Lecture 2 The Earth. I. The Interior Earth – vital statistics Planet size

```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
Planet size & mass determination
Size –
Measure distance and angular size to get actual size.
Earth – vital statistics
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
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
Using his value of 7.2 degrees
6200 km (cf. 6378 km actual!)
Baseline = Parallax
2π x distance
360o
Diameter = ang. diameter
2π x distance
360o
1
Determine the Astronomical Unit
Mass –
Newton’s laws of motion:
Newton/Kepler’s laws:
Bodies of masses M and m
in an elliptical orbit:
M+m = 4π2a3/GP2 and
1 AU = 149,597,870.7 km
M/m = rm/rM
Where P = period, a = semi-major axis and
Now defined by IAU
rm and rM = distance of M and m from the centre of mass.
If m << M then a3∝ P2 ⇒ Kepler’s third law.
Back to observed density of Earth…(5520 kg m-3)
Uncompressed densities of some important compounds
Substance
Formula
Density (kg m-3)
Liquid water
H2 O
998
Hydrated minerals
X(H2O)n
(X is rock, n≥1)
Diopside (a pyrozene) CaMgSi2O6
<2000
Forsterite (an olivine) Mg2SiO4
3270
Alkali feldspars
(Na, K)AlSi3O8
4740
Iron-nickel
Fe + 6% Ni
7925
3200
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.
2
Magnetic Mapping
Earthquakes and Seismology
Boxing Day 2004 earthquake, magnitude 9.1, Indian Ocean
– largest earthquake for 40 years, lasted ~10 minutes
Australia:
Red = stronger
Blue = weaker
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
Two main types of seismic waves
• Primary (P) are longitudinal pressure waves
• Secondary (S) are transverse sheer waves
Seismic recording from two islands in the Indian Ocean:
Cocos Island and Diego Garcia (~1000 km apart)
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.
P nor S waves (refraction/liquid).
Waves speed varies due to differences in density (faster
at lower density) and temperature (refraction).
• Faint P waves seen in the shadow
zone must have been reflected off
an inner solid core.
3
Earth – the present
Most geological activity occurs at plate boundaries.
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)
Earth sea-floor crustal age:
Red = young (10 Myr); blue = old (200 Myr)
“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).
Tectonic activity can resurface most of the Earth in ~500 Myr
Also have “transform boundaries” where plates slip past each
other (e.g. San Andreas fault). Shallow, violent earthquakes.
4
Volcanoes
• 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”.
Terrestrial Impact Craters
Barringer Meteor crater, Arizona
Radius 0.6 km, Age 0.05 Myr
Chicxulub, 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
5
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Hydrology

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