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## EART 160: Planetary Science

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Last Time

- 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)

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

Simple

Complex

Lunar Size Frequency Distribution

Nagumo & 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

Tvashtar -- Io

OIympus Mons -- Mars

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 s = E e
- Viscous materials s = h 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 – Mars

Courtesy Calvin J. Hamilton

Euler crater (terraced) -- Moon

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)

Planetary RoughnessKreslavsky, 2008, LPSC

- Mercury: all data
- Venus: tesserae (Ovda Regio)
- Earth: western US
- Mars: highlands
- Venus: typical plains

Kreslavsky, 2008, LPSC

High Gravity can restrict topography – large planets artificially smoothed

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

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?

Light cannot penetrate solid rock

What can?

Sound – Seismology

Potential Fields

Gravity

Magnetism

RADAR

How do we see inside?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

SeismologyMagnetism

Dipole Earth on Field

Indicates a Convecting Liquid Layer

Outer core on Earth

Ocean on Europa

Magnetic Stripes on Mars

Indicates Magnetized Crust

But no deeper signal

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!

GravityGRACE map of the Earth

APOD 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

Bulk Densities

- So for bodies with orbiting satellites (Sun, Mars, Earth, Jupiter etc.) M and r 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:

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

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

L = IωL: 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

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.

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

Hollow shell

Small dense core thin envelope

Core and mantle, each with constant density

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

- 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 pm

Natural 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:

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.

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

Extra gravity from mass in bulge

Determining planetary moments of inertia II

For 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.

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:

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

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