Download Chapter 9 – the Moon

The Moon
• What are the characteristics of the Moon, and
how do they compare to Earth's?
• What can the surface tell us about its history
and interior?
• How was the Moon formed?
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Basic data
Average distance from Earth = 384,400km
Mass = 7.3 x 1022 kg = 1.2% Mearth
Diameter = 3476 km = ¼ Earth’s
Density = 3344 kg/m3
Vesc
= 2.4 km/s
No atmosphere.
=> Cannot be liquids on surface.
"Camembert?"
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Libration - 59% of surface visible
• Elliptical orbit means the moon
appears to wobble: spin rate constant
but not orbital speed. Viewing angle
doesn’t change in a constant way
(angular size varies too).
• Appears to nod up and down because
the spin axis is not perpendicular to
the orbital plane
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How to Measure the Moon’s Mass
From Newton’s form of Kepler’s 3rd Law:

 3
4 2
P 
a
 G(m1  m2 ) 
2
a is mean Earth-Moon separation over orbit. P is sidereal month, m1
is Earth mass. Solve for m2. Or use same equation with artificial
satellite orbiting the Moon with known period.
Or, use fact that Moon and Earth orbit around center of mass (CM) of
Moon/Earth system.
(recall: m1r1 = m2r2, where r1 and r2
are distances to center of mass at
any point in orbit)
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Earth wobbles around Earth-Moon center of mass – Earth does not
exactly follow elliptical orbit around Sun. But center of mass does.
This wobble has period of 1 sidereal month (27.3 days) and can be
measured with precise positions of stars and planets. Can determine
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center of wobbling motion, i.e. center of mass.
Result: average distance from Earth’s center to center of mass
is rEarth = 4730 km in the direction of the Moon, i.e. still within
the Earth. So average distance from Moon to center of mass is
rMoon = 384,400 km – 4730 km = 379,670 km. Hence:
M moon rEarth
4730 km


 0.012
M Earth rmoon 379,670 km
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The surface of the Moon
• No atmosphere => surface
reflects geological history
well
• Near side has
– lunar highlands (bright
regions, mountains but no
chains)
– maria (dark regions) 2-5 km
lower than highlands
– Craters (10 times more per
unit area than highlands )
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Cratering rates
Small meteroids common, large ones rare.
So same true for craters:
Crater size
Occurrence
10 km
every 10 million years
1m
every month
Crater diameter about 10x impactor diameter.
Recall, if no water or wind erosion, the number of craters in
an area tells you the age of the surface. Also no atmosphere
for small meteoroids to burn up in.
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highlands
Are highlands or maria older?
• More heavily cratered
surface is older – so
highlands older than maria
Comparison of Earth and Moon surfaces
• Much higher crater density in
general means surface of the
Moon is older than that of the
Earth, no geological activity for
a long time (plate tectonics,
wind, water erosion)
maria
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Also on the surface: regolith
• Regolith is a powdery soil with scattered rocks – 2 -20 m
thick layer
• Made from debris from impacts that create lunar craters
• Impact speeds
several km/s
• Each crater is
surrounded by
an ejecta blanket
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Evidence for past volcanism
Mare Imbrium – the largest of the maria
facing Earth, about 1100 km across.
Maria are roughly circular – probably large early impacts.
Also smooth and dark, like volcanic flows.
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Lava “river” in a mare indicating
old volcanic flows.
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- Linear chains of craters
(but a few are due to
impacts), probably marks
ancient fault, collapsed
lava domes
And more direct evidence from…
Moon rocks
•
•
•
•
382 kg of rock samples from 9 missions:
6 Apollo landings (Apollo 11-17, 1969-72)
12 astronauts visited maria and highlands
3 Soviet Luna robotic missions (1970,72 and 76), returned
rock samples by capsule
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All returned samples are igneous  surface was molten.
Maria
– basalts
Similar to rocks formed by lava on Earth.
Highlands – anorthosites Less dense than basalt.
– breccias
Different rocks fused together in
meteoritic impacts (also in marias)
Rocks also have no trapped CO2, H2O vapor, unlike Earth rocks.
Go see a lunar rock at the Natural History Museum!
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Age of Lunar material
• Radioactive dating can give more accurate ages than crater
rates.
• Samples from Mare 3.1 – 3.8 billion years old
• Highland rocks typically 4 - 4.3 billion years, oldest rock dated
to 4.46 billion years
Oldest material on the Moon is almost as old as we believe the
Solar System to be.
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Moon's interior
• Astronauts left seismometers –
moonquakes (due to varying
tidal force from Earth) weak but
useful
• Much thicker lithosphere than
Earth, 800 km
• Relatively small iron-rich core,
700 km diameter. Only 2-3% of
mass (32% on Earth). Moon
differentiated, like Earth. Must have been molten.
• Thicker crust than Earth, 60-100 km – thicker on far side
• Largely dead geologically. Why?
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No convection moving plates around
 Moon is solid, because it has cooled off 
Cooling time  heat content /rate of cooling
 volume /area
 R3/R2
R
The smaller the world, the faster it loses internal heat, and the
less geologic activity it will show on its surface.
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Geological history
1.
Formed 4.5 Gyrs ago. How? We’ll come back
to that.
2.
Until ~4.4 Gyrs ago: top few 100 km molten,
from bombardment heat and short-lived
radioactive elements. Solidified, and crust
formed.
3.
Heaviest bombardment ended 3.8 Gyrs ago:
highland craters and large basins formed.
4.
3.8-3.1 Gyrs ago: Radioactive heating from
longer lived elements led to intense volcanic
activity, filling large basins to create maria.
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5.
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3.1 Gyrs ago: volcanism
stopped, Moon mostly
geologically dead since
then. No plate tectonics.
Surface is one solid plate.
Light bombardment
Origin of the Moon
Any theory must explain:
• Moon has lower density than Earth, must have much less
iron
• Moon lacks water and other “volatiles” (substances with
low boiling temperatures like sodium, potassium, water,
CO2), meaning moon rock experienced higher
temperatures than Earth generally did.
• Moon rocks also lack iron and high density materials,
different from Earth on average, but similar to mantle
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Theories
1.
The Fission Theory: The Moon was once part of the Earth,
then was separated
Problem: Earth is not spinning fast enough, lack of volatiles
2.
The Capture Theory: The Moon was formed elsewhere,
and then captured by Earth's gravitation
Problem: Extremely unlikely, given the Moon's size is a considerable fraction of Earth's.
3.
The Co-creation Theory: Moon and Earth condensed
together from the Solar Nebula
Problem: Moon has different density and composition; where's the iron?
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4.
The Collisional Ejection Theory: Mars-sized planetesimal
struck Earth, Moon formed in disk of ejected material.
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Moon formation movie
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Some of the strong points
• Spectacular collisions must have happened at end of planet
building. Few dozen large bodies that had been built
collided to make the few planets we have (or were ejected).
• If Earth differentiated at time of collision, little iron near
surface. Agrees with low density and iron content of
Moon
• Moon formed of Earth's mantle debris => compositional
similarities (oxygen isotope ratios)
• Lower abundances of volatile elements on Moon - rock
vaporized by collision would have lost these elements
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Crust on far side is much thicker. Volcanic material could not
reach surface. Reason seems to be that entire dense interior sags
a bit towards Earth in a kind of differentiation due to Earth’s gravity.
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Water Ice on the Moon
LCROSS impact mission
Data from LCROSS - 2009
Absorption of infrared beam by water ice in plume from impact.
About 32 ounces of water per ton. Probably from comets.
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The Roche limit
• The limiting radius inside which the tidal forces are
stronger than gravity holding object together
• Solid objects torn apart inside this radius (and cannot grow
by accretion!)
• Rings of Saturn: composed by many small particles
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Tidal forces revisited
• Tidal forces are
differences in the
gravitational pull at
different points in an
object
29
The effects of tidal forces
Earth is 80 times as massive as Moon => Earth's tidal effects on
Moon are large.
 The Moon is elongated toward the Earth.
 Rotation rate tidally locked to its rate of revolution
 Moon is moving away from the Earth
 Earth is slowing down in its rotation
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Why doesn’t Earth’s strong tidal force tear Moon apart?
Consider two rocks of mass m on either side of Moon:
Tidal force causing acceleration away
from each other is
F  2GMEarth m
Gravitational force on each rock is
3
Ratio is
2M Earthd Moon
3
M MoonrEarth Moon
d Moon
3
rEarth Moon
GMMoonm
F
2
d Moon
or 3 x 10-5
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The Roche Limit (Sec. 12.9 in text)
Can also ask: how close would they have to be to Earth to be
drawn apart? Solve for distance from Earth for which this
ratio is > 1:
1/ 3
 2M Earth 
 d Moon
r  

M
 Moon 
this is the Roche Limit,
for the Moon due to Earth’s tides
Note: Roche Limit compares tidal force with gravitational
attraction. For small objects, chemical bonds are much stronger
than gravity – Roche Limit doesn’t apply.
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Crust on far side is much thicker. Volcanic material could not
reach surface. Reason seems to be that entire dense interior sags
a bit towards Earth in a kind of differentiation due to Earth’s gravity.
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