EART 160: Planetary Science Monday, 04 February 2008 YOUR AD HERE.
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Transcript of 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