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? 1

Basic dataAverage 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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From Newton’s form of Kepler’s 3rd Law:

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.

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22

)(

4a

mmGP

How to Measure the Moon’s Mass

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(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 notexactly 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 determinecenter 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:

012.0km 670,379

km 4730

moon

Earth

Earth

moon

r

r

M

M

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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

1 m

every 10 million years

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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• More heavily cratered surface is older – so highlands older than maria

Are highlands or maria older?

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)

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highlands

maria

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

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• Impact speeds several km/s

• Each crater is surrounded by an ejecta blanket

Maria are roughly circular – probably large early impacts. Also smooth and dark, like volcanic flows.

Mare Imbrium – the largest of the maria facing Earth, about 1100 km across.

Evidence for past volcanism

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Lava “river” in a mare indicating old volcanic flows.

- Linear chains of craters (but a few are due to impacts), probably marksancient fault, collapsed lava domes

And more direct evidence from…12

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! 14

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

• 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?16

• Astronauts left seismometers – moonquakes (due to varying tidal force from Earth) weak but useful

• Much thicker lithosphere than Earth, 800 km

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 history1. 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. 3.1 Gyrs ago: volcanism stopped, Moon mostly geologically dead since then. No plate tectonics. Surface is one solid plate. Light bombardment

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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

2. The Capture Theory: The Moon was formed elsewhere, and then captured by Earth's gravitation

3. The Co-creation Theory: Moon and Earth condensed together from the Solar Nebula

Problem: Earth is not spinning fast enough, lack of volatiles

Problem: Extremely unlikely, given the Moon's size is a considerable fraction of Earth's.

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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23Moon formation movie

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 notreach surface. Reason seems to be that entire dense interior sagsa bit towards Earth in a kind of differentiation due to Earth’s gravity.

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Water Ice on the Moon

Absorption of infrared beam by water ice in plume from impact. About 32 ounces of water per ton. Probably from comets.

Data from LCROSS - 2009

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LCROSS impact mission

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

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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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3 2MoonEarth

Moon

r

dmGMF Earth

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 awayfrom each other is

Gravitational force on each rock is

Ratio is or 3 x 10-5

2Moond

mGMF

Moon

3

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MoonEarthMoon

MoonEarth

rM

dM

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Moon

Moon

Earth dM

Mr

3/12

Can also ask: how close would they have to be to Earth to bedrawn apart? Solve for distance from Earth for which thisratio is > 1:

The Roche Limit (Sec. 12.9 in text)

this is the Roche Limit,for the Moon due to Earth’s tides

Note: Roche Limit compares tidal force with gravitationalattraction. For small objects, chemical bonds are much strongerthan gravity – Roche Limit doesn’t apply.

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Crust on far side is much thicker. Volcanic material could notreach surface. Reason seems to be that entire dense interior sagsa bit towards Earth in a kind of differentiation due to Earth’s gravity.

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