/km• What happens if the air is wet?

dPM

VdP

Next Time

• Planetary Atmospheres– General Circulation– Origin / Geochemistry– Thermal Balance