Download Planetary Interiors

Interiors
• large bodies (e.g. planets) have all undergone
significant changes (in surfaces and interiors)
since their formation.
• except for the Earth and Moon, all of the data we
obtain on interiors are based completely on
“remote” observations:
¾ Density
¾ magnetic field
¾ moment of inertia.
¾ Seismic data (Earth and moon only).
• The bulk density of an object is simply its mass
divided by its volume (ρ=M/V)
• the density of an element depends on the pressure
of its environment.
¾ the pressures inside planets must mean that
their bulk densities are greater than the
densities of their components at 1 atmosphere.
• Rock is deformable and can move: even more so
under partial melting conditions
• Internal structure obeys the hydrostatic
equilibrium equation
¾ The equation of state (relating density, pressure and
temperature) for solids is generally complex. But in
practice T and density do not vary much.
Moment of Inertia and Gravity Field
• The gravity field of a planet, i.e. the gravitational force
it exerts on an external body, depends on the planet’s
internal mass distribution
• the main factors affecting the gravity field are a planet’s
shape, internal mass distribution and rotation.
• Measurements of the gravitational field of a planet,
usually from space, can be mapped and deviations from a
uniform, homogeneous sphere can be determined.
¾ This led to the discovery of mascons on the moon.
These are large lava flows that filled ancient impact
basins. The lava is denser than the surface rock,
but has not been able to sink back into hydrostatic
equilibrium
¾ Find that the centre of mass is offset from the
geometric centre of the moon and Mars
• Shows the mass distribution is not symmetric
• The moment of inertia of a body is simply its resistance
to rotation – analogous to mass which is a body’s
resistance to “straight line” motion.
• The moment of inetria for a sphere can be written as:
I = kMR2 , where M is mass, R is radius, I is the moment of
inertia and k is a constant.
¾ For a homogeneous sphere k=0.4
¾ For a hollow shell k=2/3
¾ For a point mass k=0
¾ as central concentration in a body increases,
k=I/MR2 decreases.
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Magnetic Fields
Magnetic fields are lines of force, with both magnitude
and direction.
Record of Earth’s magnetic field can be determined from
rocks
¾ When rock crystallizes in the presence of a
magnetic field, the magnetic elements of rock are
frozen in alignment
Earth’s field is continually changing strength, and position
(changes about 0.1% per year)
¾ Even changes direction, every few hundred thousand
years
A strong magnetic field present in the early solar system
would decay in around 10,000 years, so planetary
magnetic fields must be due to something else.
Dynamo theory:
¾ A conductive fluid moving through an external
magnetic field induces electrical currents in the
fluid that produce their own magnetic field.
¾ This produces a feedback loop which increases
the field strength
¾ Planetary magnetic fields required:
¾ A large volume of conductive fluid (e.g. molten
iron)
¾ Rapid rotation
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Seismology
The study of waves transmitted through bodies
¾ waves caused by quakes, impacts, volcanic
eruptions or surface explosions
Vibrations are transmitted in all directions away
from the site of origin
¾ Can be detected on “the other side”
The speed and direction of a wave depends on the
medium it travels through
Pressure (P-) waves are longitudinal waves that
compress matter along the direction of motion
¾ Can pass through solid or liquid matter
Shear (S-) waves move the material up and down, in a
direction perpendicular to the direction of motion.
¾ Can only pass through solid matter
Both types of waves can be reflected or refracted
at a boundary layer where the composition changes.
Earth’s Interior
• Crust:
¾ Thinner (5-10 km) oceanic crust is mostly
basaltic (rapidly cooling) while
¾ continental crust (20-60 km) is mainly granitic,
emblematic of much recycling.
¾ mean age of crustal rock is ~1.5Gyr – much
younger than the Earth itself.
• Mantle: Beneath the crust is a thick layer of denser
material which is mostly in a plastic state.
¾ made of silicate rocks rich in elements which
are denser than those in the crust.
¾ The temperature difference between lower and
upper mantle is sufficient to drive convection,
which moves the crustal plates above it.
• Core:
¾ rich in iron and other metals such as nickel,
sulphur and cobalt.
¾ Outer core is liquid and it is from here that the
circulation producing Earth’s magnetic field is
driven.
¾ Inner core is solid because of its higher density.
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Sources of Heating
Accretion will heat a planetesimal by conversion of
gravitational potential energy
¾ Energy is only likely to be sufficient for melting
for bodies with radii >500 km.
Differentiation is a source of heat in terrestrial planets
¾ As heavier elements sink to the core in a fluid
interior, releasing more gravitational potential
energy
Radioactivity is an important heat source
¾ Short-lived isotopes (like 26Al) can provide a lot
of heat at early times.
¾ Longer-lived isotopes (like 40K) produce more
energy over a longer timescale.
Tidal forces are important in some moons (esp. Io) and
may have been important in the past, for the Earth-Moon
system.
Energy is transported to the surface via convection,
conduction and radiation.
For Earth, the solar heat flux at the surface is ~20,000
times larger than the energy being leaked from the
interior
The giant planets have stronger heat sources, and
generate more heat internally than they receive from the
Sun
¾ Probably because they are still finishing their
slow gravitational collapse.
Terrestrial Planets: interiors
Moon:
• Lunar moment of inertia and small, ancient magnetic field suggest
small core that formed 3500-4500 Myr ago.
• Highly-fractured surface (<25 km) suggests moon started out
with Earth-mantlelike composition and then differentiated.
• Small, so cooled quickly. Lithosphere thickened to 1000-km depth:
no plate tectonics
Mercury:
• high uncompressed density suggests a large iron core with
rcore~.75 RMercury
• magnetic field implies presence of a molten outer core?
• recent libration (wobble in the rotation) measurements show
planet cannot be solid throughout
• magnetic field produced in a thin outer core?
Mars:
• significant amounts of sulfur in Mars’ core
¾ lowers melting T so core is at least partly fluid
¾ means core radius ~0.5RMars
• variations in Mars’ gravity field measured by Global Surveyor
reveal internal density fluctuations
¾ crust varies from ~20km in north to ~50km in south
Venus:
• Expect similar radiogenic heating history to Earth
• Condensation: expect less volatiles and sulfur than Earth. Core
may have less FeS.
• Smaller size, internal pressure: solid core may be smaller than
Earth. Might explain weak magnetic field.
• No evidence for plate tectonics, large crustal motions etc.
Icy Moons of outer planets
• Low mean densities and condensation theory suggests
these moons are mainly icy
• Tidal heating is dominant effect in interior structure
Callisto
• Outermost of Jupiter’s moons, and lowest in density
• Too far for significant tidal heating
• Surface: unbroken panorama of craters, no large-scale
fracture systems
• Suggests Callisto has highest ice content. Never-melted,
undifferentiated interior
Ganymede
• Largest Jupiter satellite: highly differentiated
• Magnetic field implies active interior, differentiated
core
• May be subject to some tidal heating
Europa
• Interior has been heated enough to resurface with
smooth, young, bright ice plains
• Some tidal heating: allows water to erupt and resurface
Io
• High density and active volcanism: no ice
• Initial Io may have been deficient in ice: high
temperature in proto-Jupiter nebula
Gas Giants
Jupiter
• Has a strong enough gravitational field that it retained
almost all elements, in solar-nebula proportions
¾ Therefore dominated by hydrogen
• High temperature and pressure means the hydrogen
forms a liquid/gaseous mush
• At higher pressures, interior becomes convecting, liquid
metallic hydrogen (with free electrons)
• Probably has a solid, silicate and metal core of about 15
Earth masses
Saturn
• Similar, but pressures, temperatures and densities are
lower than for Jupiter.
• Core of about 17 Earth masses, covered with ices. Above
that is a liquid hydrogen ocean.
Uranus and Neptune
• Denser than Saturn and Jupiter, and richer in heavy
elements
• Maybe unable to retain as much H and He due to smaller
size
• Also may have accreted material more slowly (due to
larger orbit) and the gas got dispersed before they
finished forming.
Exercises
1. From the bulk, uncompressed density of Earth
(4100 kg/m3), calculate the density of the core.
The core occupies 1/6th of the volume, and
assume the rest is made up of the mantle,
ρ=3300 kg/m3, uncompressed.
ρ bulk = (1 − f core ) ρ mantle + f core ρ core
Where fcore is the volume fraction occupied by the
core.
4100 = (1 − 1 / 6)3300 + (1 / 6) ρ core
ρ core = 6( 4100 ) − 5(3300 )
= 8100 kg / m .
3
The fraction of the mass in the iron core is
ρ coreVcore
M Earth
=
ρ core VEarth
M Earth
6
ρ core
=
6 ρ bulk
= 8100 /( 6 × 4100 ) = 0.33
2. The Earth’s mantle has a thermal conductivity
of ~ 1 W/m/K. Radioactive decay heats the
core to T~5000 K. Calculate the rate of heat
loss per unit area at the surface.
∆Q
dT
= kc A
∆t
dx
⎛T ⎞
⎛ ∆Q ⎞
⎟ / A ≈ −k c ⎜ ⎟
⎜
⎝R⎠
⎝ ∆t ⎠
Tcore
≈ −k c
RE
⎛ 5000 K ⎞
−2
=
0
.
00078
= −(1W / m / K )⎜
Wm
⎟
⎝ 6378km ⎠
The actual value is larger, 0.06 W/m2 partly
because convection transports energy more
efficiently than conduction. This is still much
smaller than the solar constant, 1373 W/m2.