EART 160: Planetary Science

Monday, 04 February 2008

YOUR AD HERE

• Paper Discussion– Mars Crust and Mantle (Zuber et al., 2001)– Io Volcanism (Spencer et al., 2007)

• Planetary Surfaces: Gradation– Erosion (Water, Wind, Ice)– Mass Wasting (Gravity)

Last Time

Today

• Homework 3 due Monday• Planetary Surfaces

– Summary

• Planetary Interiors– Terrestrial Planets and Icy Satellites– Structure and Composition: What all is inside?– Exploration Geophysics: How can we tell?– Heat Sources: What drives motion?– For more, take EART 162 in the Spring (Nimmo)

Planetary Surfaces: A Summary

• Impacts (Cratering)

• Volcanism (Magmatism)

• Tectonics (Extension, Compression)

• Gradation (Erosion, Mass Wasting)

Impacts• Impact velocity will be (at least)

escape velocity

• Impacts are energetic and make craters

• Crater size depends on impactor size, impact velocity, surface gravity

• Depth:diameter ~ 1:5• Impactor:crater ~ 1:10• Crater morphology changes with

increasing size – simple, complex, impact basin

• Size-frequency distribution can be used to date planetary surfaces

• Atmospheres and geological processes can affect size-frequency distributions

gRv RGM

esc 22

Simple Complex

Lunar Size Frequency DistributionNagumo & Nakamura, 2001

Volcanism• The process by which material

is brought from the deep interior of a planet to the surface

• Magmatism occurs when temperature is above the solidus– By raising T, lowering P,

lowering solidus• Forms new crustal material,

resets surface age• Time of formation can be dated

radiometrically• Most planetary crusts are

basaltic

Lava channel -- Earth

OIympus Mons -- Mars

Tvashtar -- Io

Tectonics• Compression accommodated

by normal faults, extension by reverse faults

• Planetary cooling leads to compression– Extension in ice, compression

rarely seen on icy satellites.• Elastic materials = E • Viscous materials = d/dt• Byerlee’s law: a fault will slip if

the tectonic shear stress exceeds the frictional force holding it in place (coeff. of fric. × normal stress)

• Lithostatic pressure applies no shear stress

Plate Tectonics -- Earth

Artemis Corona -- Venus

Wrinkle Ridge -- Moon

Valles Marineris-- Mars

Gradation

• Erosion: modification of surface by wind, water, ice – requires an atmosphere– valley networks,

gullies, outflow channels

• Mass Wasting: Gravity-driven slope failure

Valley Networks – MarsCourtesy Calvin J. Hamilton

Euler crater (terraced) -- Moon

Planetary Roughness• Moon: far side• Mercury: all data• Venus: tesserae

(Ovda Regio)• Earth: western US• Mars: highlands • Venus: typical

plains• Mars: lowlands

(Utopia Planitia)• Earth: plains

(Russian Plain)

Kreslavsky, 2008, LPSC

• Moon: far side

• Mercury: all data• Venus: tesserae

(Ovda Regio)• Earth: western US• Mars: highlands

• Venus: typical plains

High Gravity can restrict topography – large planets artificially smoothed

Assuming inverse linear scaling between gravity and roughness, Venus is roughest.

Kreslavsky, 2008, LPSC

Planetary Interiors

• We can see the surface• We cannot see the interior• The interior is MOST of the planet!• The deepest borehole is 12 km on Earth

(0.2% of the radius)• How can we tell anything?• What effects do the interior’s physical

properties and processes have on the surface?

How do we see inside?

• Light cannot penetrate solid rock• What can?• Sound – Seismology• Potential Fields

– Gravity– Magnetism

• RADAR

Seismology

• Seismic waves bounce off interfaces in the interior

• Detected on the Surface

• Tell us the structure of the interior– Only have this for

Earth and Moon)• Shear waves cannot

travel through liquid

Magnetism

Magnetic Stripes on MarsIndicates Magnetized Crust

But no deeper signal

Dipole Earth on FieldIndicates a Convecting Liquid Layer

Outer core on EarthOcean on Europa

Gravity

• Higher Gravity over regions of high density

• All Potential Field Methods yield non-unique solutions

• Depth hard to constrain• But can be used from

Orbit!GRACE map of the EarthAPOD 23 July 2003

RADAR

Phillips et al. LPSC (2007)SHARAD Radargram of Mars

RADAR can penetrate the surface, give us the crustal structure.

Cannot go deep

Tradeoff between depth and wavelength

Mass

• How do we know?• Observe:

– Period, P and distance, a of orbiting object (e.g. satellite)

– Planetary radius, r

• Relationship between these and mass?– Kepler’s Third Law!

– Satellite mass unimportant!23aGM

Orbital Frequency, = 2/P

r

aP

Bulk Densities• So for bodies with orbiting satellites (Sun, Mars, Earth,

Jupiter etc.) M and are trivial to obtain• For bodies without orbiting satellites, things are more difficult

– we must look for subtle perturbations to other bodies’ orbits (e.g. the effect of a large asteroid on Mars’ orbit, or the effect on a nearby spacecraft’s orbit)

• Bulk densities are an important observational constraint on the structure of a planet. A selection is given below:

Object Earth Mars Moon Mathilde Ida Callisto Io Saturn Pluto

R (km) 6378 3390 1737 27 16 2400 1821 60300 1180

(g/cc) 5.52 3.93 3.34 1.3 2.6 1.85 3.53 0.69 ~1.9

Data from Lodders and Fegley, 1998

What do the densities tell us?• Densities tell us about the different proportions of

gas/ice/rock/metal in each planet• But we have to take into account the fact that bodies with

low pressures may have high porosity, and that most materials get denser under increasing pressure

• A big planet with the same bulk composition as a little planet will have a higher density because of this self-compression (e.g. Earth vs. Mars)

• In order to take self-compression into account, we need to know the behavior of material under pressure.

• On their own, densities are of limited use. We have to use the information in conjunction with other data, like our expectations of bulk composition

Bulk composition

• Four most common refractory elements: Mg, Si, Fe, S, present in (number) ratios 1:1:0.9:0.45

• Inner solar system bodies will consist of silicates (Mg,Fe,SiO3) plus iron cores

• These cores may be sulfur-rich (Mars?)• Outer solar system bodies (beyond the snow line) will be the

same but with solid H2O mantles on top

Element C O Mg Si S FeLog10 (No. Atoms) 7.00 7.32 6.0 6.0 5.65 5.95

Condens. Temp (K) 78 -- 1340 1529 674 1337

Material Ice Rock IronUncompressed Density (g cm-3) 0.92 3.3 7.0

Bulk Modulus (GPa) 8.8 120 170

Example: Venus• Bulk density of Venus is 5.24 g/cc • Surface composition of Venus is basaltic, suggesting

peridotite mantle, with a density ~3 g/cc• Peridotite mantles have an Mg:Fe ratio of 9:1• Primitive nebula has an Mg:Fe ratio of roughly 1:1• What do we conclude?

• Venus has an iron core (explains the high bulk density and iron depletion in the mantle)

• What other techniques could we use to confirm this hypothesis?

Distribution

• Bulk density only gets us so far

• Is the planet homogeneous or differentiated?

• How to tell the difference?

• Moment of Inertia

Moment of InertiaL = Iω L: Angular momentum, ω: angular frequency, I moment of inertia

for rotation around an axis, r is distance from that axis

I is a symmetric tensor. It has 3 principal axes and 3 principal components (maximum, intermediate, minimum moment of inertia: C ≥ B ≥ A.) For a spherically symmetric body rotating around polar axis

a

0

4drr)(3

8 C r

dVr I 2a

0

2drr)(4 M r

The maximum moment of a nearly radially symmetric body is expressed as C/(Ma2), a dimensionless number. C provides information on how strongly the mass is concentrated towards the center.

Symbols: L – angular momentum, I moment of inertia (C,B,A – principal components), ω rotation frequency, s – distance

from rotation axis, dV – volume element, M – total mass, a – planetary radius (reference value), c – core radius, ρm –

mantle density, ρc –core density

C/(Ma2)=0.4 2/3 →0 0.347 for c=a/2, ρc=2ρm

0.241 for c=a/2, ρc=10ρm

Homogeneous sphere

Small dense core thin envelope

Core and mantle, each with constant density

Hollow shell

•Rotating planet flattens at the poles.

•At the same spin rate, a body will flatten less when its mass is concentrated towards the center.

•From the flattening, and spin rate, we can determine the MOI, IF the planet is in Hydrostatic Equilibrium – is this a good assumption?

MOI of Planets

• All planets have C/Ma2 < 0.4– Mercury: 0.33– Venus: 0.33– Earth: 0.3308– Moon: 0.394– Mars: 0.366

• What can we say about core sizes?

Yet Another Talk!

Cameron Wobus, University of Colorado

Can erosion drive tectonics? Case studies from the central Nepalese Himalaya

Tuesday, 4 pmNatural Sciences Annex, Room 101

Tea and refreshments in the E&MS Dreiss Lobby at 3:30PM(1st floor A-wing Mezzanine lobby -- 'knuckle')

Next Time

• Midterm Review

• Paper Discussion – Stevenson (2001)

• Planetary Interiors– Pressures Inside Planets

Determining planetary moments of inertia

McCullagh‘s formula for ellipsoid (B=A):

In order to obtain C/(Ma2), the dynamical ellipticity is needed: H = (C-A)/C. It can be uniquely determined from observation of the precession of the planetary rotation axis due to the solar torque (plus lunar torque in case of Earth) on the equatorial bulge. For solar torque alone, the precession frequency relates to H by:

2222

1

2 J)(

JMa

AC

Ma

ABC

Symbols: J2 – gravity moment, ωP precession frequency, ωorbit – orbital frequency (motion around sun), ωspin – spin

frequency, ε - obliquity

When the body is in a locked rotational state(Moon), H can be deduced from nutation.

For the Earth TP = 2π/ωP = 25,800 yr (but here also the lunar torque must be accounted)

H = 1/306 and J2=1.08×10-3 C/(Ma2) = J2/H = 0.3308.

This value is used, together with free oscillation data, to constrain the radial density distribution.

cosH2

3

spin

2orbit

P

Determining planetary moments of inertia IIFor many bodies no precession data are available. If the body rotates sufficiently rapidly and if its shape can assumed to be in hydrostatic equilibrium [i.e. equipotential surfaces are also surfaces of constant density], it is possible to derive C/(Ma2) from the degree of ellipsoidal flattening or the effect of this flattening on the gravity field (its J2-term). At the same spin rate, a body will flatten less when its mass is concentrated towards the centre.

Symbols: a –equator radius, c- polar radius, f – flattening, m – centrifugal factor (non-dimensional number)

GM

am

32spin

Darwin-Radau theory for an slightly flattened ellipsoid in hydrostatic equilibrium

measures rotational effects (ratio of centrifugal to gravity force at equator).

Flattening is f = (a-c)/a. The following relations hold approximately:

Centrifugal force

Extra gravity from mass in bulge

2

2222 3

34

15

4

3

21

2

5

15

4

3

2

2

1

2

3

Jm

Jm

Ma

C

f

m

Ma

CmJf