GE 11a, 2014, Lecture 5Spherical structure of the earth

The earth, ca. 1800

Nevil Maskelyne and the Schiehallion experiment (1774)

Schiehallion (‘Sidh Chailleann’) ScotlandNevil Maskelyne doing his impression of Ben Franklin

Ms

F = m.g.tan() = G.m.Ms/d2

F

m.g

d

m.g = G.m.ME/RE2

ME = (RE2/d2).(Ms/tan()) ~ 6.1024 kg

RE = 6.37.106 m; VE = 1.1.1021 m3

~ 5.5 g/cm2 (initially found ~ 4.5)

Densities of common substances (all in g/cc)

Ice 0.917Water 1.000Seawater 1.025Graphite 2.200Granite ~2.70Titanium 4.507Iron 7.870Copper 8.960Mercury 13.58Gas: proportional to P/RT

Two options: sub-equal mix of metal and rock or…an ideal gas, w/ high density at high P (B. Franklin)

Period of precession

Period of spin

Torque (sun and moon trying to pull earth’s tidal bulge into plane of ecliptic)

Moment of inertia

I = i mi.ri

2 miri Higher

Lower

Earth has I much less thanexpected for homogeneous sphere

Mass distribution in earth’s interior

Kraemer, 1902

View combining known density, moment of inertia,oblateness, rigidity of surface rocks, and topography

Note bad for a bunch of turn-of-the-century quacks!

Focus

Mantle

SeismographCoreS P

“sample” outer ca. 200 km,but most energy in upper 10 km

A mechanical seismograph

Minutes

Surface waves

0

P S

10 20 30 40 50

‘Primary’ (first to arrive)

‘Secondary’ (second to arrive)

Anatomy of a seismic signal

Amplitude=23 mm

Richtermagnitude

Amplitude(mm)

Inte

rval b

etw

een

S a

nd

P w

aves (

s)

Dis

tan

ce (

km

)

P S

S-wave interval = 24 secondsP-wave

measure the amplitude of the largest seismic wave…

…and the timeinterval between the P- and S-waves (I.e., the distance from the epicenter.

Connect the points to determine theRichter magnitude.

Real data is more complicated…

Look at your notes, John!

Look at your notes, John!

Look at your notes, John!

Mg2SiO4 in upper mantle

Mg2SiO4 in lower mantle

The core’s density is less than that of pure Fe. Requires a low-massAlloying agent. S? O? H? ???

The events in early earth history that controlled core/mantle segregation

Robin Canup’s movie

Animation of Theia forming in Earth's L5 point and then drifting into impact. The animation progresses in one-year steps making Earth appear not to move. The view is of the south pole.

Evidence for the ‘magma ocean’ stage of the earth is essentially erased by laterconvection, plate formation, subduction, etc. But the moon’s crust preserves

evidence planets are largely liquid early in their history.

And today Io, a moon of Jupiter, seems to possess a partially crystallized magma ocean, supported by tidal heating