1. 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?

2. 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?"

3. 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
Moon’s orbital motion is sometimes slower than or faster than its rotation. Moon’s rotation axis is 1.5 deg away from perpendicular to the ecliptic.

4. How to Measure the Moon’s Mass
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.
a from radar ranging over orbit, for example. P, m1 found earlier.
(recall: m1r1 = m2r2, where r1 and r2 are distances to center of mass at any point in orbit)

5. 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
center of wobbling motion, i.e. center of mass.

6. 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:

7. 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 )

8. 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.

9. More heavily cratered surface is older – so highlands older than maria
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

10. Also on the surface: regolith
Regolith is a powdery soil with scattered rocks – 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

11. 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.

12. - Linear chains of craters (but a few are due to impacts), probably marks
ancient fault, collapsed lava domes
Lava “river” in a mare indicating old volcanic flows.
And more direct evidence from…

13. Moon rocks 382 kg of rock samples from 9 missions:
6 Apollo landings (Apollo 11-17, )
12 astronauts visited maria and highlands
3 Soviet Luna robotic missions (1970,72 and 76), returned rock samples by capsule

14. 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)
Anorthosites thought to have risen to surface during early phase when magma ocean existed. Rocks totally dry, unlike Earth rocks which have trapped CO2, H2O vapor.
Rocks also have no trapped CO2, H2O vapor, unlike Earth rocks.
Go see a lunar rock at the Natural History Museum!

15. 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 billion years, oldest rock dated to 4.46 billion years
Uranium 4.5 Gyr, potassium 1.3 Gyr. Oldest rock: Marc Norman, LPI
Oldest material on the Moon is almost as old as we believe the Solar System to be.

16. 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, km – thicker on far side
Largely dead geologically. Why?
Earth litho km. Quakes, due to varying tidal force, much deeper than Earth. They occur at litho-astheno bdy, so thick litho. No global field. Weak fields frozen into rocks billions of years ago indicate core was once molten, weak global field existed.

17. 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.

18. Geological history Formed 4.5 Gyrs ago. How? We’ll come back to that.
Until ~4.4 Gyrs ago: top few 100 km molten, from bombardment heat and short-lived radioactive elements. Solidified, and crust formed.
Heaviest bombardment ended 3.8 Gyrs ago: highland craters and large basins formed.
Gyrs ago: Radioactive heating from longer lived elements led to intense volcanic activity, filling large basins to create maria.
4. K, U

19. 3.1 Gyrs ago: volcanism stopped, Moon mostly geologically dead since then. No plate tectonics. Surface is one solid plate. Light bombardment

20. 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
Volatiles (e.g. NA, P), “Refractories” have high boiling temperatures (Ti, Ca, Al)

21. Theories
The Fission Theory: The Moon was once part of the Earth, then was separated
The Capture Theory: The Moon was formed elsewhere, and then captured by Earth's gravitation
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?

22. The Collisional Ejection Theory: Mars-sized planetesimal struck Earth, Moon formed in disk of ejected material.

23. Coalescence rapid – 100 years or less
Moon formation movie

24. 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
Happened between 4.56 (age of Solar System) and 4.47 (age of oldest moonrocks) Gyr ago.

25. 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.

27. Water Ice on the Moon Data from LCROSS - 2009 LCROSS impact mission
Image shows Cabeus crater floor and impact scar
Absorption of infrared beam by water ice in plume from impact. About 32 ounces of water per ton. Probably from comets.

28. 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

29. Tidal forces revisited
Tidal forces are differences in the gravitational pull at different points in an object

30. 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

31. 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
Gravitational force on each rock is
Ratio is or 3 x 10-5
Don’t calculate each: find ratio, it’s simpler. What would this ratio be on Earth? About 1e-9. Tides on moon way stronger!

32. 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:
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.

33. 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.