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Earth’s structure and properties (1)
John Townend
EQC Fellow in Seismic Studies
Cotton 520, ph. 463-5411
Earth: what are we dealing with?
How big is it? Eratosthenes and the Earth’s circumference
How massive? Cavendish’s measurement of the Earth’s mass
How old? Kelvin’s konduction and Rutherford’s radioactivity
What shape is it? Foucault’s pendulum, rotation, and Earth’s shape
What do its insides look like? Mohorovičić’s and Lehmann’s seismograms
The Earth’s shape
Aristotle and his contemporaries concluded in the 4th century B.C. that the Earth was round: Its shadow on the moon during eclipses is always curved Travellers see different stars at different latitudes The sun rises/sets at different times in different places Elephants are found in Africa and Asia (!) Ships disappear over the horizon from the hull upwards
But this doesn’t tell us how big the sphere is
How big is the Earth?
Eratosthenes (c. 276–195 BC) knew That the distance from Syene to Alexandria was 5000
stades (as measured by Egyptian government surveyors after the annual Nile floods); and
That on one day of the year (the solstice), the sun was directly overhead at Syene
He assumed That the Earth was approximately spherical; and That the Earth was sufficiently far from the sun that the
sun’s rays were approximately parallel everywhere on Earth
Eratosthenes’ experiment
The fraction of a circle (x) cast by the sun’s shadow at Alexandria when the sun is directly overhead at Syene, is equal to the distance from Alexandria to Syene as a fraction of the Earth’s circumference...
xy
Syene
Alexandria
Parallel rays from the sun
km) 40,000(~ stades 250,000
1/50th
stades 5000
angle fractional
S to A from distancencecircumfere So,
ncecircumfere sEarth'
S to A from distance angle fractional
The need to know Earth’s density
By the mid-18th century, geodetic surveys were accurate enough to be affected by local variations in the Earth’s density
However, compensating for those variations was extraordinarily difficult, given the extremely small forces involved
Even Newton had previously given up in despair: “[W]hole mountains will not be sufficient to produce any sensible [measurable] effect”
Gravitation and the Earth’s mass
Newton (1642–1727) published his theory of gravitation in 1686 The gravitational force exerted by one mass on another
is proportional to the product of the masses, and inversely proportional to the square of the distance between them:
But what is G, the universal gravitational constant?
221
r
mmGF
Weighing the Earth
In modern terms, Cavendish (1731–1810) measured G to within 1% of the presently accepted value (6.672 10–11 N m–2 kg–2); in actual fact, he determined the Earth’s density directly (without G)
First, he determined the torsion constant of a thin fibre
Then he measured the force exerted on the torsion balance by two large metal spheres
Torsionfibre
The Earth’s mass and density
Knowing G, Cavendish was then able to measure the mass of the Earth directly:
mE = 5.971024 kg
Moreover, combining this with the known radius of the Earth, he could estimate an average density:
E = mE VE = mE (4/3rE3) = 5400 kg m–3
This result implies that the bulk of the Earth is made up of something much denser than the rocks we see at the surface (e.g. granite, 2700 kg m–3)
How old is the Earth?
James Hutton described geological time as having “no vestige of a beginning, no prospect of an end”
But how can we attach absolute ages to the relative timescale provided by stratigraphic and paleontological data?
One method of measuring the absolute age of the Earth would be to work out how long it must have taken for the Earth to cool to its current temperature Just like a body on CSI…
Taking the Earth’s temperature
The two primeval sources of heat Potential energy released during the initial accretion of
planetary embryos and subsequent gravitational differentiation and fusion of the core)
Ongoing radioactivity… which we’ll get to in a minute
Heat flow mechanisms Conduction (temperature-dependent vibrations of adjacent
molecules) Convection (wholesale motion of a hot fluid, like in a pot of
porridge) Radiation (transfer of energy by electromagnetic waves)
Kelvin’s model of the Earth
Assumptions: The Earth is flat The Earth’s surface
temperature has always been 0°C
The Earth’s interior temperature was initially 4000°C
Answer? 20–400 Ma, with a
final preference for ~24 Ma
020406080
100120140
0 100 200 300 400 500
Time since the Earth formed (Ma)
Geo
ther
mal
gra
die
nt
(°C
km
–1)
Compound interest for geologists
Geologists insisted the Earth must be older than Kelvin’s estimates, but found it difficult to counter mathematical sophistry with qualitative geological data
Radioactivity provided a quantitative means of estimating different rocks’ and minerals’ ages
teNNNdt
dN 0
The more you have, the faster it grows (money) or disintegrates
(radioactive material)
The basics of radiometric dating
1. Exponential decrease in number of parent atoms
2. Corresponding increase in number of daughter atoms
3. Exponential increase in daughter/parent ratio,
independent of initial number of parent atoms
Time in half-lives
Num
ber
of a
tom
sD
aughter/parent ratio
Rutherford at the Royal SocietyTo my relief, Kelvin fell fast asleep, but as I came
to the important point, I saw the old bird sit up, open an eye and cock a baleful glance at me! Then a sudden inspiration came, and I said Lord Kelvin had limited the age of the earth, provided no new source (of energy) was discovered. That prophetic utterance refers to what we are now considering tonight, radium! Behold! the old boy beamed upon me.
— Ernest Rutherford, 1904
It never rains but it pours...
“[T]he inexorable physicist [has] remorselessly struck slice after slice for his allowance of geological time.”
— Sir Archibald Geikie, 1892 “[T]he geologist who ten years ago was
embarrassed by the shortness of time allowed to him for the evolution of the earth’s crust is now still more embarrassed by the superabundance with which he is confronted.”
— Arthur Holmes, Nature, 1913
What do we know now?
The Earth is roughly spherical, with a circumference of ~40,000 km, and is several billion years old
It is losing heat and cooling, but much more slowly than originally thought because of continuous radiaoactivity
Whatever the Earth is made of, it must be pretty dense to account for the planet’s average density
Suggested reading material
Earth Science, various chapters (Tarbuck, et al., 2012)
The prism and the pendulum: the ten most beautiful experiments in science (Crease, 2003)
Plate tectonics: an insider’s history of the modern theory of the Earth (Oreskes, 2001)
The solid earth: an introduction to global geophysics (Fowler, 1990, 2004)
During an earthquake Stay inside the building during an earthquake Take shelter under doorways or desks, or beside internal walls Stay clear of areas with glass atriums or glass roofs Keep calm and help allay panic in others Stay indoors till the shaking stops and you are sure it is safe to exit
If there is no shelter Kneel on floor, face away from windows Clasp both hands behind the head, covering the neck Bury face in arms, close eyes tightly Stay in this position until the earth tremors have subsided and it is safe to get up
After the earthquake stops Extinguish small fires IF SAFE TO DO SO Help those around you if you can; treat minor injuries Account for staff, students and visitors if possible Check for signs of hazardous material spills or major structural damage If telephones are working DO NOT contact Campus Care unless immediate
assistance is required Close all smoke stop doors in your area Do not evacuate unless instructed to do so or if the area is immediately threatened by
secondary hazards (fire, gas leak) If evacuation is ordered proceed as for fire evacuation. Do not use lifts – use
stairwells
Default disaster assembly areas are Kelburn Campus – Kelburn Park Pipitea Campus – Parliament Grounds Te Aro Campus – Cobblestone Park Karori Campus – Playing Fields
Quake-safeing
ChimneysWater cylindersFoundationsRoof tilesSolid fuel stovesBookcases
And who has an earthquake kit
prepared?