The secret origins of the Moon

posted by @ulaulaman about #Moon formation #astronomy #Earth with Italo Calvino quotes

Our satellite, the Moon, is really fascinating, not only for artists and poets, but also for scientists. For example the first, precise description of the Moon was made by Galileo Galilei in the Sidereus Nuncius:

One of the problems that the astronomy try to resolve about the Moon is its origins: for example in the beginning of the Twentieth Century it was developed the Earth-Moon Theory, that was reviewed by LeRoy Hughbanks⁽⁸⁾:

"The moon," says Prof. Percival Lowell, "did not originate as a separate body, but had its birth in a rib of earth." Doctor Lowell is an ardent sup- porter of "the earth-moon theory," and his views and deductions are frankly stated in his two last scientific works, "Mars as the Abode of Life" and "Evolution of Worlds," both of which are publications of the Macmillan Company, New York.

In the discussion has a really great importance George Darwin with his works about the tidal friction⁽⁶⁾ and the viscous spheroids⁽⁵⁾:

Following Sir George Darwin, the Moon would have been detached from the Earth because to a solar tide. The attraction of the Sun acted on the covering of lighter rock (granite) as on a fluid, lifting one hand and tearing it to our planet. The waters that covering the entire Earth were largely sucked down by the abyss that had opened by the escape of the Moon (i.e. the Pacific Ocean), leaving uncovered the remaining granite, which fragmented and wrinckled itself into the continents. Without the Moon, the evolution of the life on the Earth, although it had been, would have been very different.⁽²⁾

Another good description of the earth-moon theory was given by Andrew Patterson:

In brief, the theory is that when the earth had cooled, from its molten condition sufficiently to have a crust of solidified matter something like thirty miles thick over its entire surface, it was revolving so rapidly that gravitational attraction and centrifugal force practically balanced each other. For some reason, perhaps some vast and sudden cataclysm, a large portion of this crust was thrown off the earth, and by tidal action was forced gradually outward in a spiral path. In order to form the moon, a mass of this crust about thirty miles thick and of area nearly equal to the combined areas of the present oceans on the earth must have been thrown off. It is supposed that this immense amount of crust was largely taken from the present basin of the Pacific, and that the remaining parts of the earth's crust, while it still floated on a liquid interior, split along an irregular line into two pieces which floated apart, and the gap between these two parts was later filled with the waters of the Atlantic.⁽⁷⁾

But following Gerstenkorn⁽¹¹⁾ we could arrive to a variation of this picture:

Following H. Gerstenkorn's calculations⁽¹¹⁾, developed by H. Alfven^{(9, 10)}, Earth's continents would be fragments of the Moon fell on our planet. The Moon in origin would also be a planet gravitating around the Sun, until such time as the proximity to the Earth derailed her from its orbit. Captured by Earth's gravity, the Moon came up more and more, tightening its orbit around us. At one point, the mutual attraction began to deform the surface of the two celestial bodies, raising high waves which were detached fragments whirling in space between Earth and Moon, especially fragments of lunar matter that fell on Earth. Later, under the influence of our tides, the Moon was pushed away to reach its present orbit. But part of the lunar mass, perhaps half, was left on Earth, forming the continents.⁽³⁾

Impact from kin via Jane Grant

In this case we have a capture picture⁽⁴⁾ with a subsequent impact dued by tidal forces: Gerstenkirn, a high school teacher, repeated Darwin's calculations and he demonstrated that the Moon could be an indipendent planet in the past.⁽¹⁰⁾
The modern view about the origin of the Moon is, instead, the giant impact theory: the first hypothesis of a such-type event is dued by Reginald Aldworth Daly in his 1945's paper Origin of the Moon and its topography. Daly's ideas was recovered in 1975 in Hartmann's and Davis' paper Satellite-sized planetesimals and lunar origin⁽¹²⁾: the two reserachers supposed that at the end of the planet formation period, some Moon-sized bodies could be collide or be captured by the planets. In particular one of these objects may have collided with Earth ejecting the materials that formed the Moon.
In 1986 Alastair Cameron started a series of five papers about Moon formation that continue the work proposed in 1976 with William Ward at the Lunar and Planetary Science Conference. Comeron's approach is to perform a series of numerical simulation:

Therefore more detailed simulations were needed in which the physics of the shocks and the vaporization process could be accurately treated.⁽¹³⁾

In the paper Cameron's team describes a collision between the proto-Earth and an object of about $\frac{1}{10}$ of Earth's mass. In particular in this first step they find that

The relative velocity between the impactor and the proto-Earth is relatively small (less than about 5 km/sec at infinity). If this condition is not fulfilled the impactor is completely dispersed in space.⁽¹³⁾

In the following three papers Cameron et al. the smooth particle hydrodynamics (SPH) method and finally he can describe the Giant Impact hypothesis and his consequences:

Wherever the surface of the Protoearth is hit hard by the impact, a very hot magma is produced. From this hot surface, rock vapor evaporates and forms a hot extended atmosphere around the Protoearth.⁽¹⁴⁾

The temperature to about 8 Earth's radii is 4000 K. In order to obtain similar results, the impactor has at least 10% of the Earth's mass, and, following Cameron's results, has at least 14% of Earth's mass in order to

(...) swallow up the Impactor iron core and avoid getting too much iron in the Moon. But apart from this constraint it appears from the present simulations that any division of mass between the Protoearth and the Impactor can produce a promising set of conditions.⁽¹⁴⁾

Also some physical considerations like the conservation of angular momentum could be explain with the theoretical proposal, but, in every case:

The formation of the Moon as a postcollision consequence of a Giant Impact remains a hypothesis.⁽¹⁴⁾

Some clues about the correctness of the Giant Impact theory come from chemistry: first of all Moon and Earth are identical if we study their oxygen, tungsten, chromium and titanium isotopes. Cause the relevant differences between Earth and other space bodies, the most simple explanation for these isotopic systems is that Moon was formed by a catastrofic event like a giant impact between a space bullet and the Earth.
If the details of this scenario could be discussed using different starting hypothesis, from the chemistry point of view the Giant Impact theory received on of the most ultimate corroboration by the study of the zinc isotopes⁽¹⁶⁾

Here we present high-precision zinc isotopic and abundance data which show that lunar magmatic rocks are enriched in the heavy isotopes of zinc and have lower zinc concentrations than terrestrial or Martian igneous rocks. Conversely, Earth and Mars have broadly chondritic zinc isotopic compositions. We show that these variations represent large-scale evaporation of zinc, most probably in the aftermath of the Moon-forming event, rather than small-scale evaporation processes during volcanism. Our results therefore represent evidence for volatile depletion of the Moon through evaporation, and are consistent with a giant impact origin for the Earth and Moon.⁽¹⁶⁾

Studying the zinc's isotopes could provide important clues about the origin of the Moon; indeed any precise measurements about zinc isotopic concentrations between planetary igneous rocks⁽¹⁶⁾ from, for example, Earth, Moon and Mars, could give important differences in the depletion and replenishment event, and so in their origins.

Because terrestrial, Martian and lunar rocks all lie on the same massdependent mass-fractionation line, along with all classes of chondritic meteorites, this implies that Zn from all of the analysed samples evolved from a single, isotopically homogeneous reservoir. This relationship presumably reflects Zn isotope homogeneity in the solar nebula before terrestrial planet formation and, thus, that all reported isotopic variations are due to mass-dependent fractionations.⁽¹⁶⁾

In particular the team find that the Zn isotopic fraction is in agreement with a melting event associated with the Moon formation, and so the results support a giant impact event as origin of Earyh-Moon system⁽¹⁶⁾.
If chemistry provide some importnant clues in order to confirm the Giant Impact theory, from a physical point of view, one of the most important difficulties in the simulations about this event is the evolution of the angular momentum of the Earth-Moon system, which today value furnish a constrain for the models. For example if we imagine an erosive giant impact against a fast-spinning proto-Earth, the produced Moon was the right mass with a composition primarily from Earth, but the system would have an angular momentum higher than today⁽¹⁷⁾. So the excess of angular momenutum must be lost since the impact. We can imagine two different ways: it lost during the tidal evolution of the Moon via a resonance between Earth's orbital period⁽¹⁷⁾ or through a resonance with the Sun⁽¹⁸⁾.
But this is not the only difference between the two models. In the first scenario, that I would call the punch, Cuk and Stewart considered the following ingredients: the isotopic similarity between Moon and Earth; the mass of the Moon; the mass of the lunar core. The first limits the composition and the mass of the cosmic bullet. In particular the composition is supposed more similar to Earth than Mars, so the difference in projectile mass fraction between silicate portions of the planet and disk is limited to 15% of the weight⁽¹⁷⁾.
After the mass of the satellite from the disk must be greater than or equal to one lunar mass⁽¹⁷⁾.
And finally only 10% (or less) of the weight of the disk be composed by material originating from the iron cores of the impactor and target⁽¹⁷⁾.
And so, the Earth-Moon system is born!

The punch⁽¹⁷⁾

But it has an excess of angular momentum:

After the Moon was captured in the resonance, the lunar orbit continued to evolve outward while keeping a constant precession period, which led to a rapid increase of eccentricity. The eccentricity increased until a balance between Earth and lunar tides was reached, but the exact eccentricity at which this happened is model-dependent because the mechanical properties of both Earth and the Moon are uncertain.
(...)
There was always a substantial period of balance between Earth and Moon tides, where the Moon stayed in the evection resonance with a roughly constant eccentricity. During this period, Earth tides were transferring angular momentum to the Moon, and Earth's rotation was slowing down. Satellite tides cannot remove angular momentum from lunar orbit, but the Sun can absorb angular momentum through the evection resonance.⁽¹⁷⁾

But the resonance broke, because

Tidal acceleration of the Moon at perigee weakened once the rates of Earth’s rotation⁽¹⁷⁾

and the lunar tides dominate:

Once, according to Sir George H. Darwin, the Moon was much closer to the Earth. There were the tides that gradually pushed her away: the tides caused by the Moon in waters and land and where the Earth slowly loses energy.⁽¹⁾

But, if we start from different initial conditions, we could arrive to the same Earth-Moon system.

We considered a larger impactor that is comparable in mass with that of the target itself. A final disk and planet with the same composition are then produced if the impactor contributes equally to both, which for large impactors is possible even if the disk contains substantial impactor-derived material because the impactor also adds substantial mass to the planet. For example, in the limiting case of an impactor whose mass equals that of the target and in the absence of any pre-impact rotation, the collision is completely symmetric, and the final planet and any disk that is produced will be composed of equal parts impactor and target-derived material and can thus have the same silicate compositions even if the original impactor and target did not.⁽¹⁸⁾

The kiss⁽¹⁸⁾

In this way Canup could consider a "Mars-like" composition for the bullet, so in general the composition between proto-Earth and projectile are very different, but during the impact and the following recombination the new planet and its satellite gain one similar composition. Finally, impactor and target are not rotating before collision⁽¹⁸⁾.
Last observation: Robin Canup is one of the most active contributor to the Giant Impact theory. In a paper published in 2001 on Nature⁽¹⁵⁾ he considered an impact with a bullet that is smaller than the proto-Earth:

The dancer⁽¹⁵⁾

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(1) Translated from the introduction to the short story La distanza dalla Luna (november, 1964), Italo Calvino
(2) Translated from the introduction to the short story La Luna come un fungo (16th may, 1965), Italo Calvino
(3) Translated from the introduction to the short story La molle Luna (october, 1967), Italo Calvino
(4) About the capture theory you can read also The Earth Without the Moon by Immanuel Velikovsky, or the paper Origin and Evolution of the Earth-Moon System by Alfven and Arrhenius.
(5) Darwin G.H. (1879). On the Precession of a Viscous Spheroid, and on the Remote History of the Earth, Philosophical Transactions of the Royal Society of London, 170 447-538. DOI: 10.1098/rstl.1879.0073 (archive.org)
(6) Darwin G.H. (1881). On the Tidal Friction of a Planet Attended by Several Satellites, and on the Evolution of the Solar System, Philosophical Transactions of the Royal Society of London, 172 491-535. DOI: 10.1098/rstl.1881.0009
(7) Patterson A.H. (1909). The origin of the Moon, Science, 29 (754) 936-937. DOI: 10.1126/science.29.754.936
(8) Hughbanks L. (1919). The Earth-Moon Theory, Transactions of the Kansas Academy of Science (1903-), 30 214. DOI: 10.2307/3624069
(9) Alfvén H. (1962). The early history of the Moon and the Earth, Icarus, 1 (1-6) 357-363. DOI: 10.1016/0019-1035(62)90036-2
(10) Alfven H. (1965). Origin of the Moon: Recalculation of early earth-moon distances suggests dramatic events a billion years ago, Science, 148 (3669) 476-477. DOI: 10.1126/science.148.3669.476
(11) Gerstenkorn, H. Über Gezeitenreibung beim Zweikörperproblem.. Zeitschrift für Astrophysik, Vol. 36, p.245
In english: Gerstenkorn H. (1967). The Importance of Tidal Friction for the Early History of the Moon, Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences, 296 (1446) 293-303. DOI: 10.1098/rspa.1967.0023
(12) Hartmann W.K. & Davis D.R. (1975). Satellite-sized planetesimals and lunar origin, Icarus, 24 (4) 504-515. DOI: 10.1016/0019-1035(75)90070-6
(13) Benz W., Slattery W.L. & Cameron A.G.W. (1986). The origin of the moon and the single-impact hypothesis I, Icarus, 66 (3) 515-535. DOI: 10.1016/0019-1035(86)90088-6 (pdf)
(14) Cameron A. (1997). The Origin of the Moon and the Single Impact Hypothesis V☆, Icarus, 126 (1) 126-137. DOI: 10.1006/icar.1996.5642 (pdf)
(15) Canup R.M. & Asphaug E. (2001). Origin of the Moon in a giant impact near the end of the Earth's formation, Nature, 412 (6848) 708-712. DOI: 10.1038/35089010 (pdf)
(16) Paniello R.C., Day J.M.D. & Moynier F. (2012). Zinc isotopic evidence for the origin of the Moon, Nature, 490 (7420) 376-379. DOI: 10.1038/nature11507
(17) Cuk M. & Stewart S.T. (2012). Making the Moon from a Fast-Spinning Earth: A Giant Impact Followed by Resonant Despinning, Science, 338 (6110) 1047-1052. DOI: 10.1126/science.1225542
(18) Canup R.M. (2012). Forming a Moon with an Earth-like Composition via a Giant Impact, Science, 338 (6110) 1052-1055. DOI: 10.1126/science.1226073