Earth’s structure and properties (1)

John Townend

EQC Fellow in Seismic Studies

john.townend@vuw.ac.nz

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?