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Lecture 2

The Earth. I. The Interior

• Vital statistics

• Size & mass of a planet

• Gravity & magnetic mapping

• Seismology

• Structure of Earth’s interior

• Plate tectonics

Reminder: lectures at http://www.star.le.ac.uk/~pto/planets.html

Orbital semi-major axis 1.496 x 108 km (1.0 AU)

Orbital period 365.256 days

Rotational period 23.9345 hours (sidereal day)

Inclination of rotation axis 23.45 º

Eccentricity of orbit 0.017

Diameter (at equator) 12 756 km

Mass 5.974 x 1024 kg

Mean density (observed) 5520 kg m-3

Earth – vital statistics

Planet size & mass determination

Size –

Measure distance and angular size to get actual size.

Baseline = Parallax2π x distance 360o

Diameter = ang. diameter2π x distance 360o

Size of Earth -

Eratosthenes (~200 B.C.)

measured size using angular

displacement of the Sun at

same time at 2 locations.

He used Syene and Alexandria

5000 stadia (780 km) apart.

Using his value of 7.2 degrees

get radius = ?

6200 km (cf. 6378 km actual!)

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Determine the Astronomical Unit

Use radar and apply

Newton/Kepler’s laws:

Bounce radar off Venus.

1 AU = 149,597,870.7 km

Now defined by IAU

Mass –

Newton’s laws of motion:

Bodies of masses M and m

in an elliptical orbit:

M+m = 4π2a3/GP2 and M/m = rm/rM

Where P = period, a = semi-major axis and

rm and rM = distance of M and m from the centre of mass.

If m << M then a3∝ P2 ⇒ Kepler’s third law.

Substance Formula Density (kg m-3)

Liquid water H2O 998

Hydrated minerals

(X is rock, n≥1)

X(H2O)n <2000

Diopside (a pyrozene) CaMgSi2O6 3200

Forsterite (an olivine) Mg2SiO4 3270

Alkali feldspars (Na, K)AlSi3O8 4740

Iron-nickel Fe + 6% Ni 7925

Back to observed density of Earth…(5520 kg m-3)

Uncompressed densities of some important compounds

Gravity Mapping

Australia:

Red = stronger g

Blue = weaker g

Geoid is the

surface of equal g

Small variation in gravitational acceleration.

Can also be used to map Ocean/Ice levels.

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Presume planets with strong magnetic field have an internal dynamo converting the kinetic energy of a

conducting, moving fluid into magnetic energy.

⇒ Strong evidence for molten material inside Earth

Magnetic Mapping

Australia:

Red = stronger

Blue = weaker

Boxing Day 2004 earthquake, magnitude 9.1, Indian Ocean

– largest earthquake for 40 years, lasted ~10 minutes

Earthquakes and Seismology

Seismic recording from two islands in the Indian Ocean:

Cocos Island and Diego Garcia (~1000 km apart)

Two main types of seismic waves• Primary (P) are longitudinal pressure waves

• Secondary (S) are transverse sheer waves

Waves speed varies due to differences in density (faster

at lower density) and temperature (refraction).

Observed seismic waves

• P waves travel at 5-6 km s-1 . Go

through solids, liquids and gases.

• S waves travel at 3-4 km s-1 . They cannot pass through liquid.

• “Shadow zone” receives neither

P nor S waves (refraction/liquid).

• Faint P waves seen in the shadow

zone must have been reflected off

an inner solid core.

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Most geological activity occurs at plate boundaries.

Earth – the present

Most boundaries are “compression boundaries” marked by

mountain ranges where plates collide (e.g. Himalayas) and/or

deep trenches, where old crust is subducted (e.g. Peru-Chile

Trench).

Cause the deepest and strongest earthquakes (~700 km)

“Extension boundaries” due to separation of plates on the ocean

floor (e.g. mid-Atlantic ridge). Form new crust from the mantle

material. Determine age from magnetic striping and radioactivity.

Shallow earthquakes (<25 km).

Also have “transform boundaries” where plates slip past each

other (e.g. San Andreas fault). Shallow, violent earthquakes.

Earth sea-floor crustal age:

Red = young (10 Myr); blue = old (200 Myr)

Tectonic activity can resurface most of the Earth in ~500 Myr

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• Near plate boundaries – magma comes up due to stress

fracture in crust. Etna (left) is an example.

• Over hot-spot – a buoyant mantle plume. Hawaiian island

chain best example, e.g. Kilauea (right). Hot spot moves

creating “chain”. Highest most recent – hence “Big Island”.

Volcanoes Terrestrial Impact Craters

Barringer Meteor crater, Arizona

Radius 0.6 km, Age 0.05 MyrChicxulub, Yucatan Peninsula

Radius 85 km, Age 65 Myr

Few craters (<200) known on Earth due to erosion (weathering),

volcanic resurfacing and tectonic activity.

Most < 500 Million years old. Oldest ~2 billion years old.

If impact crater size > 1 km object impactor melts completely.

Should we be worried…?

The End