Three Worlds

to Explore

Look Up?(Astronomy)

Look Down?(Geophysics)

Look at Surface?(Geology)

The Earth’s Interior

Deep wells and boreholes(4 to 12 km)

The Earth:

What’s it made

of?

Gravity

Seismology

Magnetism

S

N

Heat Flow

Astronomical Observations

Crust2.6-3.1 gm/cm3

Mantle3.3-5.7 gm/cm3

Outer Core10-12 gm/cm3

Inner Core13-14 gm/cm3

Density of Water1 gm/cm3

P and S Wave Paths

Relatively simple experiment to estimate some basic properties of the Earth’s interior:

Mass = M

Radius = R

Average Density = D

Rough Estimate of Variation of Density in

Interior

Newton’s Law of Gravitation

M

Fr

mF

Force of attraction (F) is proportional to the masses, and is inversely proportional to the square of the distances between the

masses.

€

F = GMmr2

Newton’s Law of Gravitation

MF

r

mF

Henry Cavendish (1731-1810) determined the universal constant of gravitation G in 1798.

massive lead spheres

torsion fiber

€

F = GMmR2

M

F m

R

€

M = F R2

Gm

M

F m

R

€

M = F R2

Gm

Measure the force

Use a known mass

Can measure in lab

?

If we could measure R,we could determine M.

How can we measure R?

Greek Scientist:

Eratosthenes

(276-194 BCE)

Eratosthenes (276-194 BCE)

Observed the angles of the noonday Sun in two Egyptian cities that were roughly north and south of each other.

Syene (presently Aswan) and Alexandria

Eratosthenes (276-194 BCE)

The angles differed by 7 degrees (or 1/50 of a complete circle).

Circumference of the Earth must be 50 times the distance between the cities.

Eratosthenes (276-194 BCE)

The cities are 788 km apart.

Circumference of the Earth must be 50 x 788 km= 39,400 km

R = 39,400/2 = 6,271 km (modern value = 6,371 km)

The Earth:

What’s it made

of?

Gravity

Seismology

Magnetism

S

N

Heat Flow

Astronomical Observations

M

F m

R

€

M = F R2

Gm

Measure the force

Use a known mass

Can measure in lab

M = 6x1027 gm =6,000,000,000,000,000,000,000,000,000 gm

Eratosthenes

M

R

€

Density = Mass

Volume

Average Density = 5.5 gm/cm3

€

Volume = 4

3πR3

Average density of the Earth = 5.5

gm/cm3

Average density of

crustal rocks= 2.7 gm/cm3

Density must increase with

depth.

Dense Material?

Density must increase with

depth.

But, how can we obtain a

more detailed picture of the variation of density with

depth?

Dense Material?

Astronomical Observations

Earth’s axis of rotation points towards different stars at different times.

Gravitational forces from the Sun and the Moon cause the Earth to twist and turn in its orbit around the Sun.

“Precession” of the Earth causes the North Pole to point to different parts of the sky during a 26,000 year cycle.

“Precession” of the Earth is similar to the motion of a spinning top.

From precession of the Earth it is possible to measure the moment of inertia of the Earth.

Moment of inertia is a measure of how hard it is to twist an object.

Moment of inertia is a measure of how hard it is to twist an object.

The more that the mass is concentrated towards the center of an object, the easier it is to twist the object.

Lower moment of inertia

Higher moment of inertia

Crust2.6-3.1 gm/cm3

Mantle3.5-5.7 gm/cm3

Outer Core10-12 gm/cm3

Inner Core13-14 gm/cm3

Density of Water1 gm/cm3

The Earth:

What’s it made

of?

Gravity

Seismology

Magnetism

S

N

Heat Flow

Astronomical Observations

Earthquake in JapanMagnitude 8.0

September 25, 200319:50 UTC

Izmit Turkey Seismogram

P and S Wave Paths