The Moon Luna, Selene, Artemis (Rome, Greece) Chang-o, (China) Soma (Hindu) Nwedzana, Thoth (Africa)

The Moon in Earthshine as seen by Clementine

Plus the Sun, Venus, Mars, and Saturn…

Drawing by Carter Emmart, in David Grinspoon’s “Venus Revealed”

• The Moon is a sister world that formed in orbit around Earth as the Earth formed (Laplace and others). This theory failed because it could not explain why the moon lacks iron.

• The Moon formed somewhere else in the solar system where there was little iron, and then was captured into orbit around Earth (Many). This failed when lunar rocks showed the same isotope composition as the Earth

• Early Earth was somehow spinning so fast that it flung off the Moon (George Darwin). This idea would produce a moon similar in composition to Earth's mantle, which fits the lunar sample return data reasonably well. BUT it failed because the spinning Earth would require at least ~3 times the present Earth-Moon angular momentum to do this.

• The Moon formed by a giant impact with Earth – an idea that had to await its time. - So far, so good… except for the pesky oxygen isotopes.

The Idea of Bombardment •  Pierre-Simon Laplace – “the Newton of France” – developed in the 1790’s the theory of the

protoplanetary disk and direct accretion. There were big problems, chiefly the Sun’s very slow rotation period (why would this be a problem?), but it remains the overarching theory.

•  Robert Hooke – “England’s Leonardo” – speculated critically upon the notion that planets might get bombarded into one another. In late 1664 he fired pistol bullets into a “well-temper'd mixture of Tobacco pipeclay and water” to simulate the features he had painstakingly recorded in his best early sketches of the Moon. He developed the exogenic hypothesis to lunar cratering -- that these circular features were formed by impacts of cosmic bullets of some kind.

'As to his person he was but despicable, being very crooked, tho' I have heard from himself, and others, that he was strait till about 16 Years of Age when he first grew awry, by frequent practicing, with a Turn-Lath . . . He was always very pale and lean, and laterly nothing but Skin and Bone, with a meagre aspect, his eyes grey and full, with a sharp ingenious Look whilst younger; his nose but thin, of a moderate height and length; his mouth meanly wise, and upper lip thin; his chin sharp, and Forehead large; his Head of a middle size. He wore his own hair of a dark Brown colour, very long and hanging neglected over his Face uncut and lank....'

But Hooke also had a 17th century understanding of the heavens, “for it would be difficult to imagine [from] where these bodies should come” (Micrographia, 1665).

Isaac Newton, coming immediately afterwards at Cambridge, not only “lost” Hooke’s president’s portrait (there is no known likeness) but also had some interesting things to say about chaos.

...blind fate could never make all the planets move one and the same way in orbs concentrick, some inconsiderable irregularities excepted, which may have risen from the action of comets and planets upon one another, and which will be apt to increase, till this system wants a reformation.

Proof that if you’re famous and ruthless, only handsome portraits survive. That still doesn’t mean you’re not an asshole.

Impacts and Natural Selection Classical interpretation of Darwin is one of

competition and adaptation to gradual changes.

Fossil evidence for mass extinctions and punctuated equilibrium indicates some periods of very rapid evolutionary change (extinction and speciation).

Cosmic impacts are truly catastrophic: Dinosaurs may have gone extinct in a few days, from a global firestorm…

Ability to survive a cosmic impact – global firestorm, acid rain, months of darkness, severe climate change – favors special factors, e.g. small burrowing rodents, fire-resistant seeds, ability to survive 10’s of m below the ocean surface -- not just bigger, faster, smarter.

George Darwin, the extremely well educated son of Charles, is regarded by some as the father of modern geophysics. He studied the Earth-Sun-Moon system, and solid body tides, and knew that Earth-Moon tidal coupling is sapping angular momentum from Earth and slinging the Moon into higher orbit.

He thus extrapolated backwards, to speculate that the system could once have been a single rapidly-rotating body that shed the Moon, for instance out of the Pacific. By estimating the tidal coupling he derived an age of Moon formation as ~56 Ma, which fit right in with Kelvin’s age for the Earth.

Coral from Pennsylvanian rockbeds have about 387 daily layers per year. Coral from Devonian rockbeds have about 400 daily layers per year. In the Cambrian a year was 412 days. One Precambrian stromatolite gave 435 days per year.

From bivalves, the duration of the lunar orbit is known to have been shorter; today it is 29.5 day month, and 300 Ma it was about 28.7 days per month.

These dates came post-Darwin; he argued from first principles.

The miracle of the total solar eclipse…

It’s what tourists from

Tralfamadore would visit

What are the odds of that?

How long will the show last? Another few 100 Ma, no worries

Now, fast forward…

Viktor Safronov in the 1960’s, for his PhD, developed the planetesimal hypothesis of planet formation, where you start with minor bodies and grow them into bigger ones slowly over time.

Further developed by George Wetherill and subsequent researchers in his footsteps.

By the 1970’s it was becoming apparent that planet formation is very messy, and there is a lot of big stuff roaming around for tens of millions of years. Most interestingly, it is becoming apparent that gravitational drag – an n-body particle effect – makes collisions between similar-sized bodies the most probable.

The idea of late stage giant impacts was born, and the impact hypothesis for the origin of the Moon was inevitable.

Basically, inside of ~2 AU, planets cannot possibly form directly as clumps in the protoplanetary disk, Laplace style.

Solar tides prevent any glob of gas and dust that extensive to begin collapsing (read Wetherill 1990 Ann Revs)

Must have started with hundreds of smaller Moon- to Mars-sized “embryos” which merged over the next ~30 Ma to form the Earth and other terrestrial planets.

paintings by Bill Hartmann (left) and Dan Durda (above)

After 10 Myr: Two Earth-sized planets near “Venus” and “Mars”

Initial Conditions: 50 Planetary Embryos

Planetary embryos stir one another up gravitationally

See especially Chambers and Wetherill (1998) and Agnor et al. (1999).

Simulations of terrestrial planet accretion, starting with ~100 Moon- to Mars-sized embryos between 0.5 and 4 AU

A bunch of solar systems generated on a computer by John Chambers, starting with ~100 embryos

(Actually, one of these is our own!)

Geological Implications: Planetary growth occurs by giant collisions!

Here we follow the growth of one simulated terrestrial planet

Spin Axis

Mass of Planet

Spin Period

Note two things:

(1)  Growth is catastrophic, not gradual!

(2)  Spin axis (obliquity) gets knocked around

Also note a major problem: Planets start to spin faster than is possible!

Bill Hartmann and Don Davis (LPSC 1974; Icarus 1975) were studying the work of Safronov, and ran calculations of the rate of growth of the 2nd-largest, 3rd largest, etc., bodies in the general vicinity of Earth, as the Earth itself was growing.

Just as the asteroid belt today has a largest asteroid (Ceres) at 900 km diameter, and several smaller bodies in the 300-500 km diameter range, the region of Earth's orbit would have had several bodies up to about half the size of the growing Earth. They proposed that one of these struck the Earth to make the Moon.

W. K. Hartmann

Al Cameron

Willy Benz

Willy Benz and Al Cameron at Harvard did the first impact simulations, using SPH.

Simulation Details

•  It’s kind of scary that all but one (largely ignored) published simulation of the impact formation of the protolunar disk has used the smooth particle hydrodynamics (SPH) code written by Benz (1990)

•  Equation of state (EOS) closes the partial differential equations:

P=P(ρ,u) for simple models, or {P,T}={P,T}(ρ,u) in systems which conserve thermodynamical quantities such as Helmholtz free energy F (e.g. the ANEOS code) or SESAME computed tables.

Examples: Polytrope, Perfect Gas, Grüneisen, Murnaghan, Tillotson, ANEOS, SESAME

( ) ( )ij

N

j ij

ijijiji

N

jij

j

j

i

ij

iTot

rrM

GhrWPPm

dtdv r̂,

12

122 ∑∑

==

−∇

Π++−=

ρρ

( )ijiji

N

jjiij

j

j

i

iji hrWPPm

dtdu

dtdQ

dtdVP

dtdu ,)(

2122 ∇⋅−

Π++=→+−= ∑

=

vvρρ conservation of energy.

conservation of momentum

High Angular Momentum Impact LImp ≈ 2L⊕-M MTot = 1M⊕

Earth is almost fully formed before the impact

System angular momentum must be reduced afterwards by subsequent giant impact(s)

Early-Earth Impact Limp ≈ L⊕-M

Mtot ≈ 0.65M⊕

Earth is 50% formed before the impact, and only 65% formed afterwards

Moon must avoid contamination with iron-rich and volatile-rich material while Earth accretes the last 35% of its mass

The first numerical simulations by Benz et al. formed a “cold Moon”, that is, a clump. Probably an SPH artifact at very low (3000 particle) resolution.

A single SPH particle of iron in the disk ruled out that simulation as a possibility, so they ruled out the best sweet spot in parameter space (later found by Canup and Asphaug 2001).

Cameron (1997, 2000, 2001), using a few 1000 particles, identified two candidate Moon-forming impacts, below.

The results were wrong and really threw chemists and geophysicists for a loop who bought it hook, line & sinker.

For numerical reasons, at low resolution the ejected material clumps immediately into a proto-Moon, instead of forming an accretion disk. (1) SPH likes to clump; (2) coarse resolution leads to strong gravity gradients.

This is what Stevenson (1989) explores with regard to a “cold moon”.

Dave Stevenson

B.S., M.S. (Physics), Victoria University, Wellington, New Zealand Ph.D. (Theoretical Physics) 1976, Cornell University Thesis: "Interior Structure of Jupiter"; adviser, E. E. Salpeter Professor of Planetary Science, Caltech, 1984-present Many professional honors and teaching awards

Asked all the right questions:

Giant Impact Model Constraints

1.  Sufficient orbiting material ejected beyond the Roche limit

MD ≥1.5 - 2 ML (Canup et al.; Ida et al.)

2. Iron-depleted protolunar material

Lunar core ≤ 0.03 ML Total lunar iron ≤ 0.08 ML

3. Earth-Moon system angular momentum

L⊕-M : Original rotation period of a single common body would have been ~5 hours

Some Implications of Giant Collisions •  Make differentiation into cores and mantles far more likely - deposits heat globally, in one huge melting event, rather than just on the surface

•  Make it more likely that the planets will each have unique characteristics

- tiny Mars - backwards Venus - tilted Uranus - dense Mercury - Earth-Moon - Pluto-Charon?

Impactor and target: Made by collision. Non-rotating for now. Silicate mantle and iron core. Can simulate a very massive atmosphere

Impact variables: impact parameter, impact speed, impactor-to-total mass ratio, total colliding mass

Numerical variables: resolution, choice of material and EOS, treatment of shocks (artificial viscosity), smoothing length (variable vs. fixed), and “flavor” of SPH equations

points smoothing lengths

Canup and Asphaug (2001) simulation

•  45°

•  30,000 particles

•  24-hrs simulated

•  MT = 1.02M⊕

•  LIMP = 1.2L⊕-M

•  Tillotson EOS

•  MD = 1.7ML

•  MD > aR = 1ML

•  MFe/MD = 0.02

Mars-Sized Impactor into Earth-Sized Target

Note two things: (1) Impactor’s iron core merges with target’s iron core. (2) What’s left is an accretion disk, the subject of Stevenson’s study. It may take another ~100-1000 years for the Moon to form out of this mess.

side view

Similar calculation (Canup 2003) using a real equation of state (ANEOS). Note that everything is absolutely crazy hot, with everything red being at minimum 7000°K, and the bulk of the disk around 4000°K. I think this is an artifact of SPH shearing and that Stevenson’s analysis gives a more reasonable temperature estimate.

N-body Lunar Accretion Simulation: N=10,000 solid particles

τ~100 Kepler timescales (orbital period at the Roche radius) ~ 30 days

Ida et al. (1997) start with a lunatesimal disk…

Neglects any kind of thermal evolution! Can only possibly be relevant to cold accretion, e.g. if the disk cools in place and then coalesces. (Even then the gravitational binding energy is enough to vaporize the Moon many times over.)

“Even radiating at a silicate cloudtop temperature of roughly 2000K, it would take more than 100 years to radiatively cool the Moon” (Abe et al. 1993)

Stevenson 1989

4 Ways of Making the Moon Not Re-Accrete With Earth:

a)  Ballistics b)  “Second burn” c)  Viscous coupling d)  Gravitational torques

A skeptical look at the modeling studies thus far…

Indeed probably 3 of these were wrong!

With 10-20 wt% as vapor (his Fig. 4) it will be a foam with very low sound speed… enhances wave instability thus leads to turbulence and viscous transport and possible clumping…

Interesting argument. Then by setting his computed disk spreading time equal to the disk cooling time, he obtains an effective viscosity.

Table 2 from Stevenson (1989)

What about SPH for disk evolution?

Smoothing lengths and artificial viscosity. Note that Wada (2004) gets a disk, using ~30,000,000 zones in ZEUS-MP, but it is full of shocks that SPH does not resolve, and predicts the disk will disperse rapidly and no Moon will form! In 2005 Wada stated that this problem is too complicated and he will go back to modeling galaxy collisions…

Take a step back and look at the Big Picture…

At the end of the Moon-forming impact, Earth is spinning with a period of about 5 hours

The evolution from then until the present is pretty much as George Darwin proposed it to be.

Interesting factoids… (1) The core is spinning

faster than the mantle by a factor of ~2, post-impact.

(2) The post-impact Earth is piriform and wobbling…

(3) The protolunar disk is made 50% of Earth rock and 50% of “Theia” rock.

Earth-Moon from Galileo Spacecraft